Multiscale Modeling of Plasticity in Amorphous Solids: Machine Learning Constitutive Response*

We aim to develop multiscale models of plastic flow and failure processes in amorphous solids, materials that exhibit a complete lack of crystalline order. We take metallic glass as an exemplar material and apply molecular dynamics simulation to examine the physics of deformation. We elate the evolution of the glass structure under shear to the “effective temperature” that characterizes the degree of glass disorder in building and seek to validate a constitutive model of plastic response. The constitutive model has been incorporated into a high-fidelity viscoplastic finite differencing scheme that adapts techniques originally developed for solving the Navier-Stokes equation. A novel machine learning algorithm then utilizes the atomistic data to guide the parameterization of the constitutive model so as to optimize the agreement between atomistic and continuum representations of the material. We see that a high level of agreement can be reached between the molecular dynamics data and the continuum result. In doing so we have begun to ask some fundamental questions about the coarse graining necessary to provide a rigorous connection between atomistic and continuum models, and the relation of this coarse graining to the concept of “effective temperature.”