On the multiaxial crushing of low-density open-cell foams

Under uniaxial 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. The present study investigates how this partially unstable behavior of low-density foams transfers to the multiaxial setting as follows: (i) The crushing behavior of random foams is investigated under “true” triaxial loadings. A micromechanically accurate cubical model of an Al-alloy open-cell foam with relative density of 0.08 is crushed by a numerical true triaxial apparatus in three directions for three families of radial displacement paths. For all paths studied, the foam traces the same three regime behavior observed under uniaxial compression. Local cell crushing developed in narrow bands of cells at boundaries and subsequently propagate to the rest of the domain until the whole domain is crushed. (ii) A plasticity model is presented with a Drucker-Prager type yield function 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. The constitutive model is incorporated in a cubical finite element model to simulate true triaxial crushing tests performed on the random foam in the continuum setting. Small geometric imperfections are used to trigger localized deformation in the form of planar bands of high strain. The bands broaden with the stresses tracing plateaus. For all loading paths, the calculated crushing responses reproduce those of the random foam very well. The study clearly demonstrates that the homogenized model captures the partially inhomogeneous crushing behavior of foams. (iii) The same random foam model is crushed under displacement controlled axial compression at different levels of external pressure. The study shows that such foams deform inhomogeneously under this triaxial loading also. The level of external pressure tends to lower the limit stress, the stress plateau, and the rest of the response. This behavior is subsequently simulated at the continuum level. It is demonstrated that the homogenized model again captures the three-regime response of the random foam