Geometrical non-linear finite element analysis of piezoelectric materials based on ABAQUS

The nonlinear piezoelectric finite element method, which includes geometrical nonlinearity and material nonlinearity, has gained more and more popularity and been studied by more and more researchers. A large deformation finite element analysis is presented for piezoelectric materials and structures in this paper. Green-Lagrenge strains for large deformation are incorporated into the linear piezoelectric equations. The formulations of the secant stiffness matrix and tangent stiffness matrix are presented, and the Newton-Raphson method has been used to solve the nonlinear equations. Based on the finite element package ABAQUS, eight-node plane geometrical nonlinear piezoelectric element is developed. The results using this user-developed element are found the same as those based on the piezoelectric element embedded in ABAQUS for geometrical nonlinear analysis. It indicates that ABAQUS can be used as a convenient platform for developing nonlinear piezoelectric finite element so as to study various nonlinear piezoelectric problems.