Knut Andreas Meyer | Searcharxiv

arXiv2026

Machine Learning-Accelerated Time Integration of Plasticity Models

Finite element simulations of structures with nonlinear material behavior require advanced material models to provide accurate predictions. However, the computational costs of these models can be high, as they solve coupled differential algebraic equations at each integration point, in each equilibrium iteration, in every time step. In this study, we propose a machine learning-based framework to accelerate these computations by explicitly calculating the state variable updates with neural networks, enabling large time steps with low computational costs. The neural networks operate on invariants, and the necessary and sufficient evolution directions are determined analytically based on the training data. Furthermore, the proposed framework enforces exact fulfillment of the plastic consistency condition. To evaluate the proposed framework, a prototype model with the von Mises yield criterion and nonlinear kinematic hardening is chosen. Only 10 cycles of multiaxial proportional loading are used to generate the training data. After evaluating the proposed framework in material point simulations, we incorporate it into finite element simulations to evaluate its accuracy and computational efficiency in a boundary value problem. The results from both material point and finite element simulations show a very promising numerical performance of the neural network-based time integrator. It provides very good accuracy and numerical stability, as well as a noticeable gain in computational time for a single strain increment per load segment.

cs.CE↗

arXiv2026

A Regularized Ensemble Kalman Filter for Stochastic Phase Field Models of Brittle Fracture

The phase-field approach to brittle fracture provides a continuum framework for modeling crack initiation and propagation without explicit representation of discrete crack surfaces, provided the spatial discretization is fine enough to resolve the regularization length scale. However, uncertain local material parameters due to material defects can strongly influence simulation results, such as crack paths and remaining structural strength. At the same time, the ability to continuously monitor structures using sensors allows complementing modeling predictions with, e.g., displacement measurements. In this contribution, we connect these two complementary sources of information and present a Bayesian inference procedure that allows updating the current model state with incoming sensor data. We construct a Bayesian prior for the model state (both displacements and phase-field) and employ an ensemble Kalman filter (EnKF) to perform the update. In the EnKF, the update is computed by performing a Kalman shift on each ensemble member. Since the standard EnKF may produce assimilated states that violate common modeling assumptions, we present a phase field-based regularization technique as a proximal step correction toward model-consistent updates. 1D and 2D numerical examples demonstrate the performance and accuracy of the proposed method and show that the updated state matches the ground truth reasonably well. Unlike traditional Bayesian inversion techniques, which have already been applied to brittle fracture, we infer not the model parameters but the model state, i.e., the displacement field and the phase-field. Although only displacements are observed, the strong correlation between both fields also allows inference of the posterior phase-field.

cs.CE↗