Abstract
The specific internal energy defines the constitutive relation (stress-strain function) in elastic deformations. We introduce a form for the specific internal energy that expresses the idea of small anisotropy. In this formulation, only one parameter is needed to specify the anisotropic part of the deformation.
Similar content being viewed by others
References
Ciarlet, Philippe G.:Mathematical Elasticity, Volume 1: Three-Dimensional Elasticity, North-Holland, Amsterdam, New York, 1988.
Harlow, F. and Amsden, A.: Fluid Dynamics, Los Alamos National Laboratory Monograph LA-10119, Los Alamos, 1971.
Landau, L. D. and Lifshitz, E. M.:Theory of Elasticity, Pergamon, London, Paris, Frankfurt, 1959.
Marsden, J. E. and Hughes, T. J. R.:Mathematical Foundations of Elasticity, Prentice-Hall, Englewood Cliffs, N.J., 1983.
Menikoff, Ralph and Plohr, Bradley J.: Riemann problem for fluid flow of real materials,To appear in Rev. Modern Phys. 1988.
Ogden, R. W.:Non-Linear Elastic Deformations, Ellis Horwood, New York, Chicester, 1984.
Plohr, B.: Shockless acceleration of thin plates modeled by a tracked random choice method,AIAA J. 26, (1988), 470–478.
Plohr, Bradley J. and Sharp, D.: A Conservative Eulerian Formulation of the Equations for Elastic Flow,To appear in Adv. Appl. Math. 1988.
Redei, L.:Algebra, Pergamon, Oxford, 1967.
Steinberg, D. J., Cochran, S. G., and Guinan, M. W.: A constitutive model for metals applicable at high-strain rate,J. Appl. Phys. 51 (1980), 1498–1504.
Tang, Z. and Ting, T. C. T.: Wave curves for the Riemann problem of plane waves in simple isotropic elastic solids,Internat. J. Engrg. Sci. 25 (1987), 1343–1381.
Wallace, Duane C.: Thermoelastic-plastic flow in solids, Los Alamos National Laboratory Report LA-10119, Lòs Alamos, June, 1985.
Author information
Authors and Affiliations
Additional information
Supported in part by AFOSR-88-0025.
Rights and permissions
About this article
Cite this article
Garaizar, X. The small anisotropy formulation of elastic deformation. Acta Appl Math 14, 259–268 (1989). https://doi.org/10.1007/BF01307216
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01307216