Efficient and robust nonlinear model for smart materials with application to composite magnetostrictive plates

摘要

This paper presents a computationally efficient and robust nonlinear modeling framework for smart materials. The framework describes a smart material system through a new 3D inversion scheme for coupled nonlinear constitutive equations which can be integrated with the variational form of governing equations. Building on the Newton technique, the inversion scheme can be applied to any nonlinear smart material with a differentiable direct constitutive model. To further improve computational efficiency, the inversion scheme is integrated with a reduced dimensional (2D) model for smart composite structures. The resulting coupled 2D framework is applied to an aluminum-Galfenol composite plate that operates in actuation mode, and is solved using multiphysics finite element software. Major and minor magnetostriction curves are obtained for the actuator displacements at the tip of the Galfenol element by applying unbiased and biased magnetic fields. A significant advantage in numerical convergence and computational time, an almost six-time speedup for a dynamic simulation case, is demonstrated via comparison with an existing approach for magnetostrictive material modeling. The framework is suitable for fast design and optimization of nonlinear smart material structures.