Nian Li^*

Structural Durability & Health Monitoring, Vol.13, No.4, pp. 331-346, 2019, DOI:10.32604/sdhm.2019.07521

Abstract The investigation focusing on the mechanical behaviors at the microstructural level in composite materials can provide valuable insight into the failure mechanisms at larger scales. A micromechanics damage model which comprises the coupling of the matrix constitutive model and the cohesive zone (CZM) model at fiber-matrix interfaces is presented to evaluate the transverse tensile damage behaviors of unidirectional (UD) fiber-reinforced polymer (FRP) composites. For the polymeric matrix that exhibits highly non-linear mechanical responses, special focus is paid on the formulation of the constitutive model, which characterizes a mixture of elasticity, plasticity as well as damage. The proposed constitutive model includes… More >

Leiting Dong^1,2, Satya N. Atluri^1,3

CMC-Computers, Materials & Continua, Vol.33, No.2, pp. 111-154, 2013, DOI:10.3970/cmc.2013.033.111

Abstract In this study, SGBEM Voronoi Cells (SVCs), with each cell representing a grain of the material at the micro-level, are developed for direct micromechanical numerical modeling of heterogeneous composites. Each SVC can consist of either a (each with a different) homogenous isotropic matrix, and can include micro-inhomogeneities such as inclusions, voids of a different material, and cracks. These inclusions and voids in each SVC can be arbitrarily-shaped, such as circular, elliptical, polygonal, etc., for 2D problems. Further, the cracks in each SVC can be fully-embedded, edge, branching, or intersecting types, with arbitrary curved shapes. By rearranging the weakly-singular boundary integral… More >

Yunfa Zhang¹, Zihui Xia^1,2

CMC-Computers, Materials & Continua, Vol.2, No.3, pp. 213-226, 2005, DOI:10.3970/cmc.2005.002.213

Abstract In the present study, the initiation and evolution of the interphase damage and their influences on the global stress-strain relation of composite laminates are predicted by finite element analysis on a micromechanical unit cell model. A thin layer of interphase elements is introduced and its stress-strain relation is derived based on a cohesive law which describes both normal and tangential separations at the interface between the fiber and matrix. In addition, a viscous term is added to the cohesive law to overcome the convergence difficulty induced by the so-called snap-back instability in the numerical analysis. The matrix behavior is described… More >

Leiting Dong¹, Satya N. Atluri1¹

CMC-Computers, Materials & Continua, Vol.30, No.1, pp. 39-82, 2012, DOI:10.3970/cmc.2012.030.039

Abstract In this paper, as an extension to the authors's work in [Dong and Atluri (2011a,b, 2012a,b,c)], three-dimensional Trefftz Voronoi Cells (TVCs) with ellipsoidal voids/inclusions are developed for micromechanical modeling of heterogeneous materials. Several types of TVCs are developed, depending on the types of heterogeneity in each Voronoi Cell(VC). Each TVC can include alternatively an ellipsoidal void, an ellipsoidal elastic inclusion, or an ellipsoidal rigid inclusion. In all of these cases, an inter-VC compatible displacement field is assumed at each surface of the polyhedral VC, with Barycentric coordinates as nodal shape functions. The Trefftz trial displacement fields in each VC are… More >

L. Dong¹, S. N. Atluri¹

CMC-Computers, Materials & Continua, Vol.29, No.2, pp. 169-212, 2012, DOI:10.3970/cmc.2012.029.169

Abstract In this paper, three-dimensionalT-Trefftz Voronoi Cell Finite Elements (VCFEM-TTs) are developed for micromechanical modeling of heterogeneous materials. Several types of VCFEMs are developed, depending on the types of heterogeneity in each element. Each VCFEM can include alternatively a spherical void, a spherical elastic inclusion, a spherical rigid inclusion, or no voids/inclusions at all.In all of these cases, an inter-element compatible displacement field is assumed at each surface of the polyhedral element, with Barycentric coordinates as nodal shape functions.The T-Trefftz trial displacement fields in each element are expressed in terms of the Papkovich-Neuber solution. Spherical harmonics are used as the Papkovich-Neuber… More >

Isa Ahmadi¹, M.M. Aghdam²

CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.1, pp. 21-48, 2015, DOI:10.3970/cmes.2015.108.021

Abstract In this study, a truly meshless method based on the meshless local Petrov-Galerkin method is formulated for analysis of the elastic-plastic behavior of heterogeneous solid materials. The incremental theory of plasticity is employed for modeling the nonlinearity of the material behavior due to plastic strains. The well-known Prandtl-Reuss flow rule of plasticity is used as the constitutive equation of the material. In the presented method, the computational cost is reduced due to elimination of the domain integration from the formulation. As a practical example, the presented elastic-plastic meshless formulation is employed for micromechanical analysis of the unidirectional composite material. A… More >

X. Wang¹, W.T. Ang^1,2, H. Fan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.2, pp. 81-101, 2015, DOI:10.3970/cmes.2015.107.081

Abstract A micromechanical model is proposed here for estimating the effective stiffness of a pair of parallel microscopically damaged interfaces in a trimaterial under inplane elastostatic deformations. The trimaterial is made of an orthotropic thin layer sandwiched between two orthotropic half-spaces. The microscopically damaged interfaces are modeled using periodically distributed interfacial micro-cracks. The micromechanical model is formulated and numerically solved in terms of hypersingular boundary integro-differential equations. The effects of the width of the thin layer, the micro-crack densities of the two interfaces and the material constants of the thin layer and the two half-spaces on the effective stiffness coefficients are… More >

L. Dong¹, S. N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.81, No.1, pp. 69-118, 2011, DOI:10.3970/cmes.2011.081.069

Abstract In this paper, we explore three different ways of developing T-Trefftz finite elements of quadrilateral as well as polygonal shapes. In all of these three approaches, in addition to assuming an inter-element compatible displacement field along the element boundary, an interior displacement field for each element is independently assumed as a linear combination of T-Trefftz trial functions. In addition, a characteristic length is defined for each element to scale the T-Trefftz modes, in order to avoid solving systems of ill-conditioned equations. The differences between these three approaches are that, the compatibility between the independently assumed fields at the boundary and… More >

K. Jayabal, A. Arockiarajan, S.M. Sivakumar¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 111-124, 2008, DOI:10.3970/cmes.2008.027.111

Abstract A three dimensional micromechanically motivated model is proposed here based on firm thermodynamics principles to capture the nonlinear dissipative effects in the polycrystal ferroelectrics. The constraint imposed by the surrounding grains on a subgrain at its boundary during domain switching is modeled by a suitable modification of the switching threshold in a subgrain. The effect of this modification in the dissipation threshold is studied in the polycrystal behavior after due correlation of the subgrain behavior with the single crystal experimental results found in literature. Taking into consideration, all the domain switching possibilities, the volume fractions of each of the variants… More >

D.T. Fullwood¹, S.R. Kalidindi², B.L. Adams¹, S. Ahmadi¹

CMC-Computers, Materials & Continua, Vol.9, No.1, pp. 25-40, 2009, DOI:10.3970/cmc.2009.009.025

Abstract Localization relations arise naturally in the formulation of multi-scale models. They facilitate statistical analysis of local phenomena that may contribute to failure related properties. The computational burden of dealing with such relations is high and recent work has focused on spectral methods to provide more efficient models. Issues with the inherent integrations in the framework have led to a tendency towards calibration-based approaches. In this paper a discrete Fourier transform framework is introduced, leading to an extremely efficient basis for the localization relations. Previous issues with the Green's function integrals are resolved, and the method is validated against finite element… More >