Assessment of Mixed Uniform Boundary Conditions for Predicting the Mechanical Behavior of Elastic and Inelastic Discontinuously Reinforced Composites
D. H. Pahr; and H.J. B o hm

doi:10.3970/cmes.2008.034.117
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 34, No. 2, pp. 117-136, 2008
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Keywords Mixed Uniform Boundary Conditions, Periodicity Boundary Conditions, Finite Element Simulation, Composites
Abstract The combination of heterogeneous volume elements and numerical analysis schemes such as the Finite Element method provides a powerful and well proven tool for studying the mechanical behavior of composite materials. Periodicity boundary conditions (PBC), homogeneous displacement boundary conditions (KUBC) and homogeneous traction boundary conditions (SUBC) have been widely used in such studies. Recently \relax \begingroup \catcode `\ 12\relax \catcode `\\12\relax \catcode `\$12\relax \catcode `\&12\relax \catcode `\#12\relax \catcode `\^12\relax \catcode `\_12\relax \catcode `\%12\relax \catcode `\~12\relax \endgroup \relax \cite *{Pahr2007} proposed a special set of mixed uniform boundary conditions (MUBC) for evaluating the macroscopic elasticity tensor of human trabecular bone. These boundary conditions are not restricted to periodic phase geometries, but were found to give the same predictions as PBC for the effective elastic properties of periodic open cell microstructures of orthotropic symmetry. Accordingly, they have been referred to as ``periodicity compatible MUBC'' (PMUBC).\newline The present study uses periodic volume elements that contain randomly positioned spherical particles or randomly oriented short fibers at moderate volume fractions for assessing the applicability of PMUBC to modeling composite materials via volume elements that deviate from orthotropic symmetry. Macroscopic elasticity tensors are evaluated with PBC, PMUBC and KUBC for elastic contrasts in the range$2\le s_\mathrm {r} \le 30$. For one configuration the isotropic contributions to the macroscopic elastic tensors obtained with PBC and PMUBC are extracted and compared. In addition, macroscopic elastic-plastic responses for different hardening behaviors are studied with PBC and PMUBC. Only small differences between the predictions obtained with PBC and PMUBC are found, validating the PMUBC for studying volume elements the overall behavior of which shows minor contributions of lower than orthotropic symmetry.
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