Abstract
It is shown that, in the planar case, the system of constitutive equations of the linear elasticity theory should contain five independent equations. In the classical theory, only three equations are formulated, while the other two are contained in implicit form in the postulate of diffeomorphism, which is the assumption of smoothness of the displacement field. A closed elasticity model is constructed without the assumption of diffeomorphism, and it contains a structural parameter having a dimension of length. It is shown that, in a static version, macrodeformations depend on stresses and second derivatives of stresses with respect to the coordinates, while there is dispersion of longitudinal and transverse waves in the dynamics.
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References
B. D. Annin, A. N. Kalamkarov, A. G. Kolpakov, and V. Z. Parton, Calculation and Design of Composite Materials and Structural Elements (Nauka, Novosibirsk, 1993) [in Russian].
B. D. Annin and V. M. Zhigalkin, Materials Under Complex Loading (Izd. Sib. Otd. Ross. Akad. Nauk, 1999) [in Russian].
V. D. Annin, A. F. Revuzhenko, and E. I. Shemyakin, “Deformed Solid Mechanics at the Siberian Branch, Academy of Sciences of the USSR,” Prikl. Mekh. Tekh. Fiz. 28 (4), 66–86 (1987) [J. Appl. Mech. Tech. Phys 28 (4), 531–549 (1987)].
I. A. Kunin, The Theory of an Elastic Medium with a Microstructure (Nauka, Moscow, 1975) [in Russian].
A. C. Eringen, Theory of Micropolar Elasticity (Princeton University, Princeton, 1967).
A. V. Chigarev, Stochastic and Regular Dynamics of Inhomogeneous Media (Tekhnoprint, Minsk, 2000) [in Russian].
I. S. Pavlov, “Elastic Waves in a Two-Dimensional Granular Medium,” Probl. Prochn. Plast. 67, 119–131 (2005).
M. V. Kurlenya, V. N. Oparin, A. F. Revuzhenko, and E. I. Shemyakin, “Reaction of Rocks to Near-Field Explosions,” Dokl. Akad. Nauk 293 (1), 67–70 (1997).
A. F. Revuzhenko, “Rock as a Medium with Inner Sources and Energy Sinks. Report 3,” Fiz.-Tekh. Probl. Razrab. Polez. Iskopaemykh, No. 5, 20–26 (1991).
P. V. Trusov, “Some Problems of Nonlinear Mechanics of a Deformed Body (in the Order of Discussion),” Mat. Modelir. Sistem Prots., No. 17, 85–95 (2009).
S. V. Lavrikov, O. A. Mikenina, A. F. Revuzhenko, and E. I. Shemyakin, “The Concept of a Non-Archimedean Multiscale Space and a Model of Plastic Media with Microstructures,” Fiz. Mezomekh. 11 (3), 45–60 (2008).
V. V. Vasil’ev and S. A. Lur’e, “Generalized Elasticity Theory,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 16–27 (2015).
B. P. Sibiryakov and B. A. Bobrov, “Acoustic Emission in the Case of Static Loading of Sands,” Fiz. Mezomekh. 11 (1), 80–84 (2008).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 57, No. 5, pp. 45–52, September–October, 2016.
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Revuzhenko, A.F. Version of the linear elasticity theory with a structural parameter. J Appl Mech Tech Phy 57, 801–807 (2016). https://doi.org/10.1134/S0021894416050060
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DOI: https://doi.org/10.1134/S0021894416050060