Superposition of finite-amplitude transverse waves in deformed Mooney–Rivlin and neo-Hookean materials

Abstract

In this paper, waves propagating in Mooney–Rivlin and neo-Hookean non-linear elastic materials subjected to a homogeneous pre-strain are considered. In a previous paper, Boulanger and Hayes [Finite-amplitude waves in deformed Mooney–Rivlin materials, Q. J. Mech. Appl. Math. 45 (1992) 575–593] showed, for deformed Mooney–Rivlin materials, that the superposition of two finite-amplitude shear waves polarized in different directions (orthogonal to each other) and propagating along the same direction is an exact solution of the equations of motion. The two waves do not interact. Here, we are interested in superpositions of waves propagating in different directions. Two types of superpositions are considered: superpositions of waves polarized in the same direction, and also superposition of waves polarized in different directions. It is shown that such superpositions are exact solutions of the equations of motion with appropriate choices of the propagation and polarization directions.