Multi-time scale based modeling of piezoelectric materials coupling transient electrical and dynamic fields with finite deformation damage

Abstract

This paper develops a high performance scalable computational model for simulating coupled transient electric and finite deformation dynamic fields with widely discrepant frequencies, governing the behavior of piezoelectric materials in the finite element framework. The nonlinear piezoelectric constitutive laws are formulated in the context of continuum damage models (CDM) at finite deformation. A fully coupled, total Lagrangian finite element formulation is developed for modeling the electric and mechanical fields in a staggered way. To address the computational challenge in modeling piezoelectric devices with large discrepancy in the frequenlightsghtscies of the electrical signal and mechanical vibrations, a wavelet transformation induced multi-time scaling (WATMUS) algorithm is developed. The WATMUS method projects the field with higher frequency onto the lower frequency problem through the use of orthogonal wavelet transformation. No assumption of periodic response is needed in the WATMUS scheme. While being accurate, the WATMUS algorithm significantly enhances the computational efficiency in comparison with single time scale integration methods. The accuracy and efficiency of the WATMUS algorithm are validated through piezoelectric applications.