Computational homogenization of higher‐order continua

Abstract

We introduce a novel computational framework for the multiscale simulation of higher‐order continua that allows for the consideration of first‐, second‐, and third‐order effects at both micro‐ and macro‐level. In line with classical two‐scale approaches, we describe the microstructure via representative volume elements that are attached at each integration point of the macroscopic problem. To take account of the extended continuity requirements of independent fields at micro‐ and macro‐level, we discretize both scales via isogeometric analysis (IGA). As a result, we obtain an IGA2‐method that is conceptually similar to the well‐known FE2‐method. We demonstrate the functionality and accuracy of this novel multiscale method by means of a series of multiscale simulations involving different kinds of higher‐order continua.