BOUNDARY VALUE PROBLEMS FOR NEO-HOOKEAN MATERIAL IN NONLINE ELASTICITY

Basic static solutions of boundary value problems for the generalized plane strain elastic neoHookean body in the field of body forces are obtained in closed form. Using the nominal stress tensor and the stress function allowed to write down the general solution of two holomorphic functions, and the basic boundary value problems of nonlinear elasticity theory lead to the Riemann-Hilbert problem for holomorphic vector. The final decision is recorded in quadrature with the help of the Schwarz integral. Built a universal representation of the body forces, which does not depend on the type of the specific elastic potential, which allows to record the boundary conditions, as the boundary conditions of the problem, in which there are no body forces.