Abstract
A complete and consistent review is made of the results of studies into the contact interaction of crack edges by methods of fracture mechanics. Also some new results are presented.
Similar content being viewed by others
REFERENCES
M. Abramowitz and I. A. Stegun, “Handbook of mathematical functions, with formulas, graphs and mathematical tables,” Appl. Math. Ser., 55 (1964).
J. D. Achenbach, “Dynamic effects in brittle fracture,” in: S. Nemat-Nasser (ed.), Mechanics Today, Vol. 1, Pergamon, New York (1974), pp. 1–57.
R. A. Adams, Sobolev Spaces, Academic Press, New York (1975).
M. H. Aliabadi, “Boundary element formulations in fracture mechanics,” Appl. Mech. Rev., 50, No. 2, 83–96 (1997).
M. H. Aliabadi and D. P. Rooke, Numerical Fracture Mechanics, Comput. Mech. Publ., Southampton (1991).
H. Antes and P. D. Panagiotopoulos, The Boundary Integral Approach to Static and Dynamic Contact Problems, Birkhauser, Basel-Boston-Berlin (1992).
J. Balas, J. Sladek, and V. Sladek, Stress Analysis by Boundary Element Methods, Elsevier, Amsterdam (1989).
P. K. Banerjee, Boundary Element Method in Engineering Science, McGraw Hill, New York-London (1994).
R. E. Bellman, R. E. Kalaba, and J. Lockett, Numerical Inversion of the Laplace Transform: Application to Biology, Economics, Engineering and Physics, Amer. Elsevier, New York (1966).
D. E. Beskos, “Boundary element methods in dynamic analysis,” Appl. Mech. Rev., 40, No. 1, 1–23 (1987).
D. E. Beskos, “Boundary element methods in dynamic analysis: Part II (1986-1996),” Appl. Mech. Rev., 50, No. 3, 149–197 (1997).
J. T. Chen and H.-K. Hong, “Review of dual boundary element methods with emphasis on hypersingular integrals and divergent series,” Appl. Mech. Rev., 52, No. 1, 17–33 (1999).
G. P. Cherepanov, Mechanics of Brittle Fracture, McGraw Hill, New York (1979).
S. N. Atluri, Computational Methods in the Mechanics of Fracture, North-Holland, New York (1986).
T. A. Cruse, Boundary Element Analysis in Computational Fracture Mechanics, Kluwer Academic Publishers, Dordrecht-Boston-London (1988).
J. Dominguez, Boundary Elements in Dynamics, Comput. Mech. Publ., Southampton (1993).
G. Duvaut and J.-L. Lions, Inequalities in Physics and Mechanics, Springer-Verlag, Berlin (1979).
I. Ekeland and R. Témam, Convex Analysis and Variational Problems, North-Holland, Amsterdam (1975).
A. C. Eringen and E. S. Suhubi, Linear Theory, Vol. 2 of the series Elastodynamics, Academic Press, New York (1975).
G. Fichera, “Boundary value problems of elasticity with unilateral constraints,” in: S. Flugge (ed.), Encyclopedia of Physics, Vol. Vla/2, Springer-Verlag, Berlin (1972).
H. Liebowitz (ed.), Fracture. An Advanced Treatise, Vols. 1-7, Acad. Press, New York-London (1968-1972).
G. P. Cherepanov (ed.), Fracture. A Topical Encyclopedia of Current Knowledge, Krieger Publ Comp. Malabar, Florida (1998).
L. B. Freund, Dynamic Fracture Mechanics, Cambridge University Press, New York (1990).
I. M. Gel'fand and G. E. Shilov, Generalized Functions, Vol. 1, Academic Press, New York (1964).
R. Glowinski, J.-L. Lions, and R. Tremolieres, Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam (1981).
A. N. Guz, Brittle Fracture of Materials with Initial Stresses, Vol. 2 of the four-volume five-book series Nonclassical Problems of Fracture Mechanics [in Russian], Naukova Dumka, Kiev (1991).
A. N. Guz, “Formulation of problems in dynamic fracture mechanics,” Int. Appl. Mech., 35, No. 6, 531–536 (1999).
A. N. Guz, “Description and study of some nonclassical problems of fracture mechanics and related mechanisms,” Int. Appl. Mech., 36, No. 12, 1537–1564 (2000).
