The article deals with the evolution of structural damage of an inhomogeneous body as a function of the properties of the loading system whose characteristics are taken into account by supplementing the boundaryvalue problem (1), (2) with the boundary conditions of the third kind (3) and (4). of structural disruptions, and formation of a macrodefect. Increased rigidity of the loading system makes it possible to stabilize the process of damage calculation, and this leads to an increase of limit deformations. The realization of the supercritical stage of deformation, together with energy dissipation upon structural destruction is the mechanism of adaptation of an inhomogeneous body to the loading conditions.Investigations of the regularities of the failure of polymer and composite materials [1], metals [2], and rocks [3] show that macroscopic failure of these materials is preceded by complex multistage processes accompanied by the nucleation, cumulation, and localization of disperse damage with the subsequent formation of a macrodefect. In an inhomogeneous body with a certain structure we naturally fred some difference in the nature of the development of the processes of failure determined not only by strength and strain characteristics but also by imperfections in the form of discontinuities and damage. In engineering practice it was noted that there is a substantial difference in the kinetics of damage cumulation in hydraulic and pneumatic pressure vessels and pipes which cannot be explained by structural features of the material. The data of special experimental investigations of this problem show that the fracture strength depends substantially on the rigidity of the loading system (external constraint), too [4, 5].By loading system we mean the totality of solid, liquid, and/or gaseous bodies deformed as a remit of transmission of a load to the body as a whole or to some separate part of it. The replacement of one state of the material in the region under consideration by another state leads to a change of the external load in dependence on the properties and design arrangement of the loading system whose characteristics can be taken into account in the solution of boundary-vaine problems of the mechanics of inelastic deformation and structural failure by boundary conditions of the third kind formulated in [6]. On the basis of the suggested model of a structurally inhomogeneous medium [7, 8] we investigate problems of multistage processes of damage cumulation and of the influence of the properties of the loading system on the formation of conditions determining the transition from microfailure to macrofailure.The mechanical behavior of a structurally inhomogeneous body fl, bounded by the surface Off, whose scleronomic isotropic components do not change the type of elastic symmetry in the process of damage cumulation, is described under quasistatic loading by the system of differential equations in incremental form:

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The macroscopic failure of inhomogeneons media is the result of damage accumulation on different structural levels. Under "rigid" loading, when given displacements of boundary points are ensured, irrespective of the body's resistance, the structural failure of composite materials may t~k~ place in an equilibrium regime and result in manifestation of such nonlinear-behavioral effects as a descending branch on the strain diagram [1].Support of conditions favorable to equil~rium damage accumulation and the realization of a post.critical stage of deformation, which follows the attainment of ultimate strength [2], will "extend the life" of the material in weakened zones and be a result of utilization of the strength reserves of the composites and an increase in the bearing capacity of the structures. In this connection, the problem of the optimal design of composite structures requires the acquisition of data on the mechanical behavior of the materials in the post-critical stage of deformation in an arbitrary complex stress-strain state.The purpose of the present study is to ascertain general laws governing the pseudoplastic deformation of granular composites, which is caused by structural failure. For example, ceramics and the matrices of modern carbon-carbon composites are classed among these materials.

Deformable bodies, which are succeptible to various structural modifications, sometimes reveal the property of softening at mechanical loading, reflected by the descending branch of the diagram presenting the l

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