On the design of mechanical heterogeneous specimens using multilevel topology optimization

Abstract

Sheet metal forming processes are of upmost importance in many industrial applications. Their virtualization has been addressed by numerical simulation software. However, realistic results can only be obtained when an accurate reproduction of the material behavior is achieved. This is where material characterization and model calibration procedures play a key role. The conventional procedure is time-consuming and expensive and needs to be overcome. To improve the efficiency of this process, heterogeneous mechanical tests have been proposed. Due to their rich mechanical fields and the emergence of full-field measurement techniques, a high diversity of valuable information about the material behavior can be extracted with a single test. A systematic design approach has not been found yet since the majority of the newly proposed mechanical tests have been developed based on the empirical knowledge or trial and error. However, this work aims at filling this gap by proposing a new methodology to design optimal mechanical tests. A bi-level design optimization problem is established to find out the optimal geometry for the specimen that presents the highest heterogeneity of stress states. The specimen design process gathers the design by topology optimization and the compliant mechanisms’ theory, which are responsible for the highly heterogeneous displacement fields. The test setup is also optimized, considering the use of universal testing machines. Several numerical designs are analyzed based on their ability to induce several stress states and their feasibility. The most suitable test configuration is chosen and analyzed with Digital Image Correlation (DIC) using synthetic images. An evaluation of the test in an elastoplasticity framework is also performed. The effectiveness of the methodology in designing tests with valuable information for the material characterization process is validated.