A New Method for Improving Inverse Finite Element Method Material Characterization for the Mooney–Rivlin Material Model through Constrained Optimization

Abstract

The inverse finite element method is a technique that can be used for material model parameter characterization. The literature shows that this approach may get caught in the local minima of the design space. These local minimum solutions often fit the material test data with small errors and are often mistaken for the optimal solution. The problem with these sub-optimal solutions becomes apparent when applied to different loading conditions where significant errors can be witnessed. The research of this paper presents a new method that resolves this issue for Mooney–Rivlin and builds on a previous paper that used flat planes, referred to as hyperplanes, to map the error functions, isolating the unique optimal solution. The new method alternatively uses a constrained optimization approach, utilizing equality constraints to evaluate the error functions. As a result, the design space’s curvature is taken into account, which significantly reduces the amount of variation between predicted parameters from a maximum of 1.934% in the previous paper down to 0.1882% in the results presented here. The results of this study demonstrate that the new method not only isolates the unique optimal solution but also drastically reduces the variation in the predicted parameters. The paper concludes that the presented new characterization method significantly contributes to the existing literature.