Fracture mesomechanics of a solid as a nonlinear hierarchically organized system

Any loaded solid is a multiscale nonlinear system consisting of two subsystems: a planar subsystem (surface layers and all kinds of interfaces, including shear bands) and a crystalline one. Self-consistent plastic flow within the two subsystems is realized by nonlinear waves of local structural transformations. Fracture of a solid develops as its structure-phase decomposition in a nonlinear wave of localized plastic flow characterized by a positive Gibbs thermodynamic potential. Introduction Classical fracture mechanics is based on a linear approach and treats fracture as a single-scale process 1. In the last two decades, a multiscale approach to description of fracture has been intensively developed 2. In so doing, the main challenge lies in self-consistent description covering the contiguous scales: pico–nano, nano–micro, and micro–macro, and this comes to the scope of mesomechanics 3. Physical mesomechanics uses a unified multiscale approach to describe plastic deformation and fracture of solids as nonlinear hierarchically organized systems 4, 5. The approach rests on the concept of structural scales of deformation and nonequilibrium thermodynamics of structural or structural phase transformations under highly nonequilibrium conditions. This multiscale approach is followed in the work to provide self-consistent description of fracture in a loaded hierarchically organized system. 1. Fracture as local structure-phase decomposition of a nonequilibrium crystalline state. Physical mesomechanics, as applied to structural scales of plastic deformation and fracture, classified two types of subsystems: a planar subsystem free of translation invariance (surface layers, internal interfaces, macrobands of localized deformation) and a translationally invariant crystalline subsystem of any scale. The fundamental difference of these two subsystems is in their thermodynamic state which can be expressed in terms of the Gibbs thermodynamic potential: