Cohesion field: Barenblatt’s hypothesis as formal corollary of theory of continuous media with conserved dislocations

In the paper the higher-order theory of continuous media with conserved dislocations is developed to describe the spectrum of cohesion and superficial phenomena. A new kinematic interpretation of dislocations is offered, that reflects the connection of dislocations with distortion, with change in volume (porosity), and with twisting. The main aim of the paper is to receive the strong theoretical justification for famous hypothesis of Barenblatt about cohesion field near top of crack. A new variants of the fracture criterions are discussed that based on the of the theory of media with microstructures, connection of the length of the cohesion interaction zone (a new physical constant) with parameters of the fracture mechanics is established