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Real wave propagation in the isotropic-relaxed micromorphic model
Patrizio Neff1, Angela Madeo2, Gabriele Barbagallo3
1Nonlinear Analysis and Modelling , Fakultät für Mathematik , Universität Duisburg-Essen , Mathematik-Carrée , Thea-Leymann-Straße 9 , 45127 Essen , Germany.
Proceedings. Mathematical, Physical, and Engineering Sciences
|March 8, 2017
Summary
We demonstrate that planar harmonic waves have real velocities in the isotropic-relaxed micromorphic generalized continuum model. A weaker condition than positive definite energy ensures real wave velocity, with implications for elasticity theories.
Area of Science:
- Continuum Mechanics
- Solid Mechanics
- Wave Propagation
Background:
- Generalized continuum models extend classical elasticity.
- Micromorphic and relaxed micromorphic theories incorporate microstructure.
- Wave propagation analysis is crucial for material characterization.
Purpose of the Study:
- Analyze wave velocity in the isotropic-relaxed micromorphic generalized continuum model.
- Establish conditions for real wave velocities.
- Compare findings with isotropic linear elasticity and micropolar elasticity.
Main Methods:
- Analysis of planar harmonic waves within the model.
- Derivation of conditions for real wave velocity based on energy properties.
- Comparative analysis with established elasticity theories.
Main Results:
- Planar harmonic waves possess real velocity under positive-definite energy assumption.
- A necessary and sufficient condition for real wave velocity, weaker than positive definite energy, is derived.
- Strong ellipticity does not guarantee real wave velocity in micropolar elasticity, unlike isotropic linear elasticity.
Conclusions:
- The isotropic-relaxed micromorphic model offers insights into wave behavior.
- The derived condition provides a more flexible criterion for real wave velocities.
- Distinctions in wave velocity conditions highlight differences between elasticity models.
Keywords:
acoustic tensorellipticitypositive definitenessrank-one convexityreal wave velocityrelaxed micromorphic modelMore Related Videos
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