Jiao Jia^1,*, Xin He², Zhenchen Liu³, Shiqing Wu⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.143, No.3, pp. 3215-3231, 2025, DOI:10.32604/cmes.2025.066489 - 30 June 2025

Abstract As primary load-bearing components extensively utilized in engineering applications, beam structures necessitate the design of their microstructural configurations to achieve lightweight objectives while satisfying diverse mechanical performance requirements. Combining topology optimization with fully coupled homogenization beam theory, we provide a highly efficient design tool to access desirable periodic microstructures for beams. The present optimization framework comprehensively takes into account for key deformation modes, including tension, bending, torsion, and shear deformation, all within a unified formulation. Several numerical results prove that our method can be used to handle kinds of microstructure design for beam-like structures, e.g., More >

Shanqiao Huang¹, Zifeng Yuan^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.142, No.3, pp. 2893-2924, 2025, DOI:10.32604/cmes.2025.059948 - 03 March 2025

Abstract The multiscale computational method with asymptotic analysis and reduced-order homogenization (ROH) gives a practical numerical solution for engineering problems, especially composite materials. Under the ROH framework, a partition-based unitcell structure at the mesoscale is utilized to give a mechanical state at the macro-scale quadrature point with pre-evaluated influence functions. In the past, the “1-phase, 1-partition” rule was usually adopted in numerical analysis, where one constituent phase at the mesoscale formed one partition. The numerical cost then is significantly reduced by introducing an assumption that the mechanical responses are the same all the time at the… More >

Huilin Jia¹, Shanqiao Huang¹, Zifeng Yuan^1,2,*

CMC-Computers, Materials & Continua, Vol.82, No.1, pp. 193-222, 2025, DOI:10.32604/cmc.2024.059950 - 03 January 2025

Abstract In this manuscript, we propose an analytical equivalent linear viscoelastic constitutive model for fiber-reinforced composites, bypassing general computational homogenization. The method is based on the reduced-order homogenization (ROH) approach. The ROH method typically involves solving multiple finite element problems under periodic conditions to evaluate elastic strain and eigenstrain influence functions in an ‘off-line’ stage, which offers substantial cost savings compared to direct computational homogenization methods. Due to the unique structure of the fibrous unit cell, “off-line” stage calculation can be eliminated by influence functions obtained analytically. Introducing the standard solid model to the ROH method More >

Jianghong Yang¹, Yingjun Wang^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.29, No.2, pp. 1-1, 2024, DOI:10.32604/icces.2024.011249

Abstract Multiscale structures can be more robust to partial damage than solid structures. Inspired by this, a novel fail-safe topology optimization method is proposed for multiscale structures. Computational cost is reduced by simplifying the partial damage of the truss-like microstructure and polynomial function is used to fit the effective elasticity tensor obtained via the homogenization method. Moreover, Heaviside projection is applied to speed up the convergence and yield a relatively clear configuration. Numerical examples are tested to demonstrate the advantages of the optimized multiscale structures. Numerical examples are tested to demonstrate that the optimized multiscale structures More >

Linjuan Wang^1,*, Jianxiang Wang²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.09355

Abstract The prediction of overall dynamics of composite materials has been an intriguing research topic more than a century, and numerous approaches have been developed for this topic. One of the most successful representatives is the classical micromechanical models which assume that the behavior of a composite is the same as its constituents except for the difference in mechanical properties, e.g., effective moduli. With the development of advanced composite materials in recent years, especially metamaterials, it is found that the classical micromechanical models cannot describe complex dynamic responses of composites such as the dispersion and bandgaps… More >

Hao Dong¹, Yufeng Nie^1,2, Zihao Yang¹, Yang Zhang¹, Yatao Wu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.5, pp. 395-419, 2016, DOI:10.3970/cmes.2016.111.395

Abstract In this paper, we discuss the numerical accuracy of asymptotic homogenization method (AHM) and multiscale finite element method (MsFEM) for periodic composite materials. Through numerical calculation of the model problems for four kinds of typical periodic composite materials, the main factors to determine the accuracy of first-order AHM and second-order AHM are found, and the physical interpretation of these factors is given. Furthermore, the way to recover multiscale solutions of first-order AHM and MsFEM is theoretically analyzed, and it is found that first-order AHM and MsFEM provide similar multiscale solutions under some assumptions. Finally, numerical More >

Marcin Kamiński^1,2, Bernd Lauke²

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.6, pp. 411-440, 2013, DOI:10.3970/cmes.2013.093.411

Abstract The main aim in this paper is a computational study devoted to the sensitivity gradients and probabilistic moments of the effective elastic parameters for the rubber-filled polymers. The methodology is based on least squares recovery of the polynomial functions relating the effective tensor components and the given input design/random parameters. All numerical experiments are provided with respect to Young’s moduli of the elastomer constituents. Computational analysis is possible thanks to the application of the Response Function Method, which is enriched in our approach with the weighting procedures implemented according to the Dirac-type distributions. The homogenized… More >

Veturia Chiroiu¹, Ligia Munteanu² and Antonio S. Gliozzi³

CMC-Computers, Materials & Continua, Vol.19, No.1, pp. 1-16, 2010, DOI:10.3970/cmc.2010.019.001

Abstract This paper develops a mechanical model for multifunctional reinforced carbon nanotube (CNT) beams. The model is obtained by introducing the couple stresses into the constitutive equations of linear viscoelastic theory. The material functions are determined using the homogenization method. More >

T. Asada¹, N. Ohno¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.4, No.4, pp. 201-206, 2007, DOI:10.3970/icces.2007.004.201

Abstract In this study, to determine incremental, perturbed displacement fields in periodic inelastic solids, an incremental homogenization problem is fully implicitly formulated, and an algorithm is developed to solve the homogenization problem. It is shown that the homogenization problem can be iteratively solved with quadratic convergences by successively updating strain increments in unit cells, and that the present formulation allows versatility in the initial setting of strain increments in contrast to previous studies. The homogenization algorithm developed is then examined by analyzing a holed plate, with an elastoplastic micro-structure, subjected to tensile loading. It is thus More >

Y. Tomita ¹, M. Uchida ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.3, pp. 239-248, 2005, DOI:10.3970/cmes.2005.010.239

Abstract In this study, we clarified the micro- to mesoscopic deformation behavior of a semicrystalline polymer by employing a large-deformation finite element homogenization method. The crystalline plasticity theory with a penalty method for the inextensibility of the chain direction and the nonaffine molecular chain network theory were applied for the representation of the deformation behavior of the crystalline and amorphous phases, respectively, in the composite microstructure of the semicrystalline polymer. The 3D structure of lamellae in the spherulite of high-density polyethylene was modeled, and the tensile and compressive deformation behaviors were investigated. A series of computational More >