Peer-Reviewed Journal Details
Mandatory Fields
Destrade, M,Goriely, A,Saccomandi, G
2011
July
Proceedings Of The Royal Society A-Mathematical Physical And Engineering Sciences
Scalar evolution equations for shear waves in incompressible solids: a simple derivation of the Z, ZK, KZK and KP equations
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shear waves incompressible materials soft solids KHOKHLOV-ZABOLOTSKAYA EQUATION NONLINEAR ACOUSTICS MEDIA BEAMS BURGERS
467
1823
1834
We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained 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 neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional 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 Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov-Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics.
DOI 10.1098/rspa.2010.0508
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