Summary
Materials like metals and foams change shape when pushed or pulled, and scientists use computer models to predict how they will behave under complex forces. Existing models can be slow to train and may give different results depending on how the input is divided into small steps. The authors developed a new model called Constitutive State Space (CSS) that breaks down the problem in a way that works better with the physics and computers. Their model is faster to train, more accurate, and less sensitive to how the input data is handled. This approach could help engineers better predict material behavior in real-world applications.
plasticityconstitutive modelstrain pathstate-space dynamicsnonlinear recurrent neural networkslatent statestrain incrementstrain-stress pairsparallel trainingmaterial hardening
Authors
Rui Barreira, Taylan Soydan, Francesco Scipione, Miguel A. Bessa, Dirk Mohr
Abstract
Data-driven constitutive models for path-dependent plasticity are commonly formulated using nonlinear recurrent neural networks, whose sequential state evolution limits parallel training and whose predictions may depend on the discretization of the applied strain path. We introduce a Constitutive State Space (CSS) model that reformulates structured state-space dynamics as an incremental constitutive operator. The strain increment is decomposed into magnitude and direction: the loading direction drives the latent state-space system, while the increment magnitude enters the zero-order-hold discretization of its continuous-time linear recurrence. This mechanics-tailored construction guarantees stationarity under zero increments, strongly reduces sensitivity to strain-path resolution, and retains the parallel-scan structure of S5 for efficient training on long constitutive histories. The CSS and Minimal State Cell (MSC) architectures are compared for four multiaxial path-dependent material models including isotropic J2 plasticity, pressure-sensitive foam plasticity, and combined isotropic-kinematic hardening. CSS matches or exceeds the prediction accuracy of the MSC, including one order of magnitude lower validation losses for the plastically incompressible materials. Importantly, CSS maintains low errors across large changes in strain-path discretization, whereas the MSC error increases substantially when evaluated at coarser resolutions than used for training. CSS trains substantially faster and requires fewer strain-stress pairs to attain comparable or better accuracy. Analysis of the learned state further reveals latent structure consistent with the dimensionality of the underlying physical constitutive models. These results establish mechanics-tailored structured state-space dynamics as a computational framework for efficient and discretization-robust data-driven constitutive modeling.