Elastoplastic Micromechanical Modeling of Two-Dimensional Irregular Convex and Nonconvex (Re-entrant) Hexagonal Foams

A nonlinear micromechanical model for two-dimensional irregular hexagonal foams has been developed that allows for anisotropy in morphology and/or material. Based upon the orientation, cross section, length, and material properties of each strut, the resulting microlevel beam behavior within the unit cell determines its structural properties. Nonlinearity is introduced as coupled elastoplastic beam behavior, where the elastoplastic behavior of each beam is considered. The analytical. formulation for the stiffness matrix of the general elastoplastic unit cell is. found by considering compatibility and equilibrium of the unit cell. The structural properties of the elastoplastic unit cell are embedded in a continuum finite element model as material properties, thus capturing the microstructure of the foam in an accurate and efficient model. Structural nonlinearity is therefore directly linked to localized plasticity and its evolution at the microlevel. Elastic analyses investigated the degree of anisotropy in structural properties that was induced by various morphological changes. The differences in stress and deformation behavior between a regular hexagonal foam and a re-entrant foam were also demonstrated. Plastic analyses showed how structural nonlinearity could be explained by localized microstructural behavior. The advantage of this micromechanical model is that it allows a study of the effects of morphology and/or material anisotropies on the overall foam behavior.