Elastoplastic Modelling of Cyclic Shear Deformation of Amorphous Solids

We develop an energy-landscape based elasto-plastic model to understand the behaviour of amorphous solids under uniform and cyclic shear. Amorphous solids are modeled as being composed of mesoscopic sub-volumes, each of which may occupy states - termed mesostates – drawn from a specified distribution. The energies of the mesostates under stress free conditions determine their stability range with respect to applied strain, and their plastic strain, at which they are stress free, forms an important additional property. Under applied global strain, mesostates that reach their stability limits transition to other permissible mesostates. Barring such transitions, which encompass plastic deformations that the solid may undergo, mesostates are treated as exhibiting linear elastic behavior, and the interactions between mesoscopic blocks are treated using the finite element method. The model reproduces known phenomena under uniform and cyclic shear, such as the brittle-to-ductile crossover with annealing and the Bauschinger effect for uniform shear, qualitative features of the yielding diagram under cyclic shear including the change in yielding behaviour with the degree of annealing, across a `threshold level’, and dynamic phenomena such as the divergence of failure times on approach to the yield point and the non-monotonic evolution of the local yield rate. In addition to these results, we discuss the dependence of the observed behaviour on model choices, and open questions highlighted by our work.

💡 Research Summary

In this work the authors introduce a novel elastoplastic model (EPM) for amorphous solids that is grounded in an explicit energy‑landscape description of mesoscopic regions (“mesoblocks”). Each mesoblock can occupy one of many “mesostates”, each characterized by a stress‑free plastic strain γ₀ and an inherent energy minimum E₀. The elastic energy of a block in a given mesostate is taken to be a simple quadratic form, E = E₀ + (μ/2)(γ‑γ₀)², where μ is the shear modulus of the block. Stability of a mesostate is defined by a finite strain interval γ ∈