The third- and fourth-order constants of incompressible isotropic elasticity

Michel Destrade, Raymond W Ogden

Research output: Contribution to journalArticlepeer-review

84 Citations (Scopus)


Consider the constitutive law for an isotropic elastic solid with the strain-energy function expanded up to the fourth order in the strain and the stress up to the third order in the strain. The stress–strain relation can then be inverted to give the strain in terms of the stress with a view to considering the incompressible limit. For this purpose, use of the logarithmic strain tensor is of particular value. It enables the limiting values of all nine fourth-order elastic constants in the incompressible limit to be evaluated precisely and rigorously. In particular, it is explained why the three constants of fourth-order incompressible elasticity µ, , and are of the same order of magnitude. Several examples of application of the results follow, including determination of the acoustoelastic coefficients in incompressible solids and the limiting values of the coefficients of nonlinearity for elastic wave propagation.
Original languageEnglish
Pages (from-to)3334-3343
Number of pages10
JournalJournal of the Acoustical Society of America
Issue number6
Publication statusPublished - Dec 2010


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