Скачать или смотреть Johns Hopkins seminar on geometric learning for computation plasticity with level set hardening

Geometric learning is a new field of machine learning that involves data of non-Euclidean space, such as on graphs and manifold. This presentation focuses on a newly derived framework that employs geometric learning to build interpretable macroscopic surrogate elasto-plasticity models inferred from sub-scale direction numerical simulations on granular assembles and polycrystalline materials. A graph convolutional neural network is used to deduce low-dimensional descriptors that encodes the evolutional of particle topology under path-dependent deformation and are used to replace internal variables. To circumvent the lack of interpretability of the classical black-box neural network, we introduce a higher-order supervised machine learning technique that generates multiple components of elasto-plastic models such as elasticity functional, yield function, hardening mechanisms, and plastic flow with controls on convexity and smoothness. Then, we recast the plasticity model as a Hamilton-Jacobi problem where yield function is not governed by a pre-defined hardening mechanism but may evolve in any arbitrary rules governed by the relationship between the low-dimensional descriptor interred from geometric learning and the homogenized constitutive responses. Numerical experiments reveal that the new geometric learning paradigm is capable of replicating complex elastoplastic behaviors in forward predictions.

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