A polyconvex anisotropic free energy function for electro- and magneto-rheological elastomers. (October 2016) - Itskov, Mikhail; Khiêm, Vu Ngoc
Polyconvexity is an important mathematical condition imposed on a strain energy function. In particular, it is sufficient for the ellipticity of the constitutive equation and for the material stability and becomes especially crucial in the context of nonlinear elasticity. In combination with another condition referred to as coercivity, polyconvexity ensures existence of the global minimizer of the total elastic energy which implies a solution of a boundary value problem. While a great variety of polyconvex energies are known for isotropic and have recently been proposed for anisotropic elastic solids, there are, to the best of our knowledge, no results on polyconvexity for electro- and magneto-elastic materials. In the present paper, we extend the notion of polyconvexity to the coupled electro- and magneto-elastic response and formulate polyconvex free energy functions for electro- and magneto-sensitive elastomers. In analogy to the purely elastic response, these free energy functions will ensure the positive features of the constitutive equations mentioned above, although a strict mathematical proof of this fact should be supplied later. The proposed model is able to describe the electro- and magnetostriction and demonstrates good agreement with the corresponding experimental data.