Mechanical Behavior of Cementitious Composites Reinforced with Nonwoven Fabrics: A Numerical Modeling Study

1  Introduction

The wide variety of available fiber- and mortar-based composites offers numerous possibilities for enhancing the mechanical performance of such materials. Numerous studies have already explored their behavior under mechanical loading [1–4]. Nevertheless, several emerging generations of fabric- or fiber-reinforced cementitious materials still present complex mechanical responses that are not yet fully understood. Therefore, further investigation is needed to fill the knowledge gaps, particularly for the most recent developments, such as flax nonwoven cementitious composites [5].

Reinforcements in composite materials typically consist of fibers or particles arranged in various configurations [6]. While fibers alone offer reinforcement, their arrangement into fabrics—whether woven, knitted, or nonwoven—enhances the mechanical properties of composites [7–11]. Textile-reinforced composites offer benefits like cost efficiency and wider availability. Fabrics provide lightweight structures, enhanced strength, and flexibility to conform to complex shapes, making them increasingly popular among researchers. Compared to woven or knitted fabrics, nonwovens do not require fibers to be converted into yarns before fabric formation [6,12], as they are produced by bonding fibers or filaments using thermal, chemical, or mechanical methods, using a combination of fibers with different properties or recycled materials [13–15]. Unlike woven fabrics, nonwovens allow fiber orientation in multiple directions, reinforcing the material through its thickness while minimizing damage to in-plane fibers. These fabrics provide high out-of-plane strength, reduced delamination risk, and increased binder absorption due to their high void volume [8]. As a result, nonwovens are significantly more cost-effective, making them highly versatile in various applications [4,5,13,16], and they represent one of the fastest-growing segments of multiple industries, including construction applications [12,17–19]. Nonwoven composites, consisting of multiple stacked layers of nonwoven fabrics, offer excellent flexibility and adaptability, making them suitable for applications that require high conformability [6,20]. Building upon these characteristics, flax-based nonwoven reinforcements have attracted increasing attention as sustainable alternatives for cementitious composites due to their renewability and favorable structural features [21,22]. While these materials offer promising sustainability advantages, it should be noted that durability-related aspects, such as moisture sensitivity and long-term performance, require further investigation and are not addressed in the present study.

While experimental investigations provide essential and reliable data for characterizing the mechanical behavior of fiber-reinforced cementitious composites, they are often time-consuming, costly, and limited in their ability to systematically assess the influence of multiple geometric, material, and processing parameters. With the rapid advancement of computational power and numerical methods, finite element-based simulations have emerged as a powerful complementary tool for investigating the mechanical response of composite materials [23]. Numerical modeling enables virtual trial-and-error analyses, parametric and sensitivity studies, and detailed insight into stress distribution and deformation mechanisms that are difficult to access experimentally. In particular, multi-scale modeling frameworks allow the heterogeneous nature of composites to be addressed by linking micro-structural features to macroscopic mechanical behavior. However, despite these advantages, the accuracy of such models strongly depends on the definition of appropriate constitutive laws, reliable material parameters, and experimental calibration, especially for complex and nonwoven reinforcement architectures. Consequently, a combined experimental–numerical approach is essential to ensure predictive capability and physical consistency of simulation results [23,24].

Nevertheless, numerical modeling of textile-reinforced composites remains inherently challenging due to their highly heterogeneous, hierarchical, and multiscale architecture, limiting the reliability of conventional homogenization approaches [25–29]. Recent integrated experimental–numerical studies have demonstrated that accurately capturing damage evolution and interfacial debonding requires advanced finite element frameworks that explicitly account for local stress transfer mechanisms [30–32]. As a result, owing to incomplete microstructural characterization and reliance on heuristic assumptions, multiscale approaches and advanced constitutive models are necessary to reliably predict the nonlinear and anisotropic behavior of textile-reinforced composites [33,34].

Several studies on Textile Reinforced Mortar (TRM) systems have led to the establishment of design standards and numerical models for predicting the mechanical behavior of fiber- and fabric-reinforced cementitious composites used in masonry and concrete strengthening [35]. In this context, nonlinear finite element simulations have been widely employed, demonstrating agreement with experimental data and enabling efficient parametric analyses and detailed investigation of failure mechanisms [1,2,36,37]. In addition, alternative modeling strategies, such as Concrete Damage Plasticity (CDP) and layered finite element approaches, have been proposed to capture the complex behavior of textile-reinforced cementitious composites under various loading conditions [38,39].

Representative Volume Element (RVE)–based approaches are widely employed to estimate effective composite properties by capturing microstructural features and periodic fiber arrangements. Previous studies have shown that RVE-based finite element models can successfully predict elastic properties, damage evolution, and fiber–matrix interactions in fiber- and textile-reinforced systems, particularly for woven and knitted architectures [40–43]. In addition, RVE-based and microstructure-guided numerical approaches have been applied to various composite systems, including cement-based, natural fiber, and lattice-reinforced composites, to investigate their thermal, mechanical, and structural behavior [44–47]. However, despite their proven effectiveness, the application of RVE-based modeling to nonwoven cementitious composites remains extremely limited and has not yet been reported [34,48–50].

Recent studies have increasingly focused on nonwoven fabric–reinforced cementitious composites, with experimental investigations on flax-based nonwoven systems highlighting the significant influence of microstructural features and processing parameters on mechanical performance [51–54]. By comparison, numerical modeling frameworks have been extensively developed for Textile Reinforced Mortar (TRM) systems employing woven or knitted textiles, while comparable approaches for nonwoven reinforcements remain scarce. The intrinsic randomness, heterogeneous fiber distribution, and complex microstructure of nonwoven flax fabrics pose significant challenges to conventional modeling strategies, resulting in a lack of dedicated and predictive numerical models for nonwoven-fabric reinforced cementitious composites [55]. In this study, the term “nonwoven fabric” refers to the specific reinforcement used, while the broader term “textile reinforcement” is adopted when referring to general textile-based composite systems.

Recent advances in high-fidelity modeling approaches, including image-based and data-driven frameworks, have enabled detailed reconstruction of heterogeneous composite microstructures and improved prediction of local mechanical behavior [32,44,45,56]. For instance, an image-based meso-scale modeling approach has been proposed to reconstruct the three-dimensional structure of nonwoven fabrics and assess their behavior using finite element analysis [56]. Such approaches provide valuable insights into microstructure–mechanics relationships by explicitly resolving fiber distribution and local interactions. However, they generally require extensive microstructural characterization, significant computational resources, and complex implementation procedures, which limits their applicability at the composite scale. In contrast, the present study adopts a simplified and engineering-oriented modeling framework, aiming to capture the dominant mechanical behavior of nonwoven fabric–reinforced cementitious composites while maintaining computational efficiency and practical applicability.

Consequently, despite extensive investigations on Textile Reinforced Mortar (TRM) systems, the mechanical behavior of nonwoven flax–reinforced cementitious composites remains poorly understood from a numerical perspective, and no production-scale predictive model has yet been reported [14,48,57,58]. As a result, existing TRM-based modeling frameworks currently represent the most relevant reference for comparison and model development in the absence of dedicated numerical approaches for nonwoven systems [35,59,60].

In spite of the broad body of research on textile-reinforced cementitious composites, several key gaps remain in the current literature. Most existing numerical approaches have been developed for woven or knitted textile systems, where the fiber architecture is relatively ordered and easier to represent. In contrast, nonwoven fabric–reinforced composites have received comparatively limited attention in numerical modeling and exhibit a highly heterogeneous microstructure that is not adequately captured by conventional methods. Existing modeling strategies generally fall into two categories: general macroscopic approaches that provide a global description of the composite response, and detailed microscale models that require complex material characterization and significant computational effort. As a result, there is a lack of modeling approaches that effectively bridge these two scales while remaining suitable for practical engineering applications. Furthermore, although experimental studies on nonwoven-fabric reinforced composites have been reported, there is still a lack of experimentally grounded numerical frameworks capable of consistently linking geometric parameters and material characteristics to the overall structural response.

