A constitutive model for two-dimensional nonlinear elastic foams

Abstract

A constitutive theory that describes the nonlinear elastic behavior of two-dimensional foams is formulated in terms of a strain energy function. The analytical theory is based upon micromechanical analysis of an idealized cellular material with regular hexagonal structure. The mechanics of solid films that represent the elastic cell walls is represented by a stretching compliance M and a bending compliance N, which express force-displacement relations and are assumed to be independent of strain. Terms in the strain energy that represent nonlinear response are determined by analysing finite deformations of a foam with pin-jointed structure. These terms stem from geometrical effects due to large distortion of the cells. The assumption that essential large-deformation effects are captured through neglect of film bending is supported by numerical simulations. The macroscopic mechanical response of the foam can show strong variation with strain when the dominant mechanism for microscopic distortion of the films changes from bending to stretching with increasing strain. The micromechanical basis for this model provides an evaluation of the forces in each film, which allows an assessment of critical conditions for the mechanical failure of foams. For conditions representative of a typical compression test, this theory predicts that films in the cellular material will first buckle near the load-bearing ends of the specimen.