The Nonlinear Elastic Behavior of Open-Cell Foams

A constitutive model for the nonlinear elastic behavior of isotropic low-density opencell foams with three-dimensional structure is formulated in terms of a strain energy function. The theory is based on micromechanical analysis of an idealized tetrahedral unit cell of arbitrary orientation that contains four half-struts joining at equal angles. The force-displacement relations for each strut are expressed by compliances for bending and stretching that do not depend on the magnitude of applied force. Contributions to the strain energy from large deformation effects are assumed to depend on strut reorientation and stretching, and are determined by analyzing a pin-jointed structure. The analysis is considered to be valid for finite strains below the onset of yielding associated with strut buckling.