On the null condition for nonlinearly elastic solids

Domanski, W. and Ogden, R.W. (2006) On the null condition for nonlinearly elastic solids. Archives of Mechanics, 58(4-5), pp. 339-361.

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Smooth solutions to the Cauchy problem for the equations of nonlinear elastodynamics exist typically only locally in time. However, under the assumption of small initial data and an additional restriction, the so-called null condition, global existence and uniqueness of a classical solution can be proved. In this paper, we examine this condition for the elastodynamic equations and study its connection with the property of genuine nonlinearity as well as its relation with the phenomenon of self-resonance of nonlinear elastic waves. Using a special structure of plane waves elastodynamics [13], we provide an alternative and simple formulation of the null condition. This condition is then evaluated for some examples of elastic constitutive laws in order to determine the nature of the restrictions that it imposes.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Ogden, Professor Raymond
Authors: Domanski, W., and Ogden, R.W.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Archives of Mechanics

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