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Wave equations in linear viscoelastic materials.

J P Charlier, F Crowet

    The Journal of the Acoustical Society of America
    |April 1, 1986
    PubMed
    Summary
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    This study explores wave equations in linear viscoelastic materials, crucial for modeling ultrasound in soft tissues. It details conditions for deriving these equations, especially for mean principal stress propagation.

    Area of Science:

    • Solid Mechanics
    • Viscoelasticity
    • Acoustics

    Background:

    • Linear viscoelastic materials exhibit time-dependent mechanical properties.
    • Modeling wave propagation is essential for applications like medical ultrasound.
    • Infinitesimal theory provides a simplified framework for material deformation.

    Purpose of the Study:

    • To investigate the conditions required for formulating wave equations in linear viscoelastic materials.
    • To explore the propagation of mean principal stress in these materials.
    • To suggest applications in modeling ultrasound propagation in soft biological tissues.

    Main Methods:

    • Derivation of a general wave equation for the displacement field in inhomogeneous media.
    • Analysis of the propagation of mean principal stress.

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  • Examination of conditions for homogeneous and inhomogeneous viscoelastic materials.

    • Main Results:

    • A general wave equation for displacement was obtained for inhomogeneous media.
    • Wave equations for mean principal stress are always obtainable in homogeneous viscoelastic materials.
    • Inhomogeneous materials require supplementary conditions on material properties and motion for mean principal stress wave equations.

    Conclusions:

    • The study establishes conditions for wave equation formulation in linear viscoelasticity.
    • Mean principal stress propagation is well-defined in homogeneous materials but requires further constraints in inhomogeneous ones.
    • Findings are applicable to understanding ultrasound in biological tissues and analyzing specific fluid models.