Newton–Kantorovich method in the problem of finding nonunique solutions of equilibrium equations for discrete gradient mechanical systems

An algorithm of Newton–Kantorovich method's application for finding solutions (including nonunique solutions) of nonlinear equilibrium equations in discrete mechanical systems with nonconvex potential function is suggested. The algorithm is applied for solving the problem of finding equilibrium parameters of the mechanical system that implements a triaxial stretching of an elementary cube made of a nonlinear material.