Abstract
An isolated surface that moves relative to the micropolar media and across which the first derivatives of variables are discontinuous is considered. The reduced Cosserat continuum is an elastic medium where all translations and rotations are independent. Moreover, the force stress tensor is asymmetric and the couple stress tensor is equal to zero. Continuity conditions were established and it is shown that the first derivative of the rotation vector cannot have discontinuities. It is demonstrated that the solution in this case is unique.
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REFERENCES
M. A. Kulesh, V. P. Matveenko, and I. N. Shardakov, “Constructing an analytical solution for Lamb waves using the Cosserat continuum approach,” J. Appl. Mech. Techn. Phys. 48 (1), 119–126 (2007).
M. P. Varygina, O. V. Sadovskaya, and V. M. Sadovskii, “Resonant properties of moment Cosserat continuum,” J. Appl. Mech. Techn. Phys. 51 (3), 405–414 (2010).
E. M. Suvorov, D. V. Tarlakovskii, and G. V. Fedotenkov, “The plane problem of the impact of a rigid body on a half-space modeled by a Cosserat medium,” J. Appl. Math. Mech. 76 (5), 511–518 (2012).
E. V. Zdanchuk, V. V. Kuroedov, and V. V. Lalin, “Variational formulation of dynamic problems for a nonlinear Cosserat medium,” J. Appl. Math. Mech. 81 (1), 66–70 (2017).
L. M. Schwartz, D. L. Johnson, and S. Feng, “Vibrational modes in granular materials,” Phys. Rev. Lett. 52 (10), 831–834 (1984).
E. F. Grekova and G. C. Herman, “Wave propagation in rock modeled as reduced Cosserat continuum with weak anisotropy,” in Proc. 67th Europ. Assoc. Geosci. Engin., EAGE Conf. and Exhibition, Incorporating SPE Europe 2005 (Feria de Madrid, June 13–16, 2005), pp. 2643–2646.
D. Harris, “Double-slip and spin: a generalization of the plastic potential model in the mechanics of granular materials,” Int. J. Eng. Sci. 47 (11-12), 208–1215 (2009).
M. A. Kulesh, E. F. Grekova, and I. N. Shardakov, “The problem of surface wave propagation in a reduced Cosserat medium,” Acoust. Phys. 55 (2), 218–227 (2009).
E. F. Grekova, M. A. Kulesh, and G. C. Herman, “Waves in linear elastic media with microrotations. Part 2: Isotropic reduced Cosserat model,” Bull. Seismol. Soc. Am. 99 (2B), 1423–1428 (2009).
E. F. Grekova, “Linear reduced Cosserat medium with spherical tensor of inertia, where rotations are not observed in experiment,” Mech. Solids 47 (5), 538–544 (2012).
V. A. Eremeev, “Conditions of acceleration waves’ propagation in thermoelastic micropolar media,” Vestn. Yuzhn. Nauchn. Tsentra Ross. Akad. Nauk 3 (4), 10–13 (2007).
H. Altenbach, V. A. Eremeyev, L. P. Lebedev, and L. A. Rendon, “Acceleration waves and ellipticity in thermoelastic micropolar media,” Arch. Appl Mech. 80 (3), 217–227 (2010).
V. V. Lalin and E. V. Zdanchuk, “Conditions on the surface of discontinuity for the reduced Cosserat continuum,” Mater. Phys. Mech. 31 (1–2), 28–31 (2017).
V. V. Lalin and E. V. Zdanchuk, “The initial boundary-value problem for a mathematical model for granular medium,” Appl. Mech. Mater. 725–726, 863–868 (2015).
A. I. Lurie, Nonlinear Theory of Elasticity (North Holland, 2012) [in Russian].
G. I. Petrashen’, Propagation of Waves in Anisotropic Elastic Media (Nauka, Leningrad, 1980) [in Russian].
V. B. Poruchikov, Methods of the Classical Theory of Elastodynamics (Springer, Berlin, 1993).
J. Casey, “On the derivation of jump conditions in continuum mechanics,” Int. J. Struct. Changes Solids 3, 61–84 (2011).
J. C. Slattery, Momentum, Energy, and Mass Transfer in Continua (McGraw-Hill Kogakusha Ltd., Tokyo, 1972).
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Anisimov, A.E., Zdanchuk, E.V. & Lalin, V.V. Surface of Discontinuity in Anisotropic Reduced Cosserat Continuum: Uniqueness Theorem for Dynamic Problems with Discontinuities. Mech. Solids 55, 1051–1056 (2020). https://doi.org/10.3103/S0025654420070031
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DOI: https://doi.org/10.3103/S0025654420070031