Three-dimensional nonlinear open-cell foams with large deformations

In this article, a hyperelastic formulation for light and compliant foams w hich accounts for nonlinear effects at material and kinematic levels is int roduced. This theory is applicable to a large number of 2- and 3-D irregula r open-cell structures. An expression for the strain-energy function is pro posed which includes bending and stretching contributions. Although this de scription allows for irregularity in the structure at local or cell level, it also assumes that the macro structure is homogeneous, i.e. built by repe tition of the same irregular unit cell. This micromechanical formulation ha s explicit correlation with the foam structure, and therefore it preserves in the constitutive relation the symmetries or directional properties of th e corresponding structures, including the cases of re-entrant foams which e xhibit negative Poisson's ratio effects. Due to the introduction of nonline ar kinematics, the evolution of the structure during the loading process an d its effects on the constitutive behavior can be traced, including the cas es where configurational transformations are present leading to non-convex strain-energy functions. Several examples of the stress-strain behavior for arbitrary large homogeneous deformations in a diamond-like structure are p resented. The effect of the structure reorientation on the transition of lo cal deformation mechanisms is clearly shown. The development of texture and anisotropy induced by the deformation process is also demonstrated. Finall y, the role of the deformation mechanisms on the relation between foam stif fness and foam density is analyzed. (C) 2000 Elsevier Science Ltd. All righ ts reserved.