Fast Fourier Transform computations and build-up of plastic deformation in 2D, elastic-perfectly plastic, pixelwise disordered porous media

TL;DR

This paper uses a Fast Fourier Transform method to analyze stress, strain, and plastic deformation evolution in a 2D pixelwise disordered elastic-perfectly plastic porous medium, revealing nucleation, growth, and coalescence of plastic zones.

Contribution

It introduces a FFT-based computational approach with a discrete Green function for modeling plastic deformation in disordered media, linking microscopic behavior to macroscopic stress-strain responses.

Findings

Identification of plastic cluster nucleation, growth, and coalescence.

Correlation between morphological regimes and stress-strain curves.

Efficient computation of stress and strain fields in disordered porous media.

Abstract

Stress and strain fields in a two-dimensional pixelwise disordered system are computed by a Fast Fourier Transform method. The system, a model for a ductile damaged medium, consists of an elastic-perfectly matrix containing void pixels. Its behavior is investigated under equibiaxial or shear loading. We monitor the evolution with loading of plastically deformed zones, and we exhibit a nucleation / growth / coalescence scenario of the latter. Identification of plastic ``clusters'' is eased by using a discrete Green function implementing equilibrium and continuity at the level of one pixel. Observed morphological regimes are put into correspondence with some features of the macroscopic stress / strain curves.