Hyperelastic behavior of cellular structures based on micromechanical modeling at small strain

Abstract

The present paper extends recent effective, linear anisotropic elasticity model [6, 7] for cellular materials by implying geometric nonlinearity, which is built as the constitutive relation between Green’s Lagrangean strain in the tensor and the second Piola–Kirchhoff stress tensor and strain potential formulation. Cellular materials may easily experience large deformations due to large pores-to-volume ratio, since such a deformation on the macroscopic level usually requires smaller deformations of the individual struts constituting the skeleton. The formulation based on micromechanical modeling assumes that essential macroscopic features of mechanical behavior on a macro scale, can be inferred from the deformation response of a representative volume element. Open-cell materials with diverse regular skeleton structures are considered. The initial stiffness tensor components for anisotropic continuum are expressed as fuctions of microstructural parameters, such as skeleton geometric data of representative volume element and skeleton material properties. Since large strains in skeleton structure are characteristic for elasto-plastic behavior, interest is focused on the large displacement and small strain cases. Examples involving numerical tests on cellular materials under homogenoeous strain, relevant to simple shearing and to uniaxial or biaxial loading in the tensile and compressive range, are considered.