Fast Fourier Transform computations and build-up of plastic deformation in 2D, elastic-perfectly plastic, pixelwise 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.Comment: 6 pages, 5 figures. Presented at the "11th International Symposium On Continuum Models and Discrete Systems (CMDS 11)" (Ecole des Mines, Paris, July 30- August 3 2007