Using null strain energy functions in compressible finite elasticity to generate exact solutions

Haughton, D.M. (2008) Using null strain energy functions in compressible finite elasticity to generate exact solutions. Zeitschrift für Angewandte Mathematik und Physik, 59(4), pp. 730-749. (doi: 10.1007/s00033-006-6062-y)

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In this paper we characterize those strain energy functions in unconstrained nonlinear elasticity that satisfy the equations of equilibrium identically. The idea is to construct a useful, physically reasonable strain–energy function containing one or more components which are null, in such a way that exact solutions may be obtained from the resulting equilibrium equations. We show that the dilatation is a universal null energy while there may be others that depend on the actual problem. To obtain the null energies for a given problem it is often convenient to formulate the variational problem and look at the Euler–Lagrange equations. Specific examples are used to illustrate some of the potential uses of the method in finding exact solutions for physically meaningful constitutive models.

Item Type:Articles
Keywords:Null, Lagrangian, elastic, exact, nonlinear
Glasgow Author(s) Enlighten ID:Haughton, Dr David
Authors: Haughton, D.M.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Zeitschrift für Angewandte Mathematik und Physik
Journal Abbr.:Z. Angew. Math. Phys.
Publisher:SP Birkhäuser Verlag Basel
ISSN (Online):1420-9039
Published Online:26 February 2007

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