Data-driven Constitutive Modelling of Expanded Polystyrene Foams

Sammanfattning

Expanded polystyrene (EPS) foams are widely used in energy-absorbing applications such as protective equipment and packaging. In helmets, for instance, they must dissipate energy under diverse loading conditions. Conventional constitutive models, typically calibrated on uniaxial compression, fail to capture the combined compression--shear response that dominates oblique impacts, limiting the predictive value of finite element simulations. This thesis investigates a data-driven constitutive model for EPS using the Constitutive Artificial Neural Network (CANN) framework and its inelastic extension (iCANN). Elasticity is represented through a polyconvex energy function, while plasticity is handled with a predictor--corrector formulation and a co-rotated intermediate configuration. Training is performed on artificial datasets as well as foam-like data from a crushable-foam law, with staged optimisation and regularisation to ensure stability and promote sparsity. The model reproduces the ground-truth law when trained on uniaxial data, but generalisation to other loading cases is somewhat limited. Introducing a cube-like yield surface improves agreement on previously unseen biaxial data, though biaxial yield behaviour remains under-predicted in the plastic regime. These findings demonstrate both the promise and current shortcomings of iCANN-based approaches for foam modelling, and point to future work on viscoelastic formulations, training on experimental data, and non-associated flow rules to better capture multiaxial yielding.