A mathematically well-defined criterion proposed by Demmerle and Boehler is modified in this paper, in order to realize an
objective evaluation of the stress state in the test section of biaxial tensile cruciform specimens. This criterion is based on the standard deviations of the values of the stresses in the test section, taking the homogeneity of the stress fields, the compatibility of the obtained stresses with the nominal stresses and possible stress concentrations into consideration. By using this criterion, an
optimization procedure for design of cruciform specimens is developed in terms of the
finite element analysis. This procedure is used to realize the optimization of the cruciform specimens for isotropic materials such as Shape Memory Alloys. The performances of the optimized specimen are by far better than those of the specimen by Kelly. In particular, the stress and displacement fields in the central test section exhibit an excellent homogeneity and the maximum Von Mises stress corresponds to the central part of the test section. Thus, the experiment data obtained with such an optimized specimen are realistic and can be employed for the identification of constitutive laws.The performance of the obtained optimized specimen design is also examined for anisotropic materials in off-axes tests and a good result is obtained. Furthermore, after integrating a proposed three-dimensional constitutive model into finite element software ABAQUS, the transformation behavior of CuAlNi under biaxial loading is simulated by using the optimized specimen.