EQUILIBRIUM FAILURE PROCESSES OF GRANULAR COMPOSITES

The macroscopic failure of inhomogeneous media results front damage ac cumulation on different structural levels. During rigid loading, when given displacements of boundary points are ensured, irrespective of th e body's resistance, structural-failure processes of composite materia ls take place in an equilibrium regime and result in the manifestation of such nonlinear-behavior effects as a descending branch on the stra in diagram. The structural elements of a granular composite are homoge neous and firmly connected along the interface. Their geometry and mut ual arrangement are given and do not change during deformation and fai lure of the medium, and the medium itself is macrohomogeneous. The str ength of isotropic structural elements is estimated by comparing the s econd invariant of the stress tensor with its critical value. Nonfulfi llment of the indicated strength criterion is associated with loss of ability to resist changes in form; at this point, the positive value o f the first invariant corresponds to loss of such ability to resist an increase in volume. The deformation and structural failure of the med ium are investigated as a single process that can be described under q uasi-static loading by a boundary problem consisting of a closed syste m of Eqs. (I) and (2) and boundary conditions providing for a macrohom ogeneous strain state. A principal feature of the boundary problem und er consideration is the possibility of considering in constitutive rel ationships the states of the inhomogeneous medium, which correspond to partial or complete loss of bearing capacity of the structural elemen ts. The random structural strength constants correspond to three-param eter Weibull distribution (6). The representative volume of a granular composite, which fills a domain in the form of a cube is modeled by a set of isotropic elastotbrittle structural elements, each of which is associated with a tetrahedral simplex-element. Complete equilibrium s train diagrams containing a descending branch are obtained as a result of the mathematical modeling of deformation processes and structural failure to realize a representative volume containing 384 structural e lements with different strength and similar elastic constants.