Bridging data-driven vCANN-based Contitutive Modeling and Finite-Element Simulation for Viscoelastic Materials

Kurzfassung

Viscoelastic Constitutive Artificial Neural Networks (vCANNs) offer a flexible representation of historydependent material behavior, with potential relevance to the recovery of thermoplastic shape-memory polymer mandrels in aerospace manufacturing. Their practical use raises a fundamental question: can a data-driven, history-dependent constitutive model be embedded in a finite-element (FE) solver while retaining the convergence properties and numerical robustness of a classical formulation? We couple a trained vCANN to FEniCSx through an external operator that supplies stress and a finite-difference-consistent tangent at each quadrature point, without a machine-learning runtime in the solver hot path. Correct coupling relies on the consistent tangent and on separating committed and trial states to preserve material history during Newton and linesearch evaluations. The implementation agrees with the reference constitutive driver to machine precision and achieves quadratic Newton convergence from 1% to 25% nominal strain, and, in a matched comparison from rest at 1% strain, reduces the Newton iteration count from 13 to 5 relative to a frozen Neo-Hookean tangent. The model-agnostic interface provides a reusable foundation for embedding stateful learned constitutive models in implicit FE solvers, while the open-source software stack offers a transparent basis for reproducible research and future industrial transfer.