On the Design of a Heterogeneous Mechanical Test Using a Nonlinear Topology Optimization Approach

Abstract

Numerical simulation is nowadays increasingly used to avoid the costs and time associated with the development and optimization of metal forming processes. However, the accuracy of the numerical results is still an issue. Material behavior and characteristics are required by simulation software, and these are usually obtained by performing a considerable number of classical mechanical tests. To improve this procedure, heterogeneous tests have been used instead. More and richer information can be obtained with a single test due to the heterogeneous displacement and strain fields that are induced. This work aims at designing a heterogeneous mechanical test using a topology-based optimization methodology. Highly heterogeneous displacement fields are induced on the sheet specimen by applying an extended version of the theory of compliant mechanisms. To account for large deformations, a geometrically nonlinear finite element analysis is proposed together with a consistent topology optimization approach. The material behavior is considered linear elastic. The performance of the obtained solutions is evaluated considering the heterogeneity of stress states using a mechanical indicator. Validation of the developed methodology is performed and an optimal mechanical test is obtained presenting a high diversity of stress states.