A constitutive model for amorphous solids considering intrinsic entangling of shear and dilatation, with application to studying shear-banding

Abstract

In amorphous solids, shear transformations, as elementary rearrangement events operating in local regions, are intrinsically entangled with dilatation deformation, which results in the physical process of the shear band being complex. To capture such entanglement, we propose a finite-deformation continuum framework for amorphous solids by incorporating nonequilibrium thermodynamics. Within this framework, we develop a constitutive model where the thermodynamic glass is divided into the kinetic and configurational subsystems. In the model, the dilatation is attributed to an athermal expansion of configuration. As a result, the effect of shear transformation on dilatation can be considered by generating plastic cold work to change the freedom degrees of the configurational subsystem. The effect of dilatation on shear transformation can be realized through the enthalpy change of the configurational subsystem that gives rise to physical aging. Based on the proposed model, we discuss the entangling mechanism of shear and dilatation, and predict the shear-banding behaviors of metallic glasses during tensile and compressive deformations at room temperature. We reveal that due to the shear-dilatation entanglement, the elastic deformations significantly influence the evolution of configurational temperature, which plays a pivotal role in controlling the degree of strain softening and the shear-banding mode.