Strain localization and effective medium properties
in 2D perfectly-plastic porous materials: the "dilute" limit

Francois Willot
Postdoctoral Researcher
Mechanical Engineering and Applied Mechanics
University of Pennsylvania

Abstract
This work addresses a notoriously difficult problem of nonlinear behavior and infinite contrast between two phases, one of which is a plastic solid phase, and the other one the porosity of the medium.  Such problem is of special interest to effective-medium approximations, which typically reach their limits in situations of strong nonlinearity and high contrast between the phases.

The aim of this study is to investigate how plastic strain localization manifests itself at the level of the overall effective behavior of the medium in presence of pores, and in particular in the non-trivial limit of small porosity. This question, important to the understanding of ductile damage, is examined both numerically and theoretically, in the special case of two dimensional systems, and with a deformation-theory approach of plasticity. The numerical investigations consist of quasi-exact computations of the stress and strain fields in the voided medium, by means of the Fast Fourier Transform method making use of a particular choice for Green's function. The theoretical approach makes use of exact solutions, which can be obtained in particular cases of a periodic void lattice, as well as of a recent "second-order" nonlinear homogenization approach.  The virtues of the latter are evaluated in two steps, first by studying the underlying linear anisotropic homogenization step (an essential ingredient), then by studying the nonlinear step itself. A connection between the strain/stress localization patterns and the macroscopic behavior is shown in the case of a strongly anisotropic linear material. In the nonlinear case, the nature and significance of the singularities, confirmed by FFT computations, are partly elucidated.

Thursday, September 6th
337 Towne Bldg.
2:00 – 3:00 p.m.