ABSTRACT
Many numerical models are used to describe hyperelastic contribution of rubber-like materials behavior. We can cite Mooney-Rivlin, Ogden or Arruda-Boyce numerical models. These models have been initially developed for materials that show almost no volume variation and have been improved to account for elastomeric materials with a small volume change. The use of cellular materials composed of polymers or elastomers in various applications brings questions about their numerical modeling and more specifically about the numerical modeling of their hyperelastic behavior. Indeed, contrary to elastomeric solid material that depends on the shape change behavior, the volume change contribution plays a role that cannot be neglected for cellular materials. In a previous work, Donnard et. al. have developed multiaxial experiments using an hexapod to exhibit volume and shape change behaviors occurring during combined compressive and simple shear loadings. They performed tests on polypropylene foam that show a large hyperelastic contribution. In the present work, a 2-D numerical model is proposed: it is based on a representative cell composed of a number of mechanical directions that is meshed by beams. The mechanical behavior of each beam is based on an 1-D hyperelastic and viscous model that has been identified by uniaxial tensile, compressive and relaxation tests. Complex loadings like the combination of simple shear and uniaxial compression are performed on this cell. Numerical results show good trends compared with experiments.
