Abstract
A linear thermoelastic theory of materials with voids is considered. First, we establish a uniqueness theorem with no definiteness assumption on the elasticities and in the absence of restriction that the conductivity tensor is positive definite. Then, we establish a basic relation which leads in a simple manner to the reciprocal theorem and to another uniqueness result. Some applications of the reciprocity relation are presented.
Similar content being viewed by others
References
J.W. Nunziato and S.C. Cowin, A non linear theory of elastic materials with voids. Arch. Rational Mech. Anal. 72 (1979) 175–201.
S.C. Cowin and J.W. Nunziato, Linear elastic materials with voids. J. Elasticity 13 (1983) 125.
K.Z. Markov, On the dilatation theory of elasticity. ZAMM 61 (1984) 349–358.
J. Jaric and Z. Golubovic, Theory of thermoelasticity of granular materials. Rev. Roum., Sci. Techn., Méc. Appl. 24 (1979) 793–805.
J. Jaric and S. Rancovic, Acceleration waves in granular materials. Mechanika 6 (1980) 66–76.
D. Iesan, A theory of thermoelastic materials with voids. Acta Mechanica 60 (1986) 67–89.
I. Brun, Methodes energétiques dans les systemes evolutifs lineaires. J. Mecanique 8 (1969) 125–192.
R.J. Knops and L.E. Payne, On uniqueness and continuous dependence in dynamical problems of linear thermoelasticity. Int. J. Solids Structures 6 (1970) 1173–1184.
S. Rionero and S. Chirita, The Lagrange identity method in linear thermoelasticity. Int. J. Eng. Sci. 25 (1987) 935–947.
D. Iesan, On some theorems in thermoelastodynamics. Rev. Roum. Sci. Techn. Méc. Appl. 34 (1989) 101–111.
D.E. Carlson, Linear Thermoelasticity. In Handbuch der Physik, VI a/2 (Edited by C.A. Truesdell), New York: Springer-Verlag (1972).
M.E. Gurtin, The Linear Theory of Elasticity. In Handbuch der Physik, vol. VI a/2 (Edited by C.A. Truesdell), New York: Springer-Verlag (1972).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ciarletta, M., Scalia, A. On uniqueness and reciprocity in linear thermoelasticity of materials with voids. J Elasticity 32, 1–17 (1993). https://doi.org/10.1007/BF00042245
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00042245