One-dimensional countable model of static effect of non-local interaction in composites

The paper is devoted to the static analysis of countable medium with an accumulation point in terms of a one-dimensional model of the non-local interactions in a two material interface contact area. The new approach is based on a concept of non-local interactions between the accumulation point denned as a hypothetical particle located on a theoretical boundary of two connected materials and the remaining particles of medium. The problem of solvability of the equation of equilibrium (qualitative and quantitative analyses) is formulated, i.e. the existence and uniqueness theorems are demonstrated as well as the approximate method is formulated. Numerical results given in the form of diagrams are compared with the solutions which base on a classical model of contact forces. The character of displacements of particles near the accumulation point (witin the joint region) is qualitatively consistent with the observed strain hardening (synergism) of material.