Continuum modeling of crushing of low density foams

Abstract

Under compression deformation in low-density foams localizes into narrow bands of crushed cells. Crushing spreads at nearly constant stress with crushed and relatively undeformed material coexisting. The material returns to homogeneous deformation with increasing stress when the crushing has spread over the whole specimen. This paper presents a first attempt at representing the inhomogeneous behavior exhibited by open-cell aluminum alloy foams with relative density of 8%. A plasticity model is presented with a compressible yield function calibrated to a set of multiaxial foam crushing tests coupled with a non-associated flow rule. An essential component of the modeling effort is the introduction of a softening branch to the material stress-strain response. A cubical finite element model with an irregular mesh of solid elements is used to simulate a set of numerical crushing tests on micromechanically accurate foam models performed in a true triaxial apparatus in Yang and Kyriakides (2019). Small geometric imperfections are used to trigger localized deformation in the form of planar bands of high strain normal to the loading directions of compression. The bands broaden with the stresses tracing plateaus that mimic the random foam test results. The predicted mean stress–change in volume responses perform equally well up to a volume reduction of about 50%. At higher compressions, the stresses exhibit the gradual increase characteristic of foams in the densification regime. These parts of the stress–displacement trajectories, and mean stress–change in volume responses under-predict to some degree those recorded in the random foams. The material hardening in the densification regime appears to be deformation-dependent causing this difference.