Identification of material parameters for thin sheets from single biaxial tensile test using a sequential inverse identification strategy

An inverse analysis methodology to simultaneously identify the parameters of various anisotropic yield criteria together with isotropic work-hardening models of metal sheets is outlined. This identification makes use of results of the cruciform biaxial test, i.e., the evolution of the force during the test, for the two axes of the sample, and the major and minor strain distributions along both axes, at a given moment during the test. Based on a study of the sensitivity of the constitutive parameters to the biaxial tensile test results, the inverse identification consists on a procedure that sequentially minimises the gap between experimental and numerical results. Each step of the sequence uses a distinct cost function according to the type of results to be minimised, using a gradient-based optimisation algorithm, the Levenberg-Marquardt method. The inverse methodology allows for the identification of constitutive parameters of complex constitutive models. This sequential identification strategy is compared to a strategy based on a single cost function, involving all parameters and type of results, which has lower performance.