The Effect of the Geometrical Non-Linearity on the Stress Distribution in the Infinite Elastic Body with a Periodically Curved Row of Fibers

In the framework of the piecewise homogeneous body model with the use of the three-dimensional geometrically non-linear exact equations of the theory of elasticity, the method for determination of the stress-strain state in the infinite body containing periodically located row of periodically curved fibers is developed. It is assumed that the midlines of the fibers are in the same plane. With respect to the location of the fibers according to each other the sinphase and antiphase curving cases are considered. Numerical results on the effect of the geometrical non-linearity to the values of the self balanced shear and normal stresses are presented. In particular, it is established that this effect causes to increase (to decrease) the absolute values of these stresses in compression (in tension) along the fibers.