The anti-dogbone: Evaluating and designing optimal tensile specimens for deep learning of constitutive relations

Traditional tensile testing with “dogbone”-shaped specimen (ASTM E8, first standardized in 1924) strives for strain uniformity. Multiple tests with such samples help fit simple constitutive relation parameters on real materials. With the development of deep learning, the concept of employing entirely data-driven constitutive relations to capture more intricate material behavior has arisen. Nevertheless, these methods demand experimental data that are distributed throughout the complete stress–strain configuration space to effectively train the machine learning models. This is particularly crucial for mechanisms like hardening, which are time-dependent and sensitive to loading history. In this work, we investigate the potential to efficiently gather a wider range of experimental data points in the stress–strain configuration space using non-uniform samples and displacement-field mapping, leveraging advancements in computer vision techniques. We developed a metric to quantify stress state diversity in 2D tensile experiments and used it to optimize the shape of the sheet sample. The goal was to increase stress–strain diversity obtained within a single test, particularly in the linear elastic regime. Additional geometric constraints can be introduced on the design features, considering factors such as size and curvature to adapt to the microstructural characteristics of the sample material.