Shape optimization of the X0‐specimen for biaxial experiments

Abstract

The mechanical damage and fracture behavior of ductile sheet metals strongly depend on the stress state and intensity. Thus, for adequate characterization of the material behavior, it is crucial to have specimens that cover different and preferably distinct stress states, especially in the inelastic domain. In this paper, the geometry of the X0‐specimen is optimized to achieve a distinct stress triaxiality distribution in the region of damage and fracture occurrence, depending on two different load cases in a biaxial testing environment. The shape optimization is gradient based and the gradients of the objective and constraint functions are computed analytically by means of variational principles. The resulting geometries show improvements in terms of the intensity of the stress state numerically as well as experimentally.