To address these gaps, this study proposes a simplified and engineering-oriented numerical framework based on a Representative Volume Element (RVE) approach integrated with finite element analysis. The proposed framework combines a simplified representation with key mechanical features to provide a practical and computationally efficient tool for engineering applications. In this sense, the novelty of the work lies in the application of an RVE-based approach to nonwoven fabric–reinforced cementitious composites within an engineering-oriented modeling framework.

2  Methodology

This section describes the integrated experimental–numerical methodology employed to investigate the flexural mechanical behavior of nonwoven flax–reinforced cementitious composites. The proposed methodology is deliberately formulated as a simplified and engineering-oriented modeling strategy, aiming to reduce the barrier between experimental characterization and numerical simulation. Rather than pursuing a highly complex or computationally intensive approach, the framework prioritizes practical implementation using commonly available finite element tools and experimentally measurable material properties. Experimental characterization and testing provide the geometric, material, and mechanical input data required for model definition and calibration. Based on these data, a multiscale finite element framework using a Representative Volume Element (RVE) is developed to capture the heterogeneous nature of the composite. The following subsections detail the experimental basis, RVE construction, constitutive modeling, boundary conditions, calibration strategy, and sensitivity analyses used to assess the composite response under flexural loading.

2.1 Materials

2.1.1 Matrix

A Portland cement Type I 52.5R supplied by Cementos Molins Industrial, S.A. (Spain) was used for mortar production.

2.1.2 Reinforcement

Flax fibers, having an average length of 60 mm, were provided by Institut Wlokien Naturalnych (Poland). Nonwoven fabrics with an approximate thickness of ~1 mm and an aerial weight of about 188 g/m2 were produced using these fibers. Each composite plate consisted of four to six layers of nonwoven fabric impregnated with cement paste prior to casting. The plates were manufactured using a custom-designed mold with internal dimensions of 300 mm3 × 300 mm3 × 40 mm3, specifically developed to enable a vacuum-assisted dewatering process and to apply a uniform pressure of 3.5 MPa across the specimen surface. During the vacuum-assisted lay-up procedure, the nonwoven fabric layers were cross-oriented to enhance material homogeneity. After the lay-up stage, the assembled plates were compressed to ensure proper consolidation. The main stages of the manufacturing process are presented in Fig. 1.

Figure 1: Main steps of the manufacturing process of the nonwoven fabric–reinforced cementitious composite plates used for numerical model calibration. (a) Casting mold positioned on a vacuum-assisted dewatering system for excess water removal during impregnation, (b) flax nonwoven fabric as reinforcement, (c) dewatering and compression setup, and (d) final composite plate after curing.

2.2 Mechanical Testing

For each configuration, four composite plates were manufactured, resulting in a total of twelve plates. Each plate measured 300 mm2 × 300 mm2, with a thickness ranging from 9 to 12 mm, depending on the number of reinforcement layers. From each plate, six prismatic specimens were cut, with lengths of 300 mm and widths ranging between 36 and 42 mm. Consequently, a total of 24 specimens were obtained for each configuration. Among these, six specimens per configuration were selected and tested under flexural loading.

Flexural Test

The flexural behavior of the composites was evaluated using a four-point bending test, following the procedure described in [61,62], which is based on the RILEM TFR1 and TFR4 recommendations. The tests were performed using an electromechanical testing machine (Incotecnic Lab-Pre SL, Spain) equipped with a four-point bending fixture and a 3 kN load cell.

All specimens were tested at a constant crosshead displacement rate of 20 mm/min, with a support span length (L) of 270 mm. The mid-span displacement was measured using a Linear Variable Differential Transformer (LVDT) positioned at the bottom surface of the specimen. The selected loading rate allowed the complete flexural response of the material to be captured within a test duration of approximately 1.5 to 2 min. The composite specimen and the four-point bending test setup used for the experimental flexural characterization are shown in Fig. 2.

Figure 2: Composite specimen (a) and four-point bending test setup used for the experimental flexural characterization (b).

For each configuration, the specimens exhibiting the minimum and maximum flexural responses were selected as representative bounds of the experimental variability. The corresponding force displacement curves, as well as the Yield strength (σγ) and the flexural modulus of elasticity (E3), were extracted from these tests.

2.3 Data Preprocessing

To provide a comprehensive summary of the collected input data, Fig. 3 presents a combined plot of the stress-strain data for the minimum-maximum range of the tested repetitions across all three composite configurations. This visualization highlights the differences in mechanical behavior because of various numbers of composite layers. For numerical model calibration, the minimum and maximum values were averaged to obtain representative mean stress–strain responses, which were directly used as input parameters in the simulations (see Fig. 4). Fig. 5 illustrates the stress–strain curve of the 4-layer composite derived from mean experimental values and adopted for model calibration. The curve is idealized using a bilinear representation, where Line 1 describes the elastic response and Line 2 represents the pseudo-plastic behavior, with the transition region indicating the onset of material softening.

Figure 3: Summary plot of stress-strain data for different composite repetitions (min and max sizes).

Figure 4: Comparison between experimental and calibrated numerical load–deflection responses for the 4-layer composite corresponding to the minimum mean squared error (MSE = 10 N2).

Figure 5: Mean stress-strain plot of 4-layer composite obtained from experimental data.

2.4 Finite Element Modeling

2.4.1 Simulation Setup

Finite element analyses were performed using ANSYS Workbench (version 2020 R2) to simulate the mechanical response of the composites under four-point flexural loading. Each composite was modeled using realistic dimensions consistent with the corresponding experimental specimens.

2.4.2 Material Properties Assignment

Material and geometrical parameters were defined based on the available experimental datasets to ensure consistency between the numerical and physical models. Initial isotropic elastic properties were assigned to both the cementitious mortar matrix and the flax nonwoven reinforcement.

The cementitious mortar was modeled using a Young’s modulus of 12 GPa and a Poisson’s ratio of 0.2, estimated from experimental compressive strength according to Eurocode 2 formulations and consistent with values reported in the literature for normal-weight concretes [63–66]. The flax nonwoven reinforcement was assigned effective mechanical properties derived from experimental reference values and subsequently refined through an iterative calibration process. It should be noted that the nonwoven reinforcement represents a partial composite, consisting of flax fibers and a fraction of the surrounding mortar impregnating the fabric during production. Consequently, its effective properties cannot be directly measured using conventional testing methods and were instead determined through RVE-based analysis and FEM calibration.

2.4.3 Meshing and Boundary Conditions

The finite element models were discretized using a mesh density determined through a convergence analysis to balance accuracy and computational efficiency. Three-dimensional solid elements available in ANSYS were employed for the structural simulations. A layer-resolving meshing strategy was adopted to accurately represent the multilayered composite architecture [67–69], ensuring that the number of elements through the thickness corresponded to the number of physical composite layers. Based on the convergence study, element sizes of 2, 2.5, and 3 mm were selected for the 4-, 5-, and 6-layer configurations, respectively. Further mesh refinement did not lead to significant changes in the load–deflection response, confirming mesh independence. For the RVE models, a conformal block meshing approach was employed within the ANSYS Material Designer module. The assigned material properties were used to compute homogenized elastic properties through numerical averaging.

Boundary conditions were defined to reproduce a four-point bending configuration. Displacement-controlled loading was applied at the two loading points, while the supports were modeled to prevent rigid body motion without over-constraining the system. One support was defined as a roller support by constraining only the vertical displacement (Uy = 0), allowing free movement in the longitudinal direction. The second support was constrained in both longitudinal and vertical directions (Ux = 0, Uy = 0), acting as a reference support. In addition, the out-of-plane displacement (Uz) was restrained at the reference support to ensure numerical stability. Vertical displacement was measured at the bottom mid-span of the beam, corresponding to the location of maximum deflection. The applied boundary conditions are illustrated schematically in Fig. 6.

Figure 6: Four-point bending configuration used in the numerical model, including geometry, loading scheme, and boundary conditions. Roller (Uy = 0) and pinned (Ux = Uy = 0) supports are considered, with displacement-controlled loading and mid-span deflection measurement.

