Numerical framework for anisotropic flexible piezoelectrics with large deformation

Flexible piezoelectric materials with high stretchability have been realized in industrialization production. Among them, piezoelectric fiber composites made of elastomers and piezoelectric polymers have gained widespread attentions in smart applications. In general, piezoelectric fiber composites can be considered as anisotropic materials. However, most existing piezoelectric constitutive models, especially those integrated into commercial software, only account for small deformation conditions, which are not suitable for anisotropic flexible piezoelectrics. In the present work, a novel model for anisotropic flexible piezoelectric material is established based on the anisotropic Neo-Hookean material model and electromechanical theory. The finite element framework is implemented in the commercial finite element software ABAQUS via a user element subroutine, with a monolithic algorithm procedure employed to solve the nonlinear governing equations. To validate the accuracy of finite element implementation, analytical solutions for equibiaxial stretching of transversely isotropic piezoelectric have been compared with simulated results. Furthermore, the influences of anisotropy level on electromechanical response are also discussed. Subsequently, numerical simulations of bending actuators and sensors further demonstrate the robustness of the developed elements. The obtained results show that the anisotropy direction and level have both favorable and unfavorable influences on structure performances, which could provide a reference for the design of anisotropic flexible piezoelectric structures.