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Finite amplitude elastic waves propagating in compressible solids
Michel Destrade1, Giuseppe Saccomandi
1Laboratoire de Modélisation en Mécanique, UMR 7607, CNRS, Université Pierre et Marie Curie, 4 Place Jussieu, Case 162, 75252 Paris Cedex 05, France. destrade@lmm.jussieu.fr
Summary
This study explores wave interactions in hyperelastic materials, including dissipation. Researchers derived general equations and found exact solutions, revealing destabilizing effects in nonlinear materials.
Area of Science:
- Solid Mechanics
- Nonlinear Acoustics
- Continuum Mechanics
Background:
- Investigates wave propagation in hyperelastic materials.
- Considers interactions between longitudinal and transverse waves.
- Includes material dissipation, modeled via a Stokesian fluid stress tensor.
Purpose of the Study:
- Derive general equations of motion for isotropic hyperelastic materials.
- Explore exact, closed-form solutions for wave propagation.
- Analyze wave behavior, including potential destabilizing effects.
Main Methods:
- Formulating general equations of motion for hyperelastic materials with dissipation.
- Reducing partial differential equations to ordinary differential equations.
- Applying dynamical systems theory to analyze wave properties.
Main Results:
- Obtained time-space separable solutions for wave propagation.
- Identified generalized oscillatory shearing motions and sinusoidal standing waves.
- Uncovered destabilizing effects in compressible materials with nonlinear strain energy functions.
Conclusions:
- Exact solutions are achievable for specific hyperelastic material models.
- Destabilizing effects are linked to highly nonlinear strain energy functions.
- Fourth-order elasticity does not exhibit these specific destabilizing wave phenomena.