Stress concentration in nonlinear viscoelastic composites

A nonlinear viscoelastic problem of the mechanics of composites is solved within the framework of a second-order nonlinear theory. A viscoelastic functional is used to construct general defining relations. A stochastic boundary value problem for determining the stress concentration and its relaxation in polymer composite materials (PCM) is solved. To derive the complete system of second-order viscoelastic equations, the method of successive approximation is used. A generalization of the correspondence principle to nonlinear viscoelastic media is obtained. The relaxation functions averaged over the viscoelastic matrix and elastic inclusions and the stress concentration parameters are determined. Examples are given showing the importance of the mutual influence of nonlinear elastic and viscous properties of the components on stress redistribution near inclusions in multicomponent PCMs. As a practical result, one can note the possibility of predicting the long-term strength of a material when a viscoelastic stress field is known near inclusions