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Fundamental aspects of numerical methods for the propagation of multi-dimensional nonlinear waves in solids

  • 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.

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Author:Manfred Staat, J. Ballmann
Parent Title (English):Nonlinear hyperbolic equations : theory, computations methods, and applications ; proceedings of the 2nd International Conference on Nonlinear Hyperbolic Problems, Aachen
Document Type:Conference Proceeding
Year of Completion:1989
Publishing Institution:Fachhochschule Aachen
Contributing Corporation:International Conference on Nonlinear Hyperbolic Problems <2, 1989, Aachen>
Date of the Publication (Server):2007/03/27
Tag:Multi-dimensional wave propagation; nonlinear solids; nonlinear tensor constitutive equation
GND Keyword:Nichtlineare Welle; Nichtlineare Gleichung; Festkörper; Elastodynamik
First Page:574
Last Page:588
Institutes:FH Aachen / Fachbereich Medizintechnik und Technomathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik