Accelerating nonlinear finite element analysis via residual-aware neural network constitutive models

Abstract

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 network-based 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.