Numerical homogenisation based on asymptotic theory and model reduction for coupled elastic-viscoplastic damage. (September 2020)

• Record Type: Journal Article
• Authors: Bhattacharyya, Mainak; Dureisseix, David; Faverjon, Beatrice
• Is Part Of: International journal of damage mechanics. Volume 29:Number 9(2020)
• Page Start: 1416
• Page End: 1444
• Publication Date: 2020-09
• Subjects: Asymptotic homogenisation -- viscoplasticity -- continuum damage -- micro-structure -- multi-scale -- reduced order model; Fracture mechanics -- Periodicals; 620.1126
• DOI: 10.1177/1056789520930785
• Languages: English
• ISSNs: 1056-7895

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.