Refine
Document Type
- Article (4)
- Conference Proceeding (2)
Keywords
- Bicharakteristikenverfahren (1)
- Elastizität (1)
- Elastodynamik (1)
- Festkörper (1)
- Multi-dimensional wave propagation (1)
- Nichtlineare Gleichung (1)
- Nichtlineare Welle (1)
- Technische Mechanik (1)
- Wellen (1)
- bicharacteristics (1)
- elastic solids (1)
- mechanical waves (1)
- nonlinear solids (1)
- nonlinear tensor constitutive equation (1)
The nonlinear scalar constitutive equations of gases lead to a change in sound speed from point to point as would be found in linear inhomogeneous (and time dependent) media. The nonlinear tensor constitutive equations of solids introduce the additional local effect of solution dependent anisotropy. The speed of a wave passing through a point changes with propagation direction and its rays are inclined to the front. It is an open question whether the widely used operator splitting techniques achieve a dimensional splitting with physically reasonable results for these multi-dimensional problems. May be this is the main reason why the theoretical and numerical investigations of multi-dimensional wave propagation in nonlinear solids are so far behind gas dynamics. We hope to promote the subject a little by a discussion of some fundamental aspects of the solution of the equations of nonlinear elastodynamics. We use methods of characteristics because they only integrate mathematically exact equations which have a direct physical interpretation.
The propagation of mechanical waves in plates of isotropic elastic material is investigated. After a short introduction to the understanding of focussing of stress waves in a plate with a curved boundary the method of characteristics is applied to a plate of hyperelastic material. Using this method the propagation of acceleration waves is discussed. Based on this a numerical difference scheme is developed for solving initial-boundary-value problems and applied to two examples: propagation of a point disturbance in a homogeneously finitely strained non-linear elastic plate and geometrical focussing in al linear elastic plate.
Shock waves, explosions, impacts or cavitation bubble collapses may generate stress waves in solids causing cracks or unexpected dammage due to focussing, physical nonlinearity or interaction with existing cracks. There is a growing interest in wave propagation, which poses many novel problems to experimentalists and theorists.
