Computational homogenization of higher-order continua

TL;DR

This paper presents a new multiscale computational framework using isogeometric analysis for higher-order continua, enabling detailed micro- and macro-level simulations including third-order effects.

Contribution

It introduces the IGA2-method, a novel approach combining microstructure modeling with higher-order effects at multiple scales, extending classical two-scale methods.

Findings

Demonstrates the accuracy of the IGA2-method through multiscale simulations.

Successfully models higher-order continuum effects at micro- and macro-levels.

Validates the approach with various types 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 (RVE) 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.