Nonlinear combined axial and torsional shear wave propagation in an incompressible hyperelastic solid (Q1819976)

Finite amplitude combined axial and torsional shear wave propagation in an incompressible isotropic hyperelastic solid is considered. When the strain energy function of the solid is a nonlinear function of \((I_ 1- 3)\) and \((I_ 2-3)\), where \(I_ 1\) and \(I_ 2\) are the first and second basic invariants of the left Cauchy-Green tensor, the two second order partial differential equations governing the propagation of the axial and torsional waves are nonlinear and coupled. These two coupled equations are equivalent to a hyperbolic system of first order partial differential equations and a modification of the MacCormack finite difference scheme is used to obtain numerical solutions of this system. Numerical results, which show the effect of the coupling, are presented for boundary-initial value problems of propagation into initially unstressed and initially stressed regions at rest.