Numerical Properties of Spherical and Cubical Representative Volume Elements with Different Boundary Conditions

Abstract

It has been found that, due to the smaller surface to volume ratio, the spherical representative volume elements (RVE) converge faster to the effective properties than cubical RVEs, in terms of the RVE volume (Gl¨uge et al., 2012). It remains to discuss whether one can actually draw a numerical advantage from this in the finite element calculations, since there are also some drawbacks, for example the necessarily irregular meshing. It has been demonstrated that the boundary conditions, in conjunction with different solution strategies for the linear system that emerges in the FEM, can significantly influence the numerical expense (Fritzen and B¨ohlke, 2010a). In the light of these results, we examine the numerical properties of spherical and cubical RVEs with linear displacement and periodic (resp. antipodic) boundary conditions.