A new variational framework for large strain piezoelectric hyperelastic materials

Abstract

In this paper, a novel nonlinear variational formulation is presented for the numerical modelling of piezo-hyperelastic materials. Following energy principles, a new family of anisotropic extended internal energy density functionals is introduced, dependent upon the deformation gradient tensor and the Lagrangian electric displacement field vector. The requirement to obtain solutions to well defined boundary value problems leads to the definition of energy density functionals borrowing concepts from polyconvex elasticity. Material characterisation of the constitutive models is then carried out by means of experimental matching in the linearised regime (i.e. small strains and small electric field). The resulting variational formulation is discretised in space with the help of the Finite Element Method, where the resulting system of nonlinear algebraic equations is solved via the Newton-Raphson method after consistent linearisation. Finally, a series of numerical examples are presented in order to assess the capabilities of the new formulation.