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Flat geometric-nonlinear shear strains
- Authors: Bakushev S.V1
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Affiliations:
- Penza State University of Architecture and Construction
- Issue: Vol 14, No 6 (2018)
- Pages: 516-522
- Section: Problems of theory of elasticity
- URL: https://journals.rudn.ru/structural-mechanics/article/view/20430
- DOI: https://doi.org/10.22363/1815-5235-2018-14-6-516-522
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Abstract
Aims. The problem of differential equation construction characteristics and balances is being analyzed; and also the definitions of the planar wave rotational deformation travel time in the continuum, the mechanical character of which is described by the mathematical models geometrically nonlinear analogues in continuous body, the stress-strain stain of which is described by the undefined, basically, by the cross-connections between the first tensor invariant and the second invariant deviator of the stresses and nonlinear deformations. Methods. As an example let’s plot the specific speed of the transverse waves depending on the intensive rotational transverse deformation and the meanings of the material mechanical constants for the three mathematical models of the continuum: model 1 corresponds to the geometrically nonlinear analogue of the elasticity linear theory; model 2 corresponds to the geometrically nonlinear analogue of the small quantity elastoplastic strain theory; model 3 corresponds to geometrically nonlinear analogue of deformation theory of the loose medium plasticity. Conclusions. It is stated that in half-subspace the mechanical behavior of which is described by the deformation theory equations of the loose medium plasticity, the shock waves can appear in continuous boundary conditions.
About the authors
Sergej V Bakushev
Penza State University of Architecture and Construction
Author for correspondence.
Email: bakuchsv@mail.ru
Dr Sci. (Eng.), Professor of the Department of Mechanics
28 Titov St., Penza, 440028, Russian FederationReferences
- Novatsky V.K. (1978). Volnovye zadachi teorii plastichnosti [Wave problems of plasticity theory]. Moscow, Mir Publ., 307. (In Russ.)
- Bakushev S.V. (2014). Prodol'no-poperechnye geometricheski-nelinejnye volny deformacij [Longitudinalcross geometrical non-linear waves of deformation]. Proceedings of Petrozavodsk State University. Series: Natural & Engineering Sciences, 6(143), 99–103. (In Russ.)
- Bakushev S.V. (2014). Prodol'no-poperechnye volny deformacij slabogo razryva [The longitudinal-transverse waves of deformations of the weak gap]. Problems of Strength and Plasticity, 76(2), 114–121. (In Russ.)
- Bakushev S.V. (2013). Geometricheski i fizicheski nelineinaya mekhanika sploshnoi sredy: ploskaya zadacha [Metrically and physically nonlinear mechanics of continuum: flat task]. Мoscow, LIBROKOM Publ., 312. (In Russ.)
- Doronin A.M., Erofeev V.I. (2016). Generaciya vtoroj garmoniki sdvigovoj volny v uprugo-plasticheskoj srede [The generation of the second harmonics of the transverse wave in elastoplastic circumference]. Letters on Materials, 6(2–22), 102–104. (In Russ.)
- Zveryaev Е.M. (2015). Vozniknovenie volny sdviga pri poperechnom udare po vysotnomu zdaniyu [The inception of the transverse wave at the time of the transverse impact on the high building]. Building and Reconstruction, 3(59), 67–74. (In Russ.)
- Sadovskii V.M. (2003). K issledovaniyu struktury poperechnyh udarnyh voln konechnoj amplitudy v plasticheskoj srede [To the research of the transversal shock wave structure of finite amplitude in plastic circumference]. Russian Academy of Science Report. Mechanics of the rigid solids, (5), 40–50. (In Russ.)
- Sadovskaya O.V. (2009). Chislennoe reshenie prostranstvennyh dinamicheskih zadach momentnoj teorii uprugosti s granichnymi usloviyami simmetrii [Solid dynamical problem computational solution of the bending theory of elasticity with interface conditions of symmetry]. Magazine of the numerical mathematics and mathematical physics, 49(2), 313–322. (In Russ.)
- Carcione J.M., Poletto F., Farina B., Craglietto A. (2014). Simulation of seismic waves at the earth's crust (brittle – ductile transition) based on the Burgers model. Solid Earth, 5(2), 1001–1010 doi: 10.5194/se-5-1001-2014
- Markiewicz E., Haugou G., Chaari F., Zouari B., Tounsi R., Dammak F. (2012). Experimental study of aluminium honeycomb behaviour under dynamic multiaxial loading. EPJ Web of Conferences, (26), 01050. doi: 10.1051/epjconf/20122601050
- Smirnov V.I. (1981). Kurs vysshey matematiki [Course of higher mathematics]. Vol. 4. Part 2. Moscow: Nauka Publ., 550. (In Russ.)
- Geniev G.A. (1974). K voprosu o deformatsionnoy teorii plastichnosti sypuchey sredy [To the question of deformation theory of granular media of plasticity]. Structural Mechanics and Analysis of Constructions, (4), 8–10. (In Russ.)
- Bakushev S.V. (2011). K voprosu o vozmozhnosti formirovaniya ploskih udarnyh voln v sploshnyh sredah [To the question of the possibility of creating flat shock waves in solid media]. Structural Mechanics and Analysis of Constructions, (4), 11–15. (In Russ.)
