Geometric prior of multi-resolution yielding manifolds and the local closest point projection for nearly non-smooth plasticity

Elastoplasticity models often introduce a scalar-valued yield function to implicitly represent the boundary between elastic and plastic material states. This paper introduces new alternative where envelope is represented by manifold of which topology geometry are learned from set data points in parametric space (e.g. principal stress space, ?-plane). Here, deep geometric learning enables us reconstruct highly complex breaking it down into multiple coordinate charts. The global atlas that consists these charts return allows surface via overlapping patches, each with specific local parametrization. setup provides several advantages over classical implicit representation approach. For instance, availability an integration algorithm trial may project directly on patch hence circumvent issues related non-smoothness lack convexity surfaces. Meanwhile, approach also predict hardening/softening locally even without complete knowledge surface. Comparisons non-smooth plasticity anisotropic cam-clay model provided demonstrate capacity for precise feasibility implementation algorithm.