Mixed FEM for flexoelectric effect analyses in a viscoelastic material

Abstract The correspondence principle is applied to solve general 2-d electro-viscoelastic problems with flexoelectric effect. Two competitive characteristics of strengthening and softening of micro-/nano-sized structures are considered for some advanced materials. Due to higher order derivatives of the primary solution parameters in the governing equations, the standard C0 continuous finite element method cannot be applied directly to analyze this problem. The mixed FEM (MFEM) is developed here to this end. The C0 continuous approximation is applied independently for displacement and strains; kinematic constraints between them are satisfied by a collocation method. The Stehfest’s inversion method is applied to obtain the final time-dependent solutions. Two example problems are presented to demonstrate the successful implementation of the collocation-MFEM, the first involves a cantilever beam for which analytical solution is available for verification; and the second, is a rectangular domain with an edge crack.