Abstract
In the present paper, the collision of two viscoelastic spherical shells is investigated using the wave theory of impact. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. Since the local bearing of the materials of the colliding viscoelastic shells is taken into account, the solution in the contact domain is found via the modified Hertz contact theory involving the operator representation of viscoelastic analogs of Young’s modulus and Poisson’s ratio. The collision of two elastic spherical shells is considered first, and then using Volterra correspondence principle, according to which the elastic constants in the governing equations should be replaced by the corresponding viscoelastic operators, the solution obtained for elastic shells is extended over the case of viscoelastic shells.
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This research was made possible by the Grant No. 7.22.2014/K as a Government task from the Ministry of Education and Science of the Russian Federation.
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D. Tuan Manh is at Research Center on Dynamics of Solids and Structures, Voronezh State University of Architecture and Civil Engineering, Voronezh 394006, Russian Federation, on leave from Hanoi University of Architecture.
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Rossikhin, Y.A., Shitikova, M.V. & Manh, D.T. Modelling of the collision of two viscoelastic spherical shells. Mech Time-Depend Mater 20, 481–509 (2016). https://doi.org/10.1007/s11043-016-9308-x
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DOI: https://doi.org/10.1007/s11043-016-9308-x