Yield criterion and finite strain behavior of random porous isotropic materials

TL;DR

This paper investigates the yield behavior and finite strain response of isotropic elastoplastic materials with randomly distributed voids using FFT simulations, identifying coalescence regimes and proposing a homogenized model.

Contribution

It introduces a new computational approach to determine yield surfaces and coalescence regimes in random porous materials, and proposes a homogenized model for finite strain behavior.

Findings

Identification of a Representative Volume Element size for coalescence onset

Discovery of two coalescence regimes distinguished by shear presence

Development of a homogenized model matching finite strain behavior

Abstract

The mechanical response of isotropic elastoplastic materials containing random distributions of initially spherical voids is investigated computationally based on Fast Fourier Transform simulations. Numerical limit-analysis simulations at constant stress triaxiality allow to determine the yield surfaces, leading in particular to the determination of a Representative Volume Element size for the onset of coalescence / inhomogeneous yielding. Moreover, two different coalescence regimes are observed that differ by the presence of shearing. The yield surfaces are found to be consistent with the combination of two models proposed in the literature, a GTN-type model calibrated for homogeneous yielding of random porous materials and an inhomogeneous yielding model accounting for both coalescence with or without shear. Finite strain simulations performed for different hardening moduli and stress triaxialities under axisymmetric loading conditions confirm the existence of a RVE up to the onset of inhomogeneous yielding. Coalescence strains are found to be significantly smaller for random porous materials than for periodic distribution of voids. A homogenized model is finally proposed that reproduces quantitatively the behavior of isotropic elastoplastic materials containing random distributions of voids under finite strains.