Functional relation between two symmetric second-rank tensors
- 37 Downloads
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.
Key wordssymmetric tensors tensor basis orthogonal matrices constitutive relations
Unable to display preview. Download preview PDF.
- 1.A. A. Il’yushin, “On the relationship between stresses and small strains in continuum mechanics,” Prikl. Mat. Mekh., 18, No. 6, 641–666 (1954).Google Scholar
- 2.A. A. Il’yushin, Plasticity. Principles of the General Mathematical Theory [in Russian], Izd. Akad. Nauk SSSR, Moscow (1963).Google Scholar
- 4.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).Google Scholar
- 5.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.Google Scholar
- 6.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.Google Scholar
- 9.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.Google Scholar
- 12.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.Google Scholar