2.4.4 Simulation Results to Be Analyzed

The simulations produced force–displacement responses, which were used to evaluate stiffness, deformation behavior, and load-bearing capacity. Initial discrepancies between numerical and experimental curves indicated that certain material parameters were not sufficiently captured by direct experimental measurements. To address this limitation, a Representative Volume Element (RVE)–based approach was employed to determine effective anisotropic material properties through finite element homogenization. The resulting homogenized parameters were subsequently applied to improve the accuracy of the macroscopic structural simulations.

2.4.5 Representative Volume Element (RVE) Modeling

A Representative Volume Element (RVE)–based approach was employed to determine the effective elastic properties of the nonwoven fabric–reinforced cementitious composite and to link the microscale material behavior to the macroscopic structural response. In this study, the RVE was constructed to represent the layered microstructure of the composite and modeled as a three-layer configuration consisting of alternating mortar (matrix) layers and a nonwoven fabric layer impregnated with cement paste (Fig. 7). This configuration was selected to capture the anisotropic behavior arising from the directional interaction between the reinforcement and the matrix.

Figure 7: Schematic representation of the laminate and the corresponding representative volume element (RVE). A local region is used to define a three-layer RVE, composed of two mortar sublayers (TH_m) and one mortar-impregnated nonwoven flax layer (TH_f). Periodic repetition of the RVE is assumed to represent the composite.

RVE Construction

The RVE was defined based on the experimentally characterized laminate geometry and layer thicknesses, ensuring that it accurately represents a single composite layer within the full laminate. Each RVE consists of a central nonwoven fabric layer embedded between two mortar sublayers (Fig. 7), reflecting the actual manufacturing process. The adopted RVE represents a single sandwich-like composite unit that is periodically repeated through the laminate thickness. Accordingly, a specimen composed of multiple layers is modeled as a stack of identical RVEs through the thickness, while periodicity is assumed in the in-plane directions. Each RVE therefore corresponds to one physical composite layer within the laminate structure.

In this study, the nonwoven layer refers to the mortar-impregnated nonwoven flax reinforcement. The thickness of each mortar sublayer (TH_m) was determined by subtracting the average thickness of the nonwoven flax fabric (TH_f) from the total per-layer thickness of the composite and dividing the remaining value equally between the upper and lower mortar layers. The total thickness of all mortar layers within a composite was then obtained by multiplying TH_m by the number of mortar layers in each configuration. All dimensional parameters were defined based on experimental measurements of the composite specimens. The effective properties obtained from the RVE were subsequently used in the macroscopic finite element model of the laminate. This configuration captures the essential alternation between fiber-rich and matrix-rich regions observed in the material.

In the present model, the interface between the cementitious mortar and the mortar-impregnated nonwoven flax layer is represented using a perfect-bonding assumption, enforcing full displacement compatibility across the interface. This assumption is consistent with the manufacturing process, in which the nonwoven fabric is impregnated with cement paste prior to casting and subsequently consolidated under pressure, promoting mechanical interlocking and continuous stress transfer between the matrix and the reinforcement. Experimental observations did not indicate any debonding or interfacial failure between the mortar and the impregnated nonwoven layer, supporting the validity of this assumption for the investigated configurations. Accordingly, the bonding behavior is represented through a shared-topology formulation, in which common nodes are assigned at the interface between adjacent layers, ensuring full continuity without the need for explicit contact or cohesive elements. This approach provides a computationally efficient representation and is particularly suitable for the homogenization procedure adopted in the RVE analysis. Although local phenomena such as slip, debonding, or detailed fiber–matrix interactions may occur at smaller scales, these mechanisms are not explicitly modeled. Instead, their influence is implicitly incorporated into the calibrated effective material parameters governing the global response of the composite.

RVE Meshing and Homogenization

The RVE was discretized using a conformal block meshing strategy, and the assigned material properties were used to compute the homogenized elastic response. The RVE analysis generated nine engineering constants, including Young’s modulus (E), Shear modulus (G), and Poisson’s ratios (ν) in three main orthogonal directions, characterizing the macroscopic and homogenized elastic behavior of the composite material. Due to the layered production process and the absence of a preferred in-plane orientation, the composite exhibited transversely isotropic behavior. The resulting homogenized properties were subsequently used as input parameters in the macroscopic finite element simulations and iteratively refined during the calibration phase to achieve agreement with experimental results.

In the present study, fiber distribution within the nonwoven reinforcement is not modeled at the individual fiber level due to its inherent randomness. Instead, it is represented through the number of layers and their thickness, which define the distribution of reinforcement across the composite thickness. Since the nonwoven fabric does not exhibit a well-defined fiber orientation, orientation effects are not explicitly modeled at the microscale. The relationships between these structural parameters and the mechanical response are reflected in the model parameters, where Ef and E3 represent the effective stiffness, and σy represents the effective strength of the composite.

The proposed RVE is formulated as an equivalent layered representation of the nonwoven composite, derived from the experimentally observed laminate configuration. This idealization reflects the actual manufacturing process, where nonwoven fabric layers are embedded within the mortar matrix and arranged in a controlled sequence. At the mesoscale, the RVE captures the dominant structural features governing load transfer and stiffness, while the homogenization procedure provides effective anisotropic material properties representing the averaged response of the heterogeneous system. In this sense, the influence of fiber distribution is incorporated in an equivalent manner through the layered architecture. This formulation enables a computationally efficient and physically consistent representation suitable for engineering-scale analysis within the investigated range of configurations.

Periodic boundary conditions were applied to the RVE to ensure displacement compatibility and continuity between adjacent representative elements. This formulation reflects the repetitive nature of the composite structure and allows for consistent evaluation of the effective mechanical response. The adopted RVE is considered representative as it captures the key features of the composite architecture and provides an accurate description of its global mechanical behavior within the considered modeling assumptions.

2.4.6 Parameter Calibration Process

An iterative fitting process was conducted to calibrate the material properties, ensuring agreement between the numerical and experimental force–displacement responses. The parameters were adjusted incrementally to ensure numerical stability and convergence. The calibration primarily focused on adjusting the apparent yield limit and the corresponding deformation observed in the initial linear elastic portion of the Load-deflection plot. Key parameters, including Poisson’s Ratio (ν) and Young’s modulus of flax (Ef) were refined due to their significant impact on the numerical force–displacement response. Note that the term “flax” in this context refers to the mortar-impregnated nonwoven flax reinforcement rather than pure flax fibers, accurately reflecting the material behavior observed experimentally. Subsequently, bilinear isotropic hardening was introduced to represent the nonlinear post-yield response. Initial estimates of the Yield strength (σy) and Tangent modulus (E3) were derived from bilinear representations of the experimental stress–strain data, defined by the transition between the elastic and plastic regimes. These parameters were obtained from the intersection of the linear segments (Line 1 and Line 2) shown in Fig. 5 and were subsequently refined through an iterative calibration process to minimize the discrepancy between numerical and experimental load–deflection responses. It should be noted that the calibrated parameters were obtained through an inverse calibration procedure based on matching numerical and experimental responses. While the iterative process ensures convergence toward a stable and consistent solution, such approaches may admit multiple parameter combinations that yield similar global responses. Therefore, the identified parameters should be interpreted as effective and representative values rather than strictly unique intrinsic material properties. Model accuracy during the calibration process was quantified using the Mean Squared Error (MSE) between the simulated and averaged experimental load–deflection curves. Iterations were continued until the minimum MSE was achieved (10 N2 for the 4-layer configuration), as illustrated in Fig. 4. The same calibration procedure was applied to the 5 and 6-layer composites and the results are summarized in Table 1. These calibrated datasets were subsequently used for the analysis and discussion of the numerical results presented in Section 3.

The load–deflection response reflects the underlying mechanical behavior of the composite. The initial linear region corresponds to the elastic response, where both the mortar matrix and the nonwoven reinforcement contribute to stiffness without significant damage. As the load increases, the response transitions into a nonlinear regime associated with the initiation and progressive development of micro cracking within the matrix. Although these mechanisms are not explicitly modeled at the local scale in the present study, their effects are implicitly captured in the global response through the proposed engineering-oriented framework.

