On stress-dependent elastic moduli and wave speeds

Destrade, M. and Ogden, R.W. (2013) On stress-dependent elastic moduli and wave speeds. IMA Journal of Applied Mathematics, 78(5), pp. 965-997. (doi:10.1093/imamat/hxs003)

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Publisher's URL: http://dx.doi.org/10.1093/imamat/hxs003

Abstract

On the basis of the general non-linear theory of a hyperelastic material with initial stress, initially without consideration of the origin of the initial stress, we determine explicit expressions for the stress-dependent tensor of incremental elastic moduli. In considering three special cases of initial stress within the general framework, namely hydrostatic stress, uniaxial stress and planar shear stress, we then elucidate in general form the dependence of various elastic moduli on the initial stress. In each case, the effect of initial stress on the wave speed of homogeneous plane waves is studied and it is shown how various special theories from the earlier literature fit within the general framework. We then consider the situation in which the initial stress is a pre-stress associated with a finite deformation and, in particular, we discuss the specialization to the second-order theory of elasticity and highlight connections between several classical approaches to the topic, again with special reference to the influence of higher-order terms on the speed of homogeneous plane waves. Some discrepancies arising in the earlier literature are noted.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ogden, Professor Raymond
Authors: Destrade, M., and Ogden, R.W.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:IMA Journal of Applied Mathematics
Publisher:Oxford University Press
ISSN:0272-4960
ISSN (Online):1464-3634
Published Online:30 March 2012

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