Definitions
Ray expansions approach for studying the surfaces of strong and weak discontinuity propagating in nonlinear elastic media.
Introduction
A method for solving dynamic problems of continuous media in the form of power series with respect to time behind the moving wave fronts propagating in a medium was suggested in Achenbach and Reddy (1967). Subsequently this approach was called the ray method. For the same purpose, power series in terms of the ray coordinate was utilized, measured from the surface of discontinuities (Babicheva et al. 1973). The effectiveness of the ray method for investigating the features of boundary waves propagating in deformable media was later confirmed by a number of publications, a review of which is given in Rossikhin and Shitikova (1995a) and Podil'chuk and Rubtsov (1986). In the case, when the shock wave (surface of strain discontinuity) is the leading front of...
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References
Achenbach J, Reddy D (1967) Note on wave propagation in linearly viscoelastic media. ZAMP 18(1):141–144
Babicheva LA, Bykovtsev GI, Verveiko ND (1973) Ray method of solving dynamic problems in elastic-viscoplastic media. J Appl Math Mech 37(1):132–141
Belotserkovskii OM (1984) Numerical modeling in mechanics of solids. Nauka, Moscow
Burenin AA, Chernyshov AD (1978) Shock waves in an isotropic elastic space. J Appl Math Mech 42(4):758–765
Burenin AA, Rossikhin YA (1991) Ray method for solving one-dimensional problems of nonlinear dynamic theory of elasticity with plane surfaces of strong discontinuity. In: Applied problems of mechanics of deformable media. Dal’nauka, Vladivostok, pp 129–137
Burenin AA, Zinov'ev PV (2003) On the problem of extracting discontinuity surfaces in numerical methods for the dynamics of deformable media. In: Klimov DM (ed) Problems of mechanics. Devoted to the 90-th anniversary of Ishlinsky AYu. Physmathlit, Мoscow, pp 146–155
Burenin AA, Dudko OV, Lapteva AA (2011) To the constitutive laws of deformation propagation. Siberian J Industr Math 4(4):14–23
Bykovtsev GI, Ivlev DD (1998) Theory of plasticity. Dal'nauka, Vladivostok
Chernyii GG (1988) Gas dynamics. Nauka, Moscow
Gerasimenko YA, Zavertan AV (2008) Calculations of the dynamics of an incompressible elastic medium with antiplane and twisting impact. Comput Mech Solid Media 1(3):46–56
Gerasimenko YA, Zavertan AV (2009) Ray expansions of solutions around fronts as a shock-fitting tool for shock loading simulation. Comput Math Math Phys 49(4):698–709
Godunov SK, Zabrodin AV, Ivanov MY, Prokopov GP (1976) Numerical solution of multidimensional gas dynamics problems. Nauka, Moscow
Kulikovskii AG, Sveshnikova EI (1982) Investigation of the shock adiabat of quasitransverse shock waves in a prestressed elastic medium. J Appl Math Mech 46(5):667–673
Lourier AI (1980) Nonlinear theory of elasticity. Nauka, Moscow
Podil'chuk YN, Rubtsov YK (1986) Application of the method of ray series to the investigation of axisymmetric nonstationary problems of the dynamical theory of elasticity. Sov Appl Mech 22(3):201–207
Rossikhin YA (1991) Perturbation methods in problems of wave dynamics of anisotropic bodies. DSci Dissertation, Cheboksary
Rossikhin YA, Shitikova MV (1994) A ray method of solving problems connected with a shock interaction. Acta Mech 102:103–121. https://doi.org/10.1007/BF01178521
Rossikhin YA, Shitikova MV (1995a) Ray method for solving dynamic problems connected with propagation of wave surfaces of strong and weak discontinuities. Appl Mech Rev 48(1):1–39. https://doi.org/10.1115/1.3005096
Rossikhin YA, Shitikova MV (1995b) The ray method for solving boundary problems of wave dynamics for bodies having curvilinear anisotropy. Acta Mech 109(1–4):49–64. https://doi.org/10.1007/BF01176816
Rossikhin YA, Shitikova MV (1996) Methods for solving one-dimensional boundary-value problems in a nonlinear elastic medium. Acta Mech 114(1–4):51–69. https://doi.org/10.1007/BF01170395
Thomas T (1964) Plastic flow and fracture in solids. Academic Press, New York
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Rossikhin, Y.A., Burenin, А.A., Potianikhin, D.А. (2019). Shock Waves Via Ray Expansions. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_100-1
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DOI: https://doi.org/10.1007/978-3-662-53605-6_100-1
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