Effects of shear methods on shear strengths and deformation modes of two typical transition metal carbides and their unification

Simple shear and pure shear are two common methods for investigating the mechanical responses of materials using first-principles calculations; however, the stress-strain responses and deformation modes obtained are different. Taking HfC and TaC as examples, we first investigated their mechanical responses under the two methods, then proposed a semiconstrained method that combines the advantages of the two methods and can better describe their mechanical responses. Furthermore, we extended the Mohr-Coulomb relation to unify the shear stresses obtained in different ways, which can explain the enhancement of yield shear strength caused by pressure in terms of the friction between atomic layers.