  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.
