Smooth hyperelastic potentials for bimodular materials: 3D case

Abstract

A family of one parametric infinitely differentiable hyperelastic potentials for three-dimensional problems of bimodular isotropic materials at infinitesimal strain is constructed, yielding a set of uniform approximations to the discontinuous stepwise elastic modulus adopted in the original one-dimensional bimodular formulation. The introduced potentials enable either analytical solutions or construction of the explicit governing equations for a number of static and dynamic problems. Theorem of convergence to the discontinuous bimodular modulus is proved.