The aim of this paper is to improve the shape of specimens for biaxial experiments with respect to optimal stress states, characterized by the stress triaxiality. Gradient-based optimization strategies are used to achieve this goal. Thus, it is crucial to know how the stress state changes if the geometric shape of the specimen is varied. The design sensitivity analysis (DSA) of the stress triaxiality is performed using a variational approach based on an enhanced kinematic concept that offers a rigorous separation of structural and physical quantities. In the present case of elastoplastic material behavior, the deformation history has to be taken into account for the structural analysis as well as for the determination of response sensitivities. The presented method is flexible in terms of the choice of design variables. In a first step, the approach is used to identify material parameters. Thus, material parameters are chosen as design variables. Subsequently, the design parameters are chosen as geometric quantities so as to optimize the specimen shape with the aim to obtain a preferably homogeneous stress triaxiality distribution in the relevant cross section of the specimen.

本文的目的是针对最佳应力状态（以应力三轴性为特征）改善用于双轴实验的试样的形状。基于梯度的优化策略用于实现此目标。因此，至关重要的是要知道如果试样的几何形状发生变化，应力状态将如何变化。应力三轴性的设计敏感性分析（DSA）使用基于增强运动学概念的变分方法进行，该方法提供了结构和物理量的严格分离。在当前弹塑性材料行为的情况下，必须将变形历史考虑在内，以便进行结构分析以及确定响应灵敏度。所提出的方法在设计变量的选择方面是灵活的。第一步，该方法用于识别材料参数。因此，选择材料参数作为设计变量。随后，将设计参数选择为几何量，以便优化样品形状，以在样品的相关横截面中获得优选均匀的应力三轴性分布。