A. N. Guz, “On foundation of nondestructive method of determination of three-axis stresses in solids,” Int. Appl. Mech., 37, No. 7, 899–905 (2001).
A. N. Guz, V. D. Kubenko, and M. A. Cherevko, Diffraction of Elastic Waves [in Russian], Naukova Dumka, Kiev (1978).
A. N. Guz and F. G. Makhort, “The physical fundamentals of the ultrasonic nondestructive stress analysis of solids,” Int. Appl. Mech., 36, No. 9, 1119–1149 (2000).
A. N. Guz and V. V. Zozulya, “Dynamic problems of the elasticity theory with restrictions in the form of inequalities,” Dokl. AN USSR, Ser. A, Fiz. Mat. Tekhn. Nauki, 5, 47–50 (1991).
A. N. Guz and V.V. Zozulya, “Dynamic problem for a plane with a slit, including the interaction of the edges,” Dokl. AN USSR, 318, No. 2, 304–307, (1991).
A. N. Guz. and V.V. Zozulya, “Dynamic contact problem for a plane with two cracks,” Dokl. AN USSR, 321, No. 2, 278–280 (1991).
A. N. Guz, and V. V. Zozulya, “Contact interaction between crack edges under a dynamic load,” Prikl. Mekh., 28, No. 7, 407–414 (1992).
A. N. Guz (ed.) and V. V. Zozulya, Brittle Fracture of Structural Materials under Dynamic Loading, Vol. 4, Book 2 of the four-volume five-book series Nonclassical Problems of Fracture Mechanics [in Russian] Naukova Dumka, Kiev (1993).
A. N. Guz and V. V. Zozulya, “Dynamic problems of fracture mechanic, neglecting the contact interaction of the crack edges,” Prikl. Mekh., 30, No. 10, 3–22 (1994).
A. N. Guz and V. V. Zozulya, “Dynamic problems of fracture mechanic, including the contact interaction of the crack edges,” Prikl. Mekh., 31, No. 1, 1–31 (1995).
A. N. Guz and V. V. Zozulya, “About taking into account the contact of cracks edges under dynamic loads,” Mater. Sci., 32, No. 1, 38–52 (1996).
A. N. Guz and V. V. Zozulya, “Fracture dynamics with allowance for the contact interaction of crack edges,” Int. J. Nonlin. Sci. Numer. Simul., 2, No. 3, 173–233 (2001).
J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations, Yale University Press, New Haven (1923).
I. Hlavacek, J. Haslinger, J. Necas, and J. Lovisec, Solution of Variational Inequalities in Mechanics, Springer-Verlag, New York-Berlin-Heidelberg-London-Paris-Tokyo (1988).
N. Kikuchi and J. T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods, SIAM, Philadephia (1987).
A. S. Kravchuk, “Theory of contact problems with allowance for friction on the surface of contact,” J. Appl. Mat. Mech., 44, No. 1, 122–129 (1980).
A. S. Kravchuk, “Variational method in dynamic contact problems,” in: Mechanics of Deformable Bodies and Structures [in Russian], Izd. AN Arm. SSR, Erevan (1985), pp. 235–241.
V. D. Kupradze, T. G. Gegelia, M. O. Bashelishvili, and T. V. Burkhuladze, Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity, North-Holland, Amsterdam (1979).
A. K. Mal, “Interaction of elastic waves with a Griffith crack,” Int. J. Eng. Sci., 8 No. 8, 763–776 (1970).
G. D. Manolis, “A comparative study on three boundary element method approaches to problems in elastodynamics,” Int. J. Eng. Sci., 19, No. 1, 73–91 (1983).
G. D. Manolis and D. E. Beskos, Boundary Element Methods in Elastodynamics, Unwin Hyman (Champ & Hall), London (1988).
V. V. Mikhas'kiv, “Opening-function simulation of the three-dimensional nonstationary interaction of cracks in an elastic body,” Int. Appl. Mech., 37, No. 1, 75–84 (2001).
