Accelerating Nonlinear Finite Element Analysis via Residual-Aware Neural Network Constitutive Models

Nonlinear finite element analysis (FEA) relies heavily on iterative methods such as the Newton-Raphson algorithm, with computational cost primarily driven by the repeated solution of large linear systems (global stage) and the evaluation of nonlinear constitutive laws (local stage). This work proposes a neural networkbased surrogate to accelerate the local stage by approximating explicit constitutive models. A compact feed-forward neural network is trained on synthetic data generated from standard material laws and embedded into the commercial solver Simcenter TM Samcef ® , replacing the local integration of nonlinear equations. To ensure accuracy and robustness, a residual-based safeguard is introduced to restore the original physics-based model when neural network predictions are insufficient. To further explore the benefits of the proposed approach in reducing overall simulation cost, the method is also applied within a reduced-order modeling framework. While such techniques effectively reduce the cost of solving large linear systems, the evaluation of nonlinear terms often remains a dominant bottleneck. The surrogate is therefore also assessed using the nonlinear model reduction method available in Samcef, namely the LATIN-PGD approach, although a detailed study of this method is not the focus of this paper. Beyond simplified test cases, the method is implemented and validated in full-scale, industrially relevant simulations involving elasto-viscoplastic materials. Results from academic and industrial-scale applications, including a high-pressure turbine blade, demonstrate that the proposed approach significantly reduces computation time while preserving solution accuracy. These findings highlight the potential of combining data-driven surrogates with residual-controlled correction to enhance the efficiency and scalability of nonlinear FEA workflows under realistic conditions.