Geometric deep learning for computational mechanics Part II: Graph embedding for interpretable multiscale plasticity

The composition of a macroscopic plasticity model often requires the following steps. First, there are observations of causality relations deduced by modelers to hypothesize mechanisms that lead to the plastic flow. These causality relations along with constraints inferred from physics and universally accepted principles lead to mathematical equations. For instance, the family of Gurson models employs the observation of void growth to employ the yield surface (Gurson, 1977). Crystal plasticity models relate the plastic flow with slip systems to predict the anisotropic responses of single crystals (Rice, 1971; Uchic et al., 2004; Clayton, 2010; Ma and Sun, 2020; Ma et al., 2021). Granular plasticity models propose theories that relate the fabric of force chains and porosity to the onset of plastic yielding and the resultant plastic flow (Cowin, 1985; Kuhn et al., 2015; Wang and Sun, 2018; Sun et al., 2022). Finally, the mathematical equations are then either used directly in engineering analysis and designs (e.g. the Mohr-Coulomb envelope) or are incorporated into a boundary value problem in which the approximation solution can be obtained from a partial differential equation solver that provides incremental updates of stress-strain relations. However, a subtle but significant limitation of this paradigm is that it imposes the burdens on modelers of being able to describe the mechanisms verbally via terminologies or atomic facts (cf.