P. O. Panagiotopoulos, Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functions, Birkhauser, Stuttgart (1985).
P. O. Panagiotopoulos, Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, Berlin-Heidelberg-New York (1993).
V. Z. Parton and B. C. Boriskovskii, Dynamic Fracture Mechanics [in Russian], Mashinostroenie, Moscow (1985).
V. Z. Parton and B. G. Boriskovskii, Dynamics of Brittle Fracture [in Russian], Mashinostroenie, Moscow (1988).
G. Ya. Popov and Yu. A. Morozov, “Diffraction of a torsional wave coming from a center of rotation by a semi-infinite cylindrical crack,” Int. Appl. Mech., 37, No. 11, 1458–1464 (2001).
S. L. Sobolev, “Applications of functional analysis in mathematical physics,” in: Translation of American Mathematical Society, 7, Mathematical Monograph (1963).
C. C. Spyrakos and H. Antes, “Time domain boundary element method approaches in elastodynamics: a comparative study,” Comput. Struct., 24, No. 4, 529–539 (1986).
G. E. Stavoulakis, H. Antes, and P. O. Panagiotopoulos, “Transient elasodynamics around cracks including contact and friction,” Comput. Meth. Appl. Mech. Eng., 177, No. 3/4, 427–440 (1999).
M. Tanaka, V. Sladek, and J. Sladek, “Regularization techniques applied to boundary element methods,” Appl. Mech. Rev., 47, No. 10, 457–499 (1994).
P. S. Theocaris and P. D. Panagiotopoulos, “On the consideration of unilateral contact and friction in cracks. The boundary integral method,” Int. J. Num. Meth. Eng., 35, 1697–1708 (1992).
G. P. Tolstov, Fourier Series [in Russian], Nauka, Moscow (1980).
K. Washizu, Variational Methods in Elasticity and Plasticity, Pergamon Press, New York (1982).
G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, London (1966).
J. Xing and Z. Zheng, “Some general theorems and generalized and piecewise generalized variational principles for linear elastodynamics,” Appl. Math. Mech., 13, No. 9, 825–840 (1992).
C. Zhang and D. Gross, On Wave Propagation in Elastic Solids with Cracks, Comput. Mech. Publ., Southampton (1998).
V. V. Zozulya, “On dynamic problems of the crack theory with regions of contact, engagement and slip,” Dokl. AN USSR, Ser. A, Fiz. Mat. Tekhn. Nauki, 47–50 (1990).
V. V. Zozulya, “On solvability of dynamic problems of the theory of cracks with contact, adhesion, and slip areas,” Dokl. AN USSR, Ser. A, Fiz. Mat. Tekhn. Nauki, 3, 53–55 (1990).
V. V. Zozulya, “On the action of a harmonic load on an infinite body with a crack whose edges interact,” Dokl. AN USSR, Ser. A, Fiz. Mat. Tekhn. Nauki, 4, 46–49 (1990).
V. V. Zozulya, “Integrals of Hadamard type in a dynamic problem of crack theory,” Dokl. AN USSR, Ser. A, Fiz. Mat. Tekhn. Nauki, 2, 19–22 (1991).
V. V. Zozulya, “Investigation of the contact of edges of cracks interacting with a plane, longitudinal, harmonic wave,” Sov. Appl. Mech., 27, No. 12, 1191–1195 (1991).
V. V. Zozulya, “Dynamic problem for a plane with two cracks, including the contact interaction of crack edges,” Dokl. AN USSR, Ser. A, Fiz. Mat. Tekhn. Nauki, 8, 75–80 (1991).
V. V. Zozulya, “Contact interaction between crack edges and an infinite plane under a harmonic load,” Prikl. Mekh., 28, No. 1, 61–65 (1992).
V. V. Z ozulya, “Study into the contact of crack edges under a harmonic wave,” Prikl. Mekh., 28, No. 2, 95–100 (1992).
V. V. Zozulya, “Method of boundary functionals in dynamic contact problems for bodies with cracks,” Dokl. AN Ukrainy, 2, 38–44 (1992).
V. V. Zozulya, “Harmonic loading of the edges of two colinear cracks in a plane,” Prikl. Mekh., 28, No. