Geometric deep learning for computational mechanics Part II: Graph embedding for interpretable multiscale plasticity
This work addresses interpretability and validation issues in computational mechanics for researchers and engineers, representing an incremental advancement by applying existing geometric learning methods to a specific domain problem.
The paper tackles the challenge of interpreting and validating internal variables in classical plasticity models by using geometric deep learning on graph data to embed time-history information into a low-dimensional space, enabling prediction of plastic deformation evolution and analysis of topological features.
The history-dependent behaviors of classical plasticity models are often driven by internal variables evolved according to phenomenological laws. The difficulty to interpret how these internal variables represent a history of deformation, the lack of direct measurement of these internal variables for calibration and validation, and the weak physical underpinning of those phenomenological laws have long been criticized as barriers to creating realistic models. In this work, geometric machine learning on graph data (e.g. finite element solutions) is used as a means to establish a connection between nonlinear dimensional reduction techniques and plasticity models. Geometric learning-based encoding on graphs allows the embedding of rich time-history data onto a low-dimensional Euclidean space such that the evolution of plastic deformation can be predicted in the embedded feature space. A corresponding decoder can then convert these low-dimensional internal variables back into a weighted graph such that the dominating topological features of plastic deformation can be observed and analyzed.