Numerical homogenisation based on asymptotic theory and model reduction for coupled elastic-viscoplastic damage

Abstract

This article deals with damage computation of heterogeneous structures containing locally periodic micro-structures. Such heterogeneous structure is extremely expensive to simulate using classical finite element methods, as the level of discretisation required to capture the micro-structural effects is too fine. The simulation time becomes even higher when dealing with highly non-linear material behaviour, e.g. damage, plasticity and such others. Therefore, a multi-scale strategy is proposed here that facilitates the simulation of non-linear heterogeneous material behaviour in a manner that is computationally feasible. Based on the asymptotic homogenisation theory, this multi-scale technique explores the micro–macro behaviour for elasto-(visco)plasticity coupled with damage. The theory inherently segregates the heterogeneous continua into a macroscopic homogeneous structure and an underlying heterogeneous microscopic periodic unit cell. Several heterogeneous structures have been simulated using the multi-scale method along with a one-dimensional verification with respect to a reference solution. Additionally, a reduced order modelling is used to prevent large memory requirement for storing micro-structural quantities of interest.

A convex anisotropic damage model based on the compliance tensor

“…The micromechanics-based approach to damage mechanics takes the damage mechanisms on a lower scale into account and is still subject of current research, for instance concerning mesh-size objective modeling (Liang et al., 2018), a coupling to model-order reduction (Bhattacharyya et al., 2020) or accounting for micro-computed tomography data (Luo et al., 2020). Micromechanics-informed damage models permit taking the stochastics on the microscale into account naturally, e. g., for progressive fiber breakage in fiber-reinforced composites (Ju and Wu, 2016; Wu and Ju, 2017), interfacial transition-zone effects (Chen et al., 2018), uncertainty in the elastic moduli of fiber-reinforced concrete (Liu et al., 2020), localized microcracks (Li et al., 2020) or random loading in fatigue processes (Franko et al., 2017).…”

A multiscale reduced‐order‐model strategy for transient thermoelasticity with variable microstructure

“…A reduced‐order model or a surrogate model can then be generated by truncating the optimal basis 31,32 . On the paradigm of multiscale methods, POD and its variants have been used for nonlinear heat conduction, 33 for multiscale fracture mechanics, 34 for hyper‐elastic materials at finite strains, 35 for damage analysis, 36,37 and such others.…”