On the impact of damaged bonds on bulk elasticity and deformation anisotropy of granular composites

This paper deals with the development of a phenomenological mathematical model based on tensor-nonlinear equations intended for the study of mechanical properties of media whose deformation is accompanied by a change in internal bonds. The results of static tests on stretching, compression with determination of coefficients of transverse deformation and torsion of specimens before fracture, as well as cruciform samples with repeated static stretching, allow us to reveal the effect of elasticity change, which is caused by rupture of weak damaged bonds at positive stresses and their increase at negative ones. Analysis of test results and experimental work of other authors with the help of a mathematical model led to the conclusion that the main reason for the revealed feature is the behavior of weak bonds that break at small positive deformations. Their discontinuity creates an anisotropy of the elastic properties with symmetry axes that coincide with the directions of the principal stresses. These equations, transformed to a matrix form, make it possible to obtain another equation for the connection of the mean deformation with principal stresses, including three bulk moduli called "apparent". They allow us to find the relationships for determining the longitudinal moduli of elasticity and the coefficients of transverse deformations. High values of some "apparent" moduli are several times higher than the value of the "classical" one, found from the initial experimental data in tension. They do not speak of the increasing rigidity of the material in the breaking of bonds, but indicate the smallness of the linear volume strain due to the loss of internal bonds between the particles, which causes the growth of the nonlinear part of the volume deformation-dilatancy, substantially exceeding the linear part. To determine all of these characteristics, a technique is used that makes it possible to achieve an almost complete coincidence of the theoretical curves with the experimental data for the longitudinal elastic moduli and the coefficients of transverse deformations found from the results of the tests. It is designed to determine the loosening parameter and the average value of the "apparent" moduli. Compliances, being the reciprocal of the magnitude of the moduli, as functions of the principal stresses, are smooth and inextricable. Their values can be positive, zero and negative. They allow us to determine the total volumetric deformation for any stress state and load level. According to the initial values of the "apparent" moduli or compliances, three parameters of varying elasticity quantifying the state of the bonds are determined as the ratio of the "classical" moduli to the "apparent" moduli. The latter give an idea of the extant relationships and the interactions acquired as a result of the interaction of the filler particles. At zero value of the disintegration parameter, the "apparent" moduli are equal to each other. Such calculations make it possible to determine the linear part of the average deformation, to reveal the dependence of the elastic properties on the breaking of bonds and the form of the stressed state. The anisotropy indicated by the parameters of variable elasticity and "apparent" moduli indicates the emergence of a new structure due to the development of defects.