A modified finite difference sensitivity analysis method allowing remeshing in large strain path-dependent problems

Finite difference sensitivity analysis is simple and general yet usually inefficient and inaccurate compared to the analytical sensitivity approach. Although its high computational cost is not an issue in iteratively solved problems, its inaccuracies are critical in path-dependent problems when remeshing is required. In this case, the errors caused by parametric inversion and interpolation in variables transfer to the new mesh can be as large as the gradient components. This paper presents an efficient modified finite difference approach that allows remeshing either in path-independent or path-dependent problems, not being affected by the aforementioned errors. The strategy to cope with remeshing is extensive to the semi-analytical method which, for non-linear analyses, is shown to be a particular case of the proposed finite difference sensitivity approach. With this implementation, the finite difference, the semi-analytical and the analytical sensitivity methods all have comparable computational costs. The perturbation of unstructured meshes is performed with an inverse power Laplacian smoothing. The low cost and the accuracy of the sensitivity fields obtained after remeshing are shown in two examples, considering shape and constitutive design variables