Application of Variational Principles in the Field of Thermo-piezoelectric Elastomers with Finite Deformation

To apply finite element methods in the numerical calculation of basic equations of finite deformation thermopiezoelectric elastodynamics, it is first necessary that relevant regionwise variational principles and regionwise generalized variational principles are set up. Taking thermodynamic and piezoelectric domino effects in elastomers into account, elastic regionwise variational principles are extended into the field of finite deformation piezoelectric thermoelastomers to establish three-field finite deformation thermopiezoelectric elastodynamic regionwise variational principles, on introducing Lagrangian multipliers and distinguishing them in the finite deformation thermopiezoelectric elastodynamic regionwise variational principles, six-field finite deformation thermopiezoelectric elastodynamic regionwise generalized variational principles are finally obtained.