A plasticity model for cellular materials with open-celled structure

Based on a rigid-plastic material model that obeys the von Mises yield criterion, the plastic behavior of foams with an open-celled structure is studied in this paper using a single unit cell. An approximate continuum plasticity model is developed within the framework of the upper bound theorem of plasticity to describe the yield behavior of foams. The microscopic velocity fields are derived for the unit cell, which satisfy the incompressibility and the kinematic boundary conditions, and expressed in macroscopic rate of deformation. From the microscopic velocity fields, a macroscopic yield function is developed for foams under multi-axial stresses and includes the effects of the hydrostatic stress due to the void presence and growth. The dependency of the derived yield surfaces of foams on their relative densities is studied. The plastic behavior of foams is also studied numerically using the finite element method. The newly developed plasticity model is compared with the finite element analysis results and other available foam models and then correlated with the finite element results.