Embedding Consistent Recurrent Neural Networks in Finite Element Simulations for Path-Dependent Damage Prediction

Abstract :

Capturing sheet-metal localization physics with a trained surrogate inside a finite element (FEM) solver requires the
surrogate to deliver consistent predictions irrespective of the solver’s strain-increment count, which is difficult to
control in non-linear explicit codes. We address this by re-implementing a trained recurrent neural network (RNN)
damage criterion in Fortran and embed it as a live, increment-by-increment fracture criterion inside an Abaqus/Ex-
plicit user material subroutine (VUMAT), advancing the network state alongside the solver. Two architectures are
compared: a SimpleRNN and the proposed Consistent RNN (ConsRNN), whose transition function renders predic-
tions invariant to the number of strain increments along a fixed deformation path. Both are trained on bilinear strain
paths and evaluated under varying temporal discretizations and nonlinear histories. SimpleRNN predictions drift
as the increment count increases, which disqualifies it for embedding; ConsRNN maintains a stable response, at a
modest accuracy cost relative to SimpleRNN on multilinear paths. Deployed at structural scale, the embedded Con-
sRNN surrogate reproduces the global force–displacement response of a clamped steel plate to within 0.82% of peak
force relative to an established two-parameter fracture criterion. The results establish increment-count consistency
as the decisive property for embedding recurrent surrogates in explicit FEM solvers and demonstrate the first such
deployment at structural scale.