ELASTOPLASTIC MICROMECHANICAL MODELING OF 2-DIMENSIONAL IRREGULAR CONVEX AND NONCONVEX (REENTRANT) HEXAGONAL FOAMS

A nonlinear micromechanical model for two-dimensional irregular hexago nal foams has been developed that allows for anisotropy in morphology and/or material. Based upon the orientation, cross section, length, an d material properties of each strut, the resulting microlevel beam beh avior within the unit cell determines its structural properties. Nonli nearity is introduced as coupled elastoplastic beam behavior, where th e elastoplastic behavior of each beam is considered. The analytical fo rmulation for the stiffness matric of the general elastoplastic unit c ell is found by considering compatibility and equilibrium of the unit cell. The structural properties of the elastoplastic unit cell are emb edded in a continuum finite element model as material properties, thus capturing the microstructure of the foam in an accurate and efficient mode. Structural nonlinearity is therefore directly linked to localiz ed plasticity and its evolution at the microlevel. Elastic analyses in vestigated the degree of anisotropy in structural properties that was induced by various morphological changes. The differences in stress an d deformation behavior between a regular hexagonal foam and a re-entra nt 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 stud y of the effects of morphology and/or material anisotropies on the ove rall foam behavior.