Destrade, M. and Goriely, A. and Saccomandi, G. (2010) Scalar evolution equations for shear waves in incompressible solids: A simple derivation of the Z, ZK, KZK, and KP equations. Proceedings of the Royal Society A .

PDF
199kB 
Abstract
We study the propagation of twodimensional finiteamplitude shear waves in a nonlinear prestrained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent, and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neoHookean solids (with strain energy depending only on the first principal invariant of CauchyGreen strain). However, we show that the Z equation cannot be a scalar equation for the propagation of twodimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then we introduce dispersive and dissipative terms to deduce the scalar KadomtsevPetviashvili (KP), ZabolotskayaKhokhlov (ZK) and KhokhlovZabolotskayaKuznetsov (KZK) equations of incompressible solid mechanics.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  1411 
Deposited By:  Peter Hudston 
Deposited On:  08 Nov 2011 09:50 
Last Modified:  29 May 2015 19:06 
Repository Staff Only: item control page