 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| A. D. Panov, "Theory of constitutive relations for isotropic solids," Mech. Solids. 39 (6), 20-32 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
6 |
Pages |
20-32 |
| Title |
Theory of constitutive relations for isotropic solids |
| Author(s) |
A. D. Panov (Moscow) |
| Abstract |
This paper is devoted to a method for the construction of constitutive relations for an isotropic solid. The method proposed here does not require the traditional a priori assumption of the mathematical structure of these relations or the form of the energy function, from which the constitutive relations would follow. It is shown that for the energy functions for an arbitrary stress state to be able to be uniquely defined, it is necessary and sufficient to have data obtained from two basic experiments. Constitutive relations adequately describing nonlinear effects in deformable solids are obtained (these effects are connected with tensor nonlinearities of these relations). Conditions are found for these relations to become tensor-linear. When deriving the system of governing equations, some specific properties of the logarithmic strain tensor, through which the law of state is expressed, are taken into account. In the case of small elastic strains, physically linear constitutive relations are obtained. These relations, in contrast to the corresponding constitutive relations of the classical elasticity, describe second-order geometric effects in the case of elastic deformation of isotropic solids. |
| References |
| 1. | A. D. Panov, Theory of Deformation of Isotropic Solids with Finite Strains (A New Method for the Determination of the Law of State) [in Russian], MGTA im. Kosygina, Moscow, 1998. |
| 2. | A. D. Panov, "On the determination of the limiting state of structural members made of highly plastic materials," in Proceedings of the IV-th International Seminar "Current Topics in Strength of Materials" [in Russian], Vol. 1, pp. 148-153, Novgorod, 2000. |
| 3. | A. D. Panov, "On the determination of the shear diagram for finite strains," in Problems in Science and Technology Related to Structural Reliability and Durability Prediction: Methods of Solution. Proceeding of the V-th Intern. Conf. St. Petersburg [in Russian], pp. 400-407, SPbGU,
2003. |
| 4. | A. D. Panov, "Nonlinear effects in axially symmetric deformation of a cylinder. Pointing effect," Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 27-43, 2004. |
| 5. | A. I. Lur'e, Nonlinear Theory of Elasticity [in Russian], Nauka, Moscow, 1980. |
| 6. | A. I. Lur'e, Theory of Elasticity [in Russian], Nauka, Moscow, 1970. |
| 7. | A. D. Panov, "Theory of deformation of isotropic materials with different resistance to compression and tension," in Proc. of the 2nd Intern. Conf. "Current Topics in Fundamental Sciences" [in Russian], Vol. 2, pp. 42-45, Sect. E, MGTU, Moscow, 1994. |
| 8. | A. D. Panov, "A new method for the construction of constitutive equation for isotropic solids," in Proceedings of the IV-th International Seminar "Current Topics in Strength of Materials" [in Russian], Vol. 1,
pp. 177-181, Novgorod, 1999. |
| 9. | D. V. Georgievskii, "Tensor-nonlinear effects in continuous media subjected to isothermal deformation," Uspekhi Mekhaniki [Advances in Mechanics], Vol. 1, No. 2, pp. 150-176, 2002. |
|
| Received |
02 February 2004 |
| << Previous article | Volume 39, Issue 6 / 2004 | Next article >> |
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