Abstract
The functional relationship between two symmetric second-rank tensors is considered. A new interpretation of the components of the tensors as projections onto an orthogonal tensor basis is given. It is shown that the constitutive relations can be written in the form of six functions each of which depends on one variable.
Similar content being viewed by others
References
A. A. Il’yushin, “On the relationship between stresses and small strains in continuum mechanics,” Prikl. Mat. Mekh., 18, No. 6, 641–666 (1954).
A. A. Il’yushin, Plasticity. Principles of the General Mathematical Theory [in Russian], Izd. Akad. Nauk SSSR, Moscow (1963).
V. V. Novozhilov, “The relationship between stresses and strains in initially isotropic inelastic solids (geometrical aspect),” Prikl. Mat. Mekh., 27, No. 5, 794–812 (1963).
K. F. Chernykh, “On the forms of relationship between symmetric tensors in the mechanics of continuous media,” Inzh. Zh., Mekh. Tverd. Tela., No. 3, 42–51 (1967).
K. F. Chernykh, “On the functional relationships between coaxial symmetric second-rank tensors,” in: Problems of the Mechanics of Deformable Solids [in Russian], Sudostroenie, Leningrad (1970), pp. 481–486.
B. D. Annin, “Anisotropic tensor functions,” in: Dynamics of Continuous Media (collected scientific papers) [in Russian], No. 11, Inst. of Hydrodynamics, Sib. Div., Acad. of Sci. of the USSR, Novosibirsk (1972), pp. 94–97.
D. V. Georgievskii, “Tensor-nonlinear effects in the isothermal deformation of continuous media,” Usp. Mekh., 1, No. 2, 150–176 (2002).
Ya. Rykhlevskii, “On Hooke’s law,” Prikl. Mat. Mekh., 48, No. 3, 420–435 (1984).
N. I. Ostrosablin, “Structure of the elastic tensor. Elastic eigenstates,” in: Dynamics of Continuous Media (collected scientific papers) [in Russian], No. 66, Inst. of Hydrodynamics, Sib. Div., Acad. of Sci. of the USSR, Novosibirsk (1984), pp. 113–125.
N. I. Ostrosablin, “On the structure of the elastic tensor and the classification of anisotropic materials,” j. Appl. Mech. Tech. Phys., 27, No. 4, 600–607 (1986).
N. I. Ostrosablin, “Invariants of the fourth-rank elastic tensor,” Sib. Zh. Indust. Mat., 1, No. 1, 155–163 (1998).
N. I. Ostrosablin, “Functional relationship between two symmetric second-rank tensors,” in: Deformation and Fracture of Structurally Inhomogeneous Media and Structures, Abstracts of All-Russian Conf. (Novosibirsk, Russia, October 9–13, 2006), Novosibirsk (2006), p. 96.
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 134–137, September–October, 2007.
Rights and permissions
About this article
Cite this article
Ostrosablin, N.I. Functional relation between two symmetric second-rank tensors. J Appl Mech Tech Phys 48, 734–736 (2007). https://doi.org/10.1007/s10808-007-0094-8
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10808-007-0094-8