Open-cell cellular solids: A constitutive equation for hyperelasticity with deformation induced anisotropy

A constitutive theory is developed for an open-cell flexible cellular solid consisting of a network of struts each connecting two vertex points. A hypothesis is proposed that vertex points move affinely in the large-deformation regime, when the struts buckle, and that the force carried by a strut is a function of the longitudinal and rotational change of its vertex-to-vertex vector. The forces consist of one longitudinal force, parallel with the vertex-to-vertex vector of the strut and one transverse force. The overall stress response is initially dominated by the longitudinal force whilst the addition of the transverse force becomes significant at large deformations. The model contains three parameters: longitudinal stiffness, bending stiffness and critical stretch of a strut. These three parameters are calibrated against a simple compression test. The model is then validated against independent experiments in a simple tension, simple shear and a combined shear-compression test on an isotropic flexible polyether urethane foam. Excellent agreement is obtained between the experiments and the model.