A multiscale shear-transformation-zone (STZ) model and simulation of plasticity in amorphous solids

Abstract In this work, we have developed a multiscale shear-transformation-zone (STZ) model to simulate inelastic deformations in amorphous materials at macroscale without using phenomenological constitutive modeling. The main novelties of the multiscale method are two: (1) the multiscale method employs an atomistic-based representative sampling cell (RS-cell) that is embedded in every quadrature points of macroscale finite elements, and it generically contains potential shear-transformation-zones. Thus the evolution of RS-cells can naturally allow molecular clusters having irreversible microstructure rearrangements at microscale in response to applied loads, and subsequently translate the effects of the irreversible rearrangements of molecular clusters in each RS-cell to inelastic responses at the continuum scale, i.e. delineating the defect-mediated amorphous plasticity, and (2) the method uses a Parrinello-Rahman molecular mechanics based the Cauchy-Born rule to construct an atomistically-informed constitutive model at continuum level, which is able to quantitatively measure amorphous plasticity behaviors, including plastic flow stress, inelastic hysteresis loops under cyclic loading, and strain localizations at macroscale. By doing so, we have successfully simulated plastic deformation in the Lennard-Jones binary glass (LJBG) at macroscale level. Moreover, we have shown that the multiscale shear-transformation-zone can capture cyclic plasticity and the shear band formations in LJBG material.