3  Result and Discussion

3.1 Model Calibration Results

The numerical model shows good agreement with the experimental results, as quantified by the reported error metrics. The load–deflection response reflects the underlying mechanical behavior of the composite. The initial linear region corresponds to the elastic response, where both the mortar matrix and the nonwoven reinforcement contribute to stiffness without significant damage. As the load increases, the response transitions into a nonlinear regime associated with the initiation and progressive development of cracks within the matrix. In this stage, load transfer mechanisms evolve, with the reinforcement contributing through bridging effects, allowing the composite to sustain increasing deformation. Unlike tensile behavior in some textile-reinforced systems, a distinct stage dominated solely by reinforcement is not observed under flexural loading. Instead, the mechanical response is governed by the interaction between matrix cracking and reinforcement contribution up to failure. All tested specimens exhibit a similar failure mode, characterized by crack initiation in the tensile zone followed by progressive crack propagation leading to failure.

Table 1 summarizes the experimentally measured values, derived parameters, and optimal calibrated values for the 4, 5, and 6-layer composite configurations. The table includes geometric properties, material parameters, and fitting accuracy indicators (MSE and nRMSE). The nRMSE is adopted as a normalized error metric to enable consistent comparison across different composite configurations with varying load levels and response magnitudes. The calibrated Young’s modulus of flax (Ef) represents the effective elastic response of the mortar-impregnated nonwoven reinforcement rather than an intrinsic property of flax fibers. The results confirm a good agreement between the simulation and experimental data, highlighting the model’s capability to reproduce the mechanical behavior of the composites.

Fig. 8 presents the comparison between experimental and calibrated numerical load–deflection curves obtained using the optimized parameters for all composite configurations, corresponding to the lowest MSE values.

Figure 8: Comparison of simulated and experimental load–deflection curves for 4-layer (blue), 5-layer (green), and 6-layer (red) composites.

The values reported in Table 1 suggest a clear dependence between the composite structural configuration and its apparent mechanical response. In particular, the calibrated stiffness-related parameters increase with the number of layers, indicating an enhanced load-bearing capacity for thicker laminates.

Based on the data presented in Table 1, the relationships between key calibrated parameters and geometric variables were examined. Among the investigated trends, three relationships exhibited the strongest linear correlations:

•   Tangent modulus (E3) vs. number of layers (N)

•   Yield strength (σy) vs. the thickness of the mortar layer (TH_m)

•   Young’s modulus of flax (Ef) vs. thickness of the mortar layer (TH_m)

Figs. 9–11 illustrate the linear correlations between key calibrated parameters and geometric variables, along with the corresponding fitting equations and R2 values (R2 > 0.98), confirming strong linear relationships within the investigated range.

Figure 9: Correlation between the tangent modulus (E3) and number of layers (N).

Figure 10: Correlation between the yield strength (σy) of the composite and the thickness of each layer of mortar (TH_m).

Figure 11: Correlation between the young’s modulus of flax (Ef) and the thickness of each layer of mortar (TH_m).

In Fig. 9, it is observed that the Tangent modulus (E3) increases linearly with the number of layers (N) in the composite. This relationship for the tested specimens can be expressed as:

E3=12.5N−44.2(1)

where E3 is in MPa and N is the number of layers.

The analysis is valid for N ≥ 4. The coefficient of determination for this fit is R2 = 0.9868, indicating that the linear model reliably captures the variation of the tangent modulus for varying layer counts. As the number of layers increases, the overall stiffness of the composite improves due to the added reinforcement. This trend indicates that increasing the number of reinforcement layers leads to a higher apparent stiffness of the composite under flexural loading.

In Fig. 10, an inverse linear relationship is observed between the Yield strength (σy in MPa) and the mortar layer thickness (TH_m, in mm). This relationship is expressed for the tested cases as:

σy=−0.9TH_m+2(2)

where σy is in MPa and TH_m is in mm.

This inverse relationship reveals that as the thickness of each mortar layer (TH_m) increases, the Yield strength (σy) decreases. Thicker mortar layers likely dilute the reinforcing effect of the flax layers, reducing the material’s ability to withstand stress before yielding. The coefficient of determination (R2 = 0.9996) indicates that the model closely captures the observed trend.

In Fig. 11, a linear relationship is also observed between the Young’s modulus of flax (Ef in MPa) and the mortar layer thickness (TH_m in mm), described by the equation:

Ef=−686TH_m+299(3)

where Ef is in MPa and TH_m is in mm.

This correlation is valid within the tested range of mortar layer thicknesses (0.2–0.5 mm). Outside this range, the equation may lead to non-physical results (e.g., negative values of Ef) and should not be used. The proposed relationship is not intended as a general design guideline, but rather as a configuration-specific empirical fitting applicable only within the investigated domain.

Similar to the trend observed for Yield strength (σy), this relationship indicates that increasing the thickness of each mortar layer (TH_m) reduces the stiffness contribution of the flax reinforcement. A thicker mortar layer disperses the stress across a greater volume of matrix material, thereby reducing the effective stiffness derived from the flax. Again, the coefficient of determination (R2 = 0.9967) indicates a clear correlation with the experimental data.

It should be noted that these correlations are derived from a limited number of configurations and should therefore be interpreted as indicative trends within the investigated parameter range rather than general predictive laws. Each data point represents an averaged response obtained from multiple experimental measurements, ensuring that the reported values reflect the overall behavior of each configuration rather than individual test variability. The experimental data were used to define key input parameters for the numerical model, supporting the simulation of the composite’s mechanical behavior. Through result analysis, relationships were established between measurable parameters—such as thickness, number of layers, and mortar properties—and the required model inputs. These relationships correspond to the independent and dependent parameters summarized in Table 2.

The derived relationships link measurable geometric parameters, such as the number of layers and mortar sublayer thickness, to the effective input parameters required for numerical modeling. These correlations enable the estimation of model inputs without extensive experimental campaigns, facilitating the application of the proposed framework to other nonwoven fabric–reinforced cementitious composites.

While good agreement between numerical and experimental results is observed, as quantified by the adopted error metrics, it should be emphasized that the model is calibrated using the experimental load–deflection responses of the investigated configurations. All available experimental datasets were used for model calibration, and no independent dataset was available for validation. Therefore, the reported agreement reflects the consistency of the calibration process rather than predictive capability. The nRMSE values should thus be interpreted as indicators of goodness-of-fit rather than predictive validation. A rigorous validation would require additional datasets not used in the calibration stage, which is beyond the scope of the present study.

Furthermore, key manufacturing parameters such as applied pressure, fiber orientation, and porosity were kept constant across all experimental configurations in this study. The same materials, fabrication procedure, and production conditions were used for all specimens. As a result, it is not possible to establish explicit process–parametric relationships between these variables and the mechanical response. The only parameter varied is the number of layers, which affects the composite thickness and is therefore analyzed as the primary influencing factor on the structural behavior.

From a mechanical standpoint, the observed trends can be attributed to stress transfer between the mortar matrix and the nonwoven reinforcement, as well as interactions between adjacent layers. In this sense, the fitted effective parameters do not merely provide numerical agreement with the experimental curves, but also reflect the dominant mechanisms governing flexural response at the structural scale. Although local phenomena such as crack propagation and fiber bridging are not explicitly modeled at the local scale, their effects are reflected in the global structural response captured by the model.

Finally, it should be emphasized that the proposed modeling framework is tailored to the investigated material system and loading conditions, namely flax nonwoven fabric–reinforced cementitious composites under flexural loading. Accordingly, the derived correlations are configuration-specific and valid only within the studied parameter range and their extension to other systems requires further investigation.

Sensitivity Analysis

Following the calibration of the numerical model, a series of sensitivity analyses was carried out to explore how changes in selected geometric and material parameters affect the structural response of the composites. This step aimed to identify the most influential parameters and to provide physically meaningful insights that could guide future design and material optimization. Both single-parameter and combined-parameter variations were considered to capture not only isolated effects but also potential interactions between key variables.

