Definitions
Mathematical formulation of the elastodynamic contact problem for a cracked body. The contact interaction of the crack edges in 2-D under action of the normal incidence of a harmonic tension-compression P-waves. Method of solution is the boundary integral equation method (BIE) along with a special iterative algorithm. The dependence of the stress intensity factor on (SIF) the wave number of the incident wave.
Introduction
Let us consider the phenomena occurring near the right or left tip of the crack when a harmonic tension-compression P-wave interacts with a crack. When loaded, the body goes through three phases near the crack tip: (i) the initial undeformed state (Fig. 1a), (ii) the tensile phase, corresponding to the maximum crack opening (Fig. 1b), and (iii) the compressive phase, corresponding to the maximum crack closure (Fig. 1c). Phase (iii) begins a half-period...
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References
Brogliato B (2016) Nonsmooth mechanics. Models, dynamics and control, 3rd edn. Springer, New York, 645 p
Cea J (1978) Optimization. Theory and algorithms. Springer, Berlin/Heidelberg/New York, 237 p
Cherepanov GP (1979) Mechanics of brittle fracture. McGraw Hill, New York, 935 p
Dominguez J (1993) Boundary elements in dynamics. Computational Mechanics Publications, Southampton, 707 p
Eringen AC, Suhubi ES (1975) Elastodynamics. Vol. 2. Linear theory. Academic, New York, pp 343–1003
Guz AN, Zozulya VV (2001) Fracture dynamics with allowance for a crack edges contact interaction. Int J Nonlinear Sci Numer Simul 2(3):173–233
Guz AN, Zozulya VV (2002) Elastodynamic unilateral contact problems with friction for bodies with cracks. International Applied Mechanics 38(8):895–932
Panagiotopoulos PD (1985) Inequality problems in mechanics and applications. Convex and nonconvex energy functions. Birkhauser, Stuttgart, 412 p
Sih GC, Loeber JF (1969) Wave propagation in an elastic solid with a line discontinuity of finite crack. Quarterly of Applied Mathematics 27(2):193–213
Zozulya VV (1990a) On dynamic problems on theory of cracks with contact, friction and sliding domains. Dokl Acad Nauk UkrSSR Ser A Phys Math Tech Sci 1:47–50. (in Russian)
Zozulya VV (1990b) On action of the harmonic loading on the crack in infinite body with allowance for the interaction of its edges. Dokl Acad Nauk UkrSSR Ser A Phys Math Tech Sci 4:46–49. (in Russian)
Zozulya VV (2011) Variational formulation and nonsmooth optimization algorithms in elastodynamic contact problems for cracked body. Comput Methods Appl Mech Eng 200(5–8):525–539
Zozulya VV (2015) Regularization of the divergent integrals. Comparison of classical and generalized functions approaches. Adv Comput Math 41:727–780
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Zozulya, V.V. (2019). Dynamical Contact Problems of Fracture Mechanics. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_278-1
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DOI: https://doi.org/10.1007/978-3-662-53605-6_278-1
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