PSI - Issue 32

Denis N. Sheydakov et al. / Procedia Structural Integrity 32 (2021) 313–320 Denis N. Sheydakov, Irina B. Mikhailova / Structural Integrity Procedia 00 (2021) 000 – 000

320

8

h = 0.05

h = 0.10

3.0 p

3.0 p

1.5

1.5

r * = 1 r * = 2 r * = 5 r * = 10

r * = 1 r * = 2 r * = 5 r * = 10

0

0.05

0.10

0

0.05

0.10





Fig. 3.Influence of initial extension of the coating   0.1    on the micropolar rod stability in the case of combinedloading. As in the case of simple loading, the revealed influence of initial (residual) deformation is more pronounced for rods with a thick coating.In addition, the stability of the considered composite structure under combined loading also increases with a decrease in its overall size (scale) due to the effect of material microstructure. Acknowledgements This work was carried out partially with the financial support of the Russian Foundation for Basic Research (grants 19-01-00719-a, 19-48-230042-r_a) and as part of the implementation of the State assignment for the Southern Scientific Centre of Russian Academy of Sciences (SSC RAS), state registration number 01201354242. References Cosserat, E., Cosserat, F., 1909.Theorie des Corps Deformables.LibrairieScientifique A, Hermann etFils, Paris. Eremeyev, V.A., Pietraszkiewicz, W., 2012. Material symmetry group of the non-linear polar-elastic continuum. International Journal of Solids and Structures 49, 1993 – 2005. Eremeyev, V.A., Zubov, L.M., 1994. On the stability of elastic bodies with couple-stresses. Mechanics of Solids 29, 172 – 181. Eringen, A.C., 1999. Microcontinuum Field Theory. I. Foundations and Solids. Springer, New York. Kafadar, C.B., Eringen, A.C., 1971. Micropolar media – I.The classical theory. International Journal of Engineering Science 9, 271 – 305. Lakes, R., 1995.Experimental methods for study of Cosserat elastic solids and other generalized elastic continua. In: Continuum models for materials with micro-structure. Muhlhaus, H. (Ed.). Wiley, New York, pp. 1 – 22. Levin, V.A., 2017. Equilibrium of micropolar bodies with predeformed regions.The superposition of large deformations. Journal of Applied Mathematics and Mechanics 81, 223 – 227. Lurie, A.I., 1990. Non-linear Theory of Elasticity.North-Holland, Amsterdam. Pietraszkiewicz, W., Eremeyev, V.A., 2009.On natural strain measures of the non-linear micropolar continuum. International Journal of Solids and Structures 46, 774 – 787. Sheydakov, D.N., 2011. Buckling of elastic composite rods of micropolar material subjected to combined loads. In: Advanced Structured Materials. Vol. 7.Mechanics of Generalized Continua.Altenbach, H., Maugin, G.A., Erofeev, V. (Eds.). Springer, Berlin, pp. 255 – 271. Sheydakov, D.N., Altenbach, H., 2016. Stability of inhomogeneous micropolar cylindrical tube subject to combined loads. Mathematics and Mechanics of Solids 21, 1082 – 1094. Sheydakov, D.N., Mikhailova, I.B. Sheydakov, N.E., 2020. Stability of composite micropolar cylinders with prestressed parts.Nauka Yuga Rossii 16, 3 – 11. (In Russian). Toupin, R.A., 1964. Theories of elasticity with couple-stress. Archive for Rational Mechanics and Analysis 17, 85 – 112. Truesdell, C., 1977. A First Course in Rational Continuum Mechanics. Academic Press, New York. Zubov, L.M., 1997. Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies.Springer, Berlin. Zubov, L.M., 2016. Universal deformations of micropolar isotropic elastic solids. Mathematics and Mechanics of Solids 21, 152 – 167.