The sensitivity analysis focused on parameters that are both physically meaningful and practically justifiable. In particular, variations in layer thickness and material stiffness (flax modulus and mortar modulus) were examined. Here, the term “flax modulus” refers to the effective Young’s modulus of the mortar-impregnated nonwoven flax reinforcement layer described in the RVE model, rather than that of pure flax fibers. Such variations can be realistically achieved in practical applications.

This approach provides insights that are transferable to practice. For instance, the possibility of using stiffer or more flexible mortars, or alternative fibers with different Young’s moduli, could help design ad-hoc composite compositions for a given application. Such analyses also serve as a basis for exploring hybrid composites, where fibers of different stiffness levels may be combined. The relationships between the independent input parameters and the derived quantities are summarized in Table 2.

For the sensitivity analysis, reference values were taken from experimental data and systematically varied around these references within physically meaningful ranges. This approach ensured that all parametric variations remained anchored to experimentally validated configurations while enabling a detailed assessment of their influence on the composite response.

In this framework, parameters are varied individually while all other variables are kept constant to ensure a controlled evaluation of their influence. In particular, material properties, fabrication conditions, and layer thickness of the nonwoven reinforcement are assumed to remain unchanged unless explicitly stated. This approach allows the isolated effect of each parameter on the mechanical response to be systematically quantified.

Thickness Effect

Fig. 12 quantitatively demonstrates the influence of flax layer thickness (TH_f) on the apparent stiffness of the composite across all configurations. The parameter ranges and variation levels used in this analysis are defined in Table 3. The results reveal a consistent and positive correlation, indicating that increasing TH_f leads to a systematic enhancement in structural stiffness.

Figure 12: Apparent stiffness (N/mm) vs. flax layer thickness (TH_f) for 4-, 5-, and 6-layer composites. Each curve corresponds to a different mortar sub-layer thickness (TH_m), as indicated in the legend.

In addition, Variations in mortar sub-layer thickness (TH_m) produce a measurable shift in the stiffness response, highlighting the role of matrix distribution in governing load transfer efficiency. The results further indicate that increasing the number of composite layers significantly amplifies the stiffness response, with the 6-layer configuration consistently exhibiting the highest stiffness values. Building upon these findings, the influence of total composite thickness (TH_c) on the apparent stiffness was quantitatively evaluated, as presented in Fig. 13.

Figure 13: Effect of total composite thickness (TH_c) on the apparent stiffness for 4-, 5-, and 6-layer composites. Each line style represents a different composite configuration, while colors correspond to variations in the mortar sub-layer thickness (TH_m), as indicated in the legend. The flax layer thickness (TH_f) varied from 0.25 to 3 mm.

Total Thickness

Fig. 13 quantifies the relationship between the total composite thickness (TH_c) and the resulting apparent stiffness. The results indicate an approximately linear dependency, demonstrating that TH_c is a dominant parameter controlling the global flexural response. This trend reflects the fundamental role of laminate thickness in bending mechanics, where increased thickness leads to higher bending stiffness and load-carrying capacity. Furthermore, the results show that increases in flax layer thickness (TH_f) contribute directly to TH_c, thereby amplifying the overall stiffness response of the composite system.

Young’s Modulus Analysis

To further quantify the influence of material properties on structural performance, a parametric analysis was conducted by varying the Young’s modulus of flax (Ef) and the Young’s modulus of the concrete (Ec). The variation levels of the flax Young’s modulus (Ef), defined as multiples of the calibrated reference values, are summarized in Table 4.

The results, presented in Fig. 14, reveal a nonlinear relationship between Ef and apparent stiffness. Specifically, the stiffness increases rapidly at lower Ef values and gradually approaches a plateau at higher values. This behavior indicates a diminishing sensitivity of the structural response to further increases in reinforcement stiffness. This saturation effect suggests that beyond a critical stiffness threshold, the composite response becomes governed primarily by load transfer mechanisms rather than reinforcement stiffness alone. Moreover, the influence of Ef is more pronounced in configurations with a higher number of layers, indicating enhanced interlayer interaction and more efficient stress redistribution.

Figure 14: Apparent stiffness–Young’s modulus of flax (Ef) relationships for (a) 4-layer, (b) 5-layer, and (c) 6-layer composites. Each curve corresponds to a different mortar Young’s modulus (Ec = 6000–36,000 MPa), illustrating the influence of reinforcement stiffness on the flexural response.

Coupled Effects

The combined influence of reinforcement and matrix stiffness is illustrated in Fig. 15 through three-dimensional response surfaces. These results quantitatively demonstrate the interaction between Ef and Ec in controlling the apparent stiffness. The response surfaces reveal a clear transition from a matrix-dominated regime at low Ef values to a reinforcement-dominated regime at higher Ef values. Beyond this transition, the stiffness response stabilizes, indicating reduced sensitivity to further increases in Ef. In contrast, variations in Ec exhibit a comparatively minor influence on the global response, confirming that matrix stiffness plays a secondary role once effective load transfer between layers is established.

Figure 15: 3D surface plots showing the combined influence of the flax modulus (Ef) and the mortar modulus (Ec) on the apparent stiffness for (a) 4-layer, (b) 5-layer, and (c) 6-layer composites. Color gradients indicate stiffness magnitude (N/mm), highlighting nonlinear matrix–reinforcement coupling effects.

3.2 Parametric Sensitivity Results

The parametric sensitivity analysis provides a quantitative hierarchy of the governing parameters influencing the flexural response of the composite system. The parameters considered in the sensitivity analysis and their respective variation ranges are summarized in Table 5.

The results demonstrate that flax layer thickness (TH_f) and mortar sub-layer thickness (TH_m) exert a strong and quantifiable influence on the reaction force and apparent stiffness. In particular, thinner mortar layers improve stress transfer efficiency, resulting in higher load-bearing capacity for a given displacement. The total composite thickness (TH_c) exhibits an approximately linear relationship with structural stiffness, confirming its dominant role in governing bending behavior. In contrast, the influence of the concrete Young’s modulus (Ec) remains limited within the investigated range, whereas the Young’s modulus of flax (Ef) emerges as a key controlling parameter. The response to Ef is characterized by an initial rapid increase followed by a plateau, indicating stiffness saturation.

Overall, these results establish a clear hierarchy of geometric and material parameters governing the composite response and provide guidance for the selection and balance of design parameters in practical applications. It should be noted that the identified relationships are specific to the material system and configuration investigated in this study. Their applicability to other fiber types, geometries, or manufacturing conditions remains uncertain. Therefore, the extension of the proposed framework beyond the investigated parameter range requires further experimental and numerical studies.

From an engineering perspective, the results highlight the importance of balancing matrix and reinforcement properties to achieve an efficient composite response. Increasing the stiffness of the flax reinforcement enhances structural performance only up to a certain threshold, beyond which further increases result in limited gains due to stiffness saturation. Similarly, excessively thick mortar layers reduce the efficiency of load transfer between layers, limiting the contribution of the reinforcement. These findings indicate that optimized combinations of layer thickness and material properties are required to maximize structural efficiency, rather than simply increasing individual parameters.

The present sensitivity analysis is based on parametric variation of calibrated input parameters and does not include a formal uncertainty quantification framework. Its objective is to evaluate the relative influence of key parameters on the composite response rather than to provide a probabilistic assessment. Parameters directly controlled during manufacturing, such as layer number and mortar thickness, exhibit relatively low uncertainty, while parameters with higher variability are represented by calibrated values derived from multiple experimental measurements. Accordingly, the results should be interpreted within this context.

4  Conclusion

This study proposed a numerical modeling framework to reproduce the flexural behavior of nonwoven fabric–reinforced cementitious composites, based on existing experimental data and a Representative Volume Element (RVE)–based multiscale approach. The model was calibrated by iteratively adjusting key effective parameters—namely the Young’s modulus of flax reinforcement (Ef), Yield strength (σy), Tangent modulus (E3)—resulting in a good agreement between numerical results and experimental load–deflection responses for the 4-, 5-, and 6-layer composites. The corresponding normalized RMSE values of 5.2%, 4.6%, and 2.1% indicate a consistent fit across the investigated configurations.

