Peridynamic computational homogenization theory for materials with evolving microstructure and damage

Abstract

This study aims to establish a framework for multiscale assessment of damage for materials with evolving microstructure based on a recently proposed peridynamic computational homogenization theory. The framework starts with replacing a material with complex microstructure with a constitutively equivalent material that is microstructurally homogenous. Constitutive equivalence between the original and the substitute materials is achieved through enforcing strain energy equivalence via the so-called nonlocal Hill’s lemma. The damage law is obtained by numerically solving boundary volume constraint problem of an RVE. The result from the analysis of the RVE problem was compared with the previously published result to establish the validity of the proposed framework. The comparison shows good agreement between result obtained using the proposed framework and those reported in the literature.

Modelling of viscoelastic materials using non-ordinary state-based peridynamics

“…Therefore, evolving discontinuity, such as the initiation and propagation of cracks, is treated as an inherent characteristic of the material and is thus modelled using the PD fundamental equation of motion without the need for additional assumptions or modifications. This advantage has motivated a growing interest in using PD to characterise materials with strong or evolving discontinuous response [6][7][8][9][10][11][12][13][14][15][16][17][18].…”