Scalar evolution equations for shear waves in incompressible solids: A simple derivation of the Z, ZK, KZK, and KP equations
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 e...
| मुख्य लेखकों: | , , |
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| स्वरूप: | Journal article |
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2010
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| _version_ | 1826276116237647872 |
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| author | Destrade, M Goriely, A Saccomandi, G |
| author_facet | Destrade, M Goriely, A Saccomandi, G |
| author_sort | Destrade, M |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T23:09:09Z |
| format | Journal article |
| id | oxford-uuid:64de5003-2bf6-4cce-9c5a-dfb00c515774 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:09:09Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:64de5003-2bf6-4cce-9c5a-dfb00c5157742022-03-26T18:21:44ZScalar evolution equations for shear waves in incompressible solids: A simple derivation of the Z, ZK, KZK, and KP equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:64de5003-2bf6-4cce-9c5a-dfb00c515774Mathematical Institute - ePrints2010Destrade, MGoriely, ASaccomandi, GWe 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. |
| spellingShingle | Destrade, M Goriely, A Saccomandi, G Scalar evolution equations for shear waves in incompressible solids: A simple derivation of the Z, ZK, KZK, and KP equations |
| title | Scalar evolution equations for shear waves in incompressible solids: A simple derivation of the Z, ZK, KZK, and KP equations |
| title_full | Scalar evolution equations for shear waves in incompressible solids: A simple derivation of the Z, ZK, KZK, and KP equations |
| title_fullStr | Scalar evolution equations for shear waves in incompressible solids: A simple derivation of the Z, ZK, KZK, and KP equations |
| title_full_unstemmed | Scalar evolution equations for shear waves in incompressible solids: A simple derivation of the Z, ZK, KZK, and KP equations |
| title_short | Scalar evolution equations for shear waves in incompressible solids: A simple derivation of the Z, ZK, KZK, and KP equations |
| title_sort | scalar evolution equations for shear waves in incompressible solids a simple derivation of the z zk kzk and kp equations |
| work_keys_str_mv | AT destradem scalarevolutionequationsforshearwavesinincompressiblesolidsasimplederivationofthezzkkzkandkpequations AT gorielya scalarevolutionequationsforshearwavesinincompressiblesolidsasimplederivationofthezzkkzkandkpequations AT saccomandig scalarevolutionequationsforshearwavesinincompressiblesolidsasimplederivationofthezzkkzkandkpequations |