The parametric and sensitivity analyses provided clear physical insights into the governing mechanisms of flexural response. In particular, the thickness of the flax reinforcement layer and its effective stiffness were identified as the dominant parameters controlling apparent stiffness and load-bearing capacity, while the mortar sub-layer thickness primarily influenced stress transfer efficiency between layers. The tangent modulus exhibited a strong dependence on the number of reinforcement layers, highlighting the role of laminate configuration in governing post-yield stiffness and pseudo-plastic behavior.

The results further reveal stiffness saturation effects at high reinforcement moduli, indicating a transition from matrix-dominated to reinforcement-dominated behavior. This observation emphasizes the importance of balanced material design rather than excessive stiffness enhancement. Importantly, these findings enable the establishment of simplified relationships between measurable geometric parameters and effective model inputs, supporting parameter-based design exploration without the need for extensive experimental campaigns.

Overall, the developed framework is intentionally conceived as a simplified and engineering-oriented numerical tool, offering a robust yet computationally efficient solution for the design and optimization of nonwoven fabric–reinforced cementitious composites. By explicitly accounting for fiber-scale mechanics through an RVE-based strategy while relying on experimentally accessible input parameters and standard finite element tools, the approach effectively contributes toward bridging the gap between experimental characterization and numerical simulation, supporting the practical development of bio-based cementitious composites with tailored mechanical performance.

It should be noted that the proposed framework is developed based on a limited set of experimental configurations and has not been validated against independent datasets. Therefore, its applicability is currently restricted to the investigated material system and loading conditions, and further experimental studies are required to assess its generalization.

Acknowledgement: This research was partially funded by the research project PID2022-137156OB-I00, financed by MCIN/AEI/10.13039/501100011033/FEDER, EU. The fourth author is a Serra Húnter Fellow.

Funding Statement: This research was partially funded by the research project PID2022-137156OB-I00, financed by MCIN/AEI/10.13039/501100011033/FEDER, EU.

Author Contributions: Conceptualization: Bahareh Ramzikhalesi, Josep Claramunt-Blanes, Ernest Bernat-Maso. Methodology: Bahareh Ramzikhalesi, Ernest Bernat-Maso. Software: Bahareh Ramzikhalesi, Ernest Bernat-Maso. Validation: Bahareh Ramzikhalesi. Formal analysis: Bahareh Ramzikhalesi. Investigation: Bahareh Ramzikhalesi. Resources: Josep Claramunt-Blanes, Ernest Bernat-Maso. Data curation: Bahareh Ramzikhalesi, Ali Rakhsh-Mahpour, Josep Claramunt-Blanes. Writing—original draft: Bahareh Ramzikhalesi. Writing—review & editing: Bahareh Ramzikhalesi, Ali Rakhsh-Mahpour, Josep Claramunt-Blanes, Ernest Bernat-Maso. Visualization: Bahareh Ramzikhalesi. Supervision: Josep Claramunt-Blanes, Ernest Bernat-Maso. Project administration: Ernest Bernat-Maso. Funding acquisition: Ernest Bernat-Maso. All authors reviewed and approved the final version of the manuscript.

Availability of Data and Materials: The data that support the findings of this study are available from the corresponding author upon reasonable request.

Ethics Approval: Not applicable. This study does not involve human participants or animal subjects.

Conflicts of Interest: The authors declare no conflicts of interest.

Abbreviations

References

1. Boem I. Characterization of textile-reinforced mortar: state of the art and detail-level modeling with a free open-source finite-element code. J Compos Constr. 2022;26(5):04022060. doi:10.1061/(asce)cc.1943-5614.0001240. [Google Scholar] [CrossRef]

2. Bernat-Maso E, Gil L, Escrig C. Analysis of brick masonry walls strengthened with fibre reinforced polymers and subjected to eccentric compressive loads. Constr Build Mater. 2015;84:169–83. doi:10.1016/j.conbuildmat.2015.02.078. [Google Scholar] [CrossRef]

3. Dananjaya SAV, Chevali VS, Dear JP, Potluri P, Abeykoon C. 3D printing of biodegradable polymers and their composites—current state-of-the-art, properties, applications, and machine learning for potential future applications. Prog Mater Sci. 2024;146(2012):101336. doi:10.1016/j.pmatsci.2024.101336. [Google Scholar] [CrossRef]

4. Ghalme S, Hayat M, Harne M. A comprehensive review of natural fibers: bio-based constituents for advancing sustainable materials technology. J Renew Mater. 2025;13(2):273–95. doi:10.32604/jrm.2024.056275. [Google Scholar] [CrossRef]

5. Barbhuiya S, Das BB, Kapoor K, Das A, Katare V. Mechanical performance of bio-based materials in structural applications: a comprehensive review. Structures. 2025;75(1):108726. doi:10.1016/j.istruc.2025.108726. [Google Scholar] [CrossRef]

6. Faridul Hasan KM, Horváth PG, Alpár T. Potential fabric-reinforced composites: a comprehensive review. J Mater Sci. 2021;56(26):14381–415. doi:10.1007/s10853-021-06177-6. [Google Scholar] [CrossRef]

7. Mahpour AR, Ventura H, Ardanuy M, Rosell JR, Claramunt J. The effect of fibres and carbonation conditions on the mechanical properties and microstructure of lime/flax composites. Cem Concr Compos. 2023;138:104981. doi:10.1016/j.cemconcomp.2023.104981. [Google Scholar] [CrossRef]

8. Patnaik PK, Swain PTR, Mishra SK, Purohit A, Biswas S. Recent developments on characterization of needle-punched nonwoven fabric reinforced polymer composites—a review. Mater Today Proc. 2020;26:466–70. doi:10.1016/j.matpr.2019.12.086. [Google Scholar] [CrossRef]

9. Rakhsh Mahpour A, Ardanuy M, Ventura H, Rosell JR, Claramunt J. Rheology, mechanical performance and penetrability through flax nonwoven fabrics of lime pastes. In: Proceedings of the Construction Technologies and Architecture; 2021 Jun 16–18; Barcelona, Spain. p. 480–90. doi:10.4028/www.scientific.net/cta.1.480. [Google Scholar] [CrossRef]

10. Mahpour AR, Claramunt J, Ardanuy M, Rosell JR. Flax fabric-reinforcement lime composite as a strengthening system for masonry materials: study of adhesion. In: International RILEM Conference on Synergising Expertise towards Sustainability and Robustness of Cement-Based Materials and Concrete Structures. Cham, Switzerland: Springer; 2023. p. 1297–306. doi:10.1007/978-3-031-33211-1_116. [Google Scholar] [CrossRef]

11. Rakhsh Mahpour A, Claramunt J, Ardanuy Raso M, Ramon Rosell J. Fabric-reinforced lime composite as a strengthening system for masonry materials: a study of adhesion using flexural and tensile testing. In: Smart & sustainable infrastructure: building a greener tomorrow. Cham, Switzerland: Springer; 2024. p. 482–92. doi:10.1007/978-3-031-53389-1_45. [Google Scholar] [CrossRef]

12. Palanisamy S, Yadav A, Bajya M, Choudhary AK. Development of sustainable multilayer composite nonwoven fibrous assembly for thermal insulation application. AATCC J Res. 2025;12(1):1–11. doi:10.1177/24723444241300382. [Google Scholar] [CrossRef]

13. Dubrovski PD, Čebašek PF. Analysis of the mechanical properties of woven and nonwoven fabrics as an integral part of compound fabrics. Fibres Text East Eur. 2005;13(3):51. [Google Scholar]

14. Mahpour AR, Ardanuy M, Ventura H, Rosell JR, Claramunt J. Comparing the mechanical performance of flax nonwoven fabric reinforced lime composites modified with two types of lime. In: Proceedings of the 5th International Conference on Bio-Based Building Materials; 2023 Jun 21–23; Vienna, Austria. [Google Scholar]

