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Wave velocity
formulas to evaluate elastic constants of soft biological
tissues
Pham Chi Vinh and Jose Merodio |
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Vol. 8 (2013), No. 1, 51–64
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Abstract |
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We use the equations governing infinitesimal motions superimposed on a finite deformation in order to establish formulas for the velocity of (plane homogeneous) shear bulk waves and surface Rayleigh waves propagating in soft biological tissues subject to uniaxial tension or compression. Soft biological tissues are characterized as transversely isotropic incompressible nonlinearly elastic solids. The constitutive model is given as an strain-energy density expanded up to fourth order in terms of the Green strain tensor. The velocity formulas are written as where is the mass density, is the wave velocity, are functions in terms of the elastic constants and is the elongation in the loading direction. These formulas can be used to evaluate the elastic constants since they determine the exact behavior of the elastic constants of second, third, and fourth orders in the incompressible limit. |
Keywords
incompressible transversely isotropic elastic solids, soft
biological tissues, shear bulk waves, Rayleigh waves, wave
velocity, elastic constants
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Milestones
Received: 23 August 2012
Revised: 15 November 2012
Accepted: 17 November 2012
Published: 28 March 2013
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Authors |
| Pham Chi Vinh | |
| Faculty of Mathematics, Mechanics
and Informatics Hanoi University of Science 334, Nguyen Trai Str., Thanh Xuan Hanoi 1000 Vietnam |
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| Jose Merodio | |
| Department of Continuum Mechanics
and Structures E.T.S. Ingeniería de Caminos, Canales e Puertos Universidad Politecnica de Madrid 28040 Madrid Spain |
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