Data Driven Finite Element Method: Theory and Applications

Abstract: A data driven finite element method (DDFEM) that accounts for more than two material state variables has been presented in this work. DDFEM framework is motivated from (1,2) and can account for multiple state variables, viz. stresses, strains, strain rates, failure stress, material degradation, and anisotropy which has not been used before. DDFEM is implemented in the context of linear elements of a nonlinear elastic solid. The presented framework can be used for variety of applications by directly using experimental data. This has been demonstrated by using the DDFEM framework to predict deformation, degradation and failure in diverse applications including nanomaterials and biomaterials for the first time. DDFEM capability of predicting unknown and unstructured dataset has also been shown by using Delaunay triangulation strategy for scattered data having no structure or order. The framework is able to capture the strain rate dependent deformation, material anisotropy, material degradation, and failure which has not been presented in the past. The predicted results show a very good agreement between data set taken from literature and DDFEM predictions without requiring to formulate complex constitutive models and avoiding tedious material parameter identification.