15. Rakhsh Mahpour A. Suitability of new lime nonwoven layered flax fiber composite as a reinforcement masonry historical structures system: microstructural, mechanical, durability and sustainability assessment [master’s thesis]. Barcelona, Spain: Universitat Politècnica de Catalunya; 2024. doi:10.5821/dissertation-2117-450697. [Google Scholar] [CrossRef]

16. Alcalá-Sánchez D, Tapia-Picazo JC, Rodríguez-Romero JA, Luna-Bárcenas G, Bonilla-Petriciolet A. Bio-based terpolymers: synthesis, characterization, wet-spinning, and evaluation as geotextile. Fibres Polym. 2025;26(9):3729–50. doi:10.1007/s12221-025-01035-7. [Google Scholar] [CrossRef]

17. EL Wazna M, Ouhaibi S, Gounni A, Belouaggadia N, Cherkaoui O, EL Alami M, et al. Experimental and numerical study on the thermal performance of alternative insulation materials based on textile waste: a finite-difference approach. J Ind Text. 2020;49(10):1281–303. doi:10.1177/1528083718811104. [Google Scholar] [CrossRef]

18. Mohsin A, Zahid U. SABZ; developing a sustainable, all-natural, biodegradable, and zero-waste non-woven textile material. J Des Text. 2025;4(2):28–62. doi:10.32350/jdt.42.02. [Google Scholar] [CrossRef]

19. Nazarov VG, Ivanov LA, Dedov AV, Bokova ES, Statnik ES. Gradient non-woven fabrics with a modified surface nanolayer for water filtration in construction industry. Nanotekhnologii Stroit. 2023;15(2):117–23. doi:10.15828/2075-8545-2023-15-2-117-123. [Google Scholar] [CrossRef]

20. Atalie D, Abtew MA, Zhao L. Recent advances in bio-based nonwoven materials: sustainable production, applications, and circular economy. J Nat Fibres. 2025;22(1):2565661. doi:10.1080/15440478.2025.2565661. [Google Scholar] [CrossRef]

21. Mijatov S, Savić S, Brzić S, Ivanović S, Simić M, Milošević M, et al. From nature to function: green composites using camphoric acid-based unsaturated polyester resin and bamboo/flax non-woven reinforcements. Polymers. 2025;17(22):3038. doi:10.3390/polym17223038. [Google Scholar] [PubMed] [CrossRef]

22. Claramunt J, Ventura H, Fernández-Carrasco LJ, Ardanuy M. Tensile and flexural properties of cement composites reinforced with flax nonwoven fabrics. Materials. 2017;10(2):215. doi:10.3390/ma10020215. [Google Scholar] [PubMed] [CrossRef]

23. Kibrete F, Trzepieciński T, Gebremedhen HS, Woldemichael DE. Artificial intelligence in predicting mechanical properties of composite materials. J Compos Sci. 2023;7(9):364. doi:10.3390/jcs7090364. [Google Scholar] [CrossRef]

24. Advani SG, Laird GW. Opportunities and challenges of multiscale modeling and simulation in polymer composite processing. Int J Mater Form. 2009;2(1):39. doi:10.1007/s12289-009-0601-y. [Google Scholar] [CrossRef]

25. Di Sarno L, Albuhairi D, Medeiros JMP. Exploring innovative resilient and sustainable bio-materials for structural applications: hemp-fibre concrete. Structures. 2024;68(17):107096. doi:10.1016/j.istruc.2024.107096. [Google Scholar] [CrossRef]

26. Dixit A, Mali HS. Modeling techniques for predicting the mechanical properties of woven-fabric textile composites: a review. Mech Compos Mater. 2013;49(1):1–20. doi:10.1007/s11029-013-9316-8. [Google Scholar] [CrossRef]

27. Kavvadias IE, Tsongas K, Bantilas KE, Falara MG, Thomoglou AK, Gkountakou FI, et al. Mechanical characterization of MWCNT-reinforced cement paste: experimental and multiscale computational investigation. Materials. 2023;16(15):5379. doi:10.3390/ma16155379. [Google Scholar] [PubMed] [CrossRef]

28. Prasetiyo I, Sihar I, Brahmana F, Gunawan. Enhancing nonwoven fabric material sound absorption using embedded labyrinthine rigid structures. Appl Acoust. 2022;195(6):108852. doi:10.1016/j.apacoust.2022.108852. [Google Scholar] [CrossRef]

29. Pastore CM. Opportunities and challenges for textile reinforced composites. Mech Compos Mater. 2000;36(2):97–116. doi:10.1007/BF02681827. [Google Scholar] [CrossRef]

30. AhmadvashAghbash S, Verpoest I, Swolfs Y, Mehdikhani M. Methods and models for fibre-matrix interface characterisation in fibre-reinforced polymers: a review. Int Mater Rev. 2023;68(8):1245–319. doi:10.1080/09506608.2023.2265701. [Google Scholar] [CrossRef]

31. Zhang H, Yu R. Inclined fiber pullout from a cementitious matrix: a numerical study. Materials. 2016;9(10):800. doi:10.3390/ma9100800. [Google Scholar] [PubMed] [CrossRef]

32. Congro M, Vieira JD, de Andrade Silva F, Roehl D. Integrated workflow for experimental and numerical analysis of damage mechanisms at the fiber/matrix interface in cement composite materials. Constr Build Mater. 2025;479(9):141493. doi:10.1016/j.conbuildmat.2025.141493. [Google Scholar] [CrossRef]

33. Rawal A, Majumdar A, Kumar V. Textile architecture for composite materials: back to basics. Oxf Open Mater Sci. 2023;3(1):itad017. doi:10.1093/oxfmat/itad017. [Google Scholar] [CrossRef]

34. Zhao Z, Li B, Ma P. Advances in mechanical properties of flexible textile composites. Compos Struct. 2023;303(12):116350. doi:10.1016/j.compstruct.2022.116350. [Google Scholar] [CrossRef]

35. Mercedes L, Escrig C, Bernat-Masó E, Gil L. Analytical approach and numerical simulation of reinforced concrete beams strengthened with different FRCM systems. Materials. 2021;14(8):1857. doi:10.3390/ma14081857. [Google Scholar] [PubMed] [CrossRef]

36. Larrinaga P, Chastre C, Biscaia HC, San-José JT. Experimental and numerical modeling of basalt textile reinforced mortar behavior under uniaxial tensile stress. Mater Des. 2014;55(6):66–74. doi:10.1016/j.matdes.2013.09.050. [Google Scholar] [CrossRef]

37. Cao P, Cao L, Chen G, Zhi Z, Wang J, Yuan Z, et al. Numerical modelling of flexural performance of textile reinforced mortar strengthened concrete beams. Mater Des. 2024;244(2):113227. doi:10.1016/j.matdes.2024.113227. [Google Scholar] [CrossRef]

38. Belyakov N, Smirnova O, Alekseev A, Tan H. Numerical simulation of the mechanical behavior of fiber-reinforced cement composites subjected dynamic loading. Appl Sci. 2021;11(3):1112. doi:10.3390/app11031112. [Google Scholar] [CrossRef]

39. El Kadi M, Nahum L, Peled A, Tysmans T. Layered finite element (FE) modelling of structural concrete beams non-uniformly reinforced with carbon textile fabrics. Mater Struct. 2021;54(5):183. doi:10.1617/s11527-021-01776-w. [Google Scholar] [CrossRef]

40. Sun CT, Vaidya RS. Prediction of composite properties from a representative volume element. Compos Sci Technol. 1996;56(2):171–9. doi:10.1016/0266-3538(95)00141-7. [Google Scholar] [CrossRef]

41. Balasubramani NK, Zhang B, Chowdhury NT, Mukkavilli A, Suter M, Pearce GM. Micro-mechanical analysis on random RVE size and shape in multiscale finite element modelling of unidirectional FRP composites. Compos Struct. 2022;282:115081. doi:10.1016/j.compstruct.2021.115081. [Google Scholar] [CrossRef]

42. Liu Y, van der Meer FP, Sluys LJ. A dispersive homogenization model for composites and its RVE existence. Comput Mech. 2020;65(1):79–98. doi:10.1007/s00466-019-01753-9. [Google Scholar] [CrossRef]

43. Sultana J, Rahman MM, Varga G, Szávai S, Bin Rayhan S. Machine learning–based prediction and comparison of numerical and theoretical elastic moduli in plant fiber-based unidirectional composite representative volume elements. J Exp Theor Anal. 2025;3(4):36. doi:10.3390/jeta3040036. [Google Scholar] [CrossRef]

44. Das S, Aguayo M, Rajan SD, Sant G, Neithalath N. Microstructure-guided numerical simulations to predict the thermal performance of a hierarchical cement-based composite material. Cem Concr Compos. 2018;87(Part B):20–8. doi:10.1016/j.cemconcomp.2017.12.003. [Google Scholar] [CrossRef]

45. Han M, Wang H. Computational microstructure modeling of transverse thermal behavior in cementitious composites filled with randomly dispersed natural fibers coated by functionally graded interphase. Int J Heat Mass Transf. 2021;180(5):121772. doi:10.1016/j.ijheatmasstransfer.2021.121772. [Google Scholar] [CrossRef]

46. Kamble M, Jopson R, Wollschlager J, Oberste C. Composite lattice reinforced part optimization with FEA: an automotive door component case study. In: Proceedings of the SPE Automotive Composites Conference & Exhibition (ACCE); 2024 Sep 4–6; Novi, MI, USA. [Google Scholar]

47. Sultana J, Varga G. Design and analysis of natural fiber-reinforced jute woven composite RVEs using numerical and statistical methods. J Compos Sci. 2025;9(6):283. doi:10.3390/jcs9060283. [Google Scholar] [CrossRef]

48. Xie J, Guo Z, Shao M, Zhu W, Jiao W, Yang Z, et al. Mechanics of textiles used as composite preforms: a review. Compos Struct. 2023;304(12):116401. doi:10.1016/j.compstruct.2022.116401. [Google Scholar] [CrossRef]

49. Wielhorski Y, Mendoza A, Rubino M, Roux S. Numerical modeling of 3D woven composite reinforcements: a review. Compos Part A Appl Sci Manuf. 2022;154(6):106729. doi:10.1016/j.compositesa.2021.106729. [Google Scholar] [CrossRef]

50. Šejnoha M, Vorel J, Valentová S, Tomková B, Novotná J, Marseglia G. Computational modeling of polymer matrix based textile composites. Polymers. 2022;14(16):3301. doi:10.3390/polym14163301. [Google Scholar] [PubMed] [CrossRef]

51. Saraireh D, Walls S, Suryanto B, Starrs G, McCarter WJ. The influence of multiple micro-cracking on the electrical impedance of an engineered cementitious composite. In: Strain-hardening cement-based composites. Dordrecht, The Netherlands: Springer; 2017. p. 292–9. doi:10.1007/978-94-024-1194-2_34. [Google Scholar] [CrossRef]

52. Pisupati A, Curto M, Laurent T, Cosson B, Park CH, Dhakal HN. Influence of cooling rate on the flexural and impact properties of compression molded non-woven flax/PLA biocomposites. Polymers. 2025;17(4):493. doi:10.3390/polym17040493. [Google Scholar] [PubMed] [CrossRef]

53. Lu J, Krugl S, Pidancier C, L’Hostis G, Wang P. Analysis and optimization of the deformability of flax fiber nonwoven tapes during the tape-laying process. Int J Adv Manuf Technol. 2025;137(7):3641–56. doi:10.1007/s00170-025-15351-y. [Google Scholar] [CrossRef]

54. Kalauova AS, Palchikova EE, Makarov IS, Shandryuk GA, Abilkhairov AI, Kalimanova DZ, et al. Specificity of thermal destruction of nonwoven mixture systems based on bast and viscose fibers. Polymers. 2025;17(9):1223. doi:10.3390/polym17091223. [Google Scholar] [PubMed] [CrossRef]

55. Gereke T, Cherif C. A review of numerical models for 3D woven composite reinforcements. Compos Struct. 2019;209:60–6. doi:10.1016/j.compstruct.2018.10.085. [Google Scholar] [CrossRef]

56. Ke Z, Yu L, Wang G, Sun R, Zhu M, Dong H, et al. Three-dimensional modeling of spun-bonded nonwoven meso-structures. Polymers. 2023;15(3):600. doi:10.3390/polym15030600. [Google Scholar] [PubMed] [CrossRef]

57. Khalel HH, Khan M. Modelling fibre-reinforced concrete for predicting optimal mechanical properties. Materials. 2023;16(10):3700. doi:10.3390/ma16103700. [Google Scholar] [PubMed] [CrossRef]

58. Fang J, Chen L, Xie J, Wang J, Jiao W. A review of fiber-scale modeling for composite preforms. Compos Struct. 2025;370(3):119362. doi:10.1016/j.compstruct.2025.119362. [Google Scholar] [CrossRef]

59. Oddo MC, Minafó G, Di Leto M, La Mendola L. Numerical modelling of the constitutive behaviour of FRCM composites through the use of truss elements. Materials. 2023;16(3):1011. doi:10.3390/ma16031011. [Google Scholar] [PubMed] [CrossRef]

60. Hanif A, Kim Y, Park C. Numerical validation of two-parameter weibull model for assessing failure fatigue lives of laminated cementitious composites—comparative assessment of modeling approaches. Materials. 2019;12(1):110. doi:10.3390/ma12010110. [Google Scholar] [CrossRef]

61. Mahpour AR, Sadrolodabaee P, Ardanuy M, Haurie L, Lacasta AM, Rosell JR, et al. Serviceability parameters and social sustainability assessment of flax fabric reinforced lime-based drywall interior panels. J Build Eng. 2023;76(11):107406. doi:10.1016/j.jobe.2023.107406. [Google Scholar] [CrossRef]

62. Rakhsh Mahpour A, Ardanuy M, Ventura H, Rosell JR, Claramunt J. Mechanical properties and durability of biobased fabric-reinforced lime composites intended for strengthening historical masonry structures. Constr Build Mater. 2024;414:134916. doi:10.1016/j.conbuildmat.2024.134916. [Google Scholar] [CrossRef]

63. Wang Z, Gao Z, Wang Y, Cao Y, Wang G, Liu B, et al. A new dynamic testing method for elastic, shear modulus and Poisson’s ratio of concrete. Constr Build Mater. 2015;100(1):129–35. doi:10.1016/j.conbuildmat.2015.09.060. [Google Scholar] [CrossRef]

64. Carrillo J, Ramirez J, Lizarazo-Marriaga J. Modulus of elasticity and Poisson’s ratio of fiber-reinforced concrete in Colombia from ultrasonic pulse velocities. J Build Eng. 2019;23(5):18–26. doi:10.1016/j.jobe.2019.01.016. [Google Scholar] [CrossRef]

65. Persson B. Poisson’s ratio of high-performance concrete. Cem Concr Res. 1999;29(10):1647–53. doi:10.1016/S0008-8846(99)00159-3. [Google Scholar] [CrossRef]

66. Wang H, Li Q. Prediction of elastic modulus and Poisson’s ratio for unsaturated concrete. Int J Solids Struct. 2007;44(5):1370–9. doi:10.1016/j.ijsolstr.2006.06.028. [Google Scholar] [CrossRef]

67. Marszałek J, Stadnicki J, Danielczyk P. Finite element model of laminate construction element with multi-phase microstructure. Sci Eng Compos Mater. 2020;27(1):405–14. doi:10.1515/secm-2020-0044. [Google Scholar] [CrossRef]

68. Li D. Layerwise theories of laminated composite structures and their applications: a review. Arch Comput Meth Eng. 2021;28(2):577–600. doi:10.1007/s11831-019-09392-2. [Google Scholar] [CrossRef]

69. Astanin VV, Bogdan SY. Finite element model of laminated shells of composite materials. Strength Mater. 2021;53(2):265–71. doi:10.1007/s11223-021-00284-0. [Google Scholar] [CrossRef]