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 >

L. Dong¹, S. N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.2, pp. 183-220, 2012, DOI:10.32604/cmes.2012.083.183

Abstract In this paper, we develop T-Trefftz Voronoi Cell Finite Elements (VCF -EM-TTs) for micromechanical modeling of composite and porous materials. In addition to a homogenous matrix in each polygon-shaped element, three types of arbitrarily-shaped heterogeneities are considered in each element: an elastic inclusion, a rigid inclusion, or a void. In all of these three cases, an inter-element compatible displacement field is assumed along the element outer-boundary, and interior displacement fields in the matrix as well as in the inclusion are independently assumed as T-Trefftz trial functions. Characteristic lengths are used for each element to scale the T-Trefftz trial functions, in… More >