Parameter identifiability analysis: Mitigating the non-uniqueness issue in the inverse identification of an anisotropic yield function

Abstract

A large number of conventional mechanical tests are required to calibrate advanced anisotropic yield functions. A well-designed non-conventional mechanical test generating information-rich inhomogeneous strain fields enables to reduce the experimental effort via inverse identification methods. Gradient-based inverse identification methods have repeatedly been reported to yield non-unique solutions for advanced anisotropic yield functions. Although the generic design of non-conventional mechanical tests progressively improves by maximizing the information content using indicators for describing the inhomogeneity of the strain field, it remains questionable whether the uniqueness problem can be avoided for advanced anisotropic yield functions. The latter problem is studied in this paper through the concept of parameter identifiability. A general identifiability analysis framework is proposed enabling to efficiently quantify the parameters sensitivity strength as well as parameter interactions. The feasibility of the framework is assessed through the inverse identification of the Yld2000-2d yield function using a virtual experiment, i.e. a complex notched tensile specimen designed via shape optimization to maximize the strain field inhomogeneity. The advanced synthetic experimentation approach is crucial to avoid errors due to the choice of an inappropriate constitutive model, yet allows accounting for the intrinsic Digital Image Correlation (DIC) filter. For the non-conventional mechanical test under investigation, it is shown that the individual parameter sensitivity and parameter interaction jointly determine the inverse identification quality. It is observed that the detrimental effect of low individual parameter sensitivity on the identification quality can be mitigated by proper parameter subset selection. In addition, it is shown that the orientation of the principal material axes enables to significantly improve the identifiability of the sought model parameters of the anisotropic yield function. The virtual experiment shows that the studied notched tensile test with a tensile direction of 45° from the rolling direction enables to reliably identify all anisotropy parameters of the Yld2000-2d yield function. Finally, actual experiments confirm the importance of identifiability analysis and material orientation for the inverse identification of an anisotropic yield function, yet further research is required to arrive at a sufficiently accurate inverse identification quality.