Top-down constitutive modelling to capture nanoscale shear localization

Deformation localization as exemplified by earthquakes, landslides, shear banding in solids, and failure of engineering components is of utmost importance. In practice, differentiating the mechanical behavior in such generative narrow bands from the rest part, with difference by orders of magnitude in characteristic size, flow strength, temperature, and shearing rate, is both experimentally and computationally formidable. Here we propose a machine-learning-based constitutive modeling framework to overcome this barrier borne from conventional top-down continuum modelling approach. The model enables us to realize ultra-fine resolutions for deformation in those narrow bands with high efficiency. Taking metallic glasses (MGs) as an example, our model captures well shear localization in BMGs across a broad range of temperatures (0 K to its melting point of ∼1000 K) and strain rates (10−4 to 108/s). We verify through this model the width of shear bands (SBs) in MGs is on the order of 5 to 8 nanometers, which is resulted from a cascade of (intervening) events, from localized shearing to plastic heating, subsequent temperature rise to thermal softening, and accelerated flow rate to strain-rate hardening. Temperature rise in SBs is a resultant of heat flow and plastic dissipation, but strongly depend on thermal conductivity: Low thermal conductivity facilitates strain localization and great temperature rise. It explains the current controversy upon experimentally measured temperature rise ranging from several K to ∼1000 K. Lastly, strain rates within SBs are approximately one to two orders of magnitude higher than externally applied strain rates, and in general shearing in adiabatic SBs is faster than that in isothermal condition.