Visco-hyperelastic constitutive law for modeling of foam’s behavior

This paper proposes a new visco-hyperelastic constitutive law for modeling the finite-deformation strain rate-dependent behavior of foams as compressible elastomers. The proposed model is based on a phenomenological Zener model, which consists of a hyperelastic equilibrium spring and a Maxwell element parallel to it. The hyperelastic equilibrium spring describes the steady state response. The Maxwell element, which captures the rate-dependency behavior, consists of a nonlinear viscous damper connected in series to a hyperelastic intermediate spring. The nonlinear damper controls the rate-dependency of the Maxwell element. Some strain energy potential functions are proposed for the two hyperelastic springs. compressibility effect in strain energy is described by entering the third invariant of deformation gradient tensor into strain energy functions. A history integral method has been used to develop a constitutive equation for modeling the behavior of the foams. The applied history integral method is based on the Kaye–BKZ theory. The material constant parameters, appeared in the formulation, have been determined with the aid of available uniaxial tensile experimental tests for a specific material.