Superconvergence of the effective Cauchy stress in computational homogenization of inelastic materials

Abstract We provide theoretical investigations and empirical evidence that the effective stresses in computational homogenization of inelastic materials converge with a higher rate than local solution fields. Due to complexity industrial‐scale microstructures, methods often utilize rather crude approximation microstructure, favoring regular grids over accurate boundary representations. As accuracy such an approach has been under continuous verification for decades, it appears astonishing this strategy is successful homogenization, but seldom used on component scale. A part puzzle solved recently, as was shown elastic properties twice strain stress Thus, although mechanical fields may be inaccurate, averaging process leads cancellation errors improves significantly. Unfortunately, original argument based energetic considerations. The straightforward extension setting provides superconvergence (pseudoelastic) potentials, does not cover primary quantity interest: tensor. purpose work at hand twofold. On one hand, we extensive numerical experiments convergence quantities fast Fourier transform. These indicate effect valid stresses, well. Moreover, justification avoids reasoning.