Reproduce “A deep learning energy-based method for classical elastoplasticity” on OpenResearch

About this paper

Junyan He, Diab Abueidda, Rashid Abu Al-Rub, Seid Koric, Iwona Jasiuk

Researchers from the University of Illinois at Urbana-Champaign and Khalifa University extended the Deep Energy Method (DEM) to solve classical elastoplasticity problems by redefining its loss function and integrating classical plasticity algorithms. The proposed framework accurately modeled path-dependent stress-strain responses and handled material heterogeneity, outperforming the Deep Collocation Method (DCM) by over 20 times in speed and with higher accuracy. Notably, a DEM model trained on a coarse mesh could infer high-resolution solutions on meshes 40 times finer in approximately half the total time required by FEM for the same fine mesh.

Key insights

• Energy-based physics-informed neural networks can model complex, path-dependent material behaviors like elastoplasticity through an adapted free energy functional.
• The combination of a neural network for displacement approximation with classical radial return for plastic updates ensures physical consistency and accuracy.
• Deep Energy Method (DEM) outperforms Deep Collocation Method (DCM) in terms of accuracy, computational time (20x faster), and memory efficiency for elastoplastic problems.
• A DEM model trained on a coarser mesh can generalize and infer solutions with high accuracy on much finer meshes, enabling efficient high-resolution simulations.

Summary by alphaXiv.