Mesoscopic Modeling of the Non-Linear Deformation in Amorphous Solids

Results of Monte Carlo simulations of plastic deformation and associated structural relaxations in amorphous solids are presented. The model is based on the notion of local inelastic transformations (LITs) of pure shear character which are identified as the elemental events of macroscopic plasticity. Structurally specific details of plasticity in amorphous materials are treated as internal parameters of the shear transformations. Then, the global elastic interactions of the transformations are accounted for faithfully, giving rise to a remarkably simple, yet non-trivial model. Various aspects of inelasticity in amorphous solids are reproduced correctly, including apparent distributions of structural relaxations, strain softening, strain rate, pressure, and temperature dependences of the plastic response at constant strain rate, creep, and cyclic loading conditions. It is argued that much of the distributed kinetics of structural relaxations and plasticity can be attributed to the disorder related misfit stresses prevalent in the amorphous solids. An attempt is made at incorporating the internal stress variability into a constitutive equation of rate-dependent plasticity in amorphous solids.