Finite element solver for data-driven finite strain elasticity

A nominal finite element solver is proposed for data-driven strain elasticity. It bypasses the need a constitutive model by considering database of deformation gradient/first Piola–Kirchhoff stress tensors pairs. The boundary value problem reformulated as constrained minimization distance between (i) mechanical states, i.e. strain–stress, in body and (ii) material states coming from database. corresponding constraints are two types: kinematical, displacement–strain relation, mechanical, conservation linear angular momenta. uses alternated minimization: determined local search using an efficient tree-based nearest neighbor algorithm, result standard addressed with augmented Lagrangian approach. performance demonstrated means 2D sanity check examples: solution converges to classical when increasingly approximates model. In addition, we demonstrate that balance momentum, which was classically not taken into account previous studies, must be enforced constraint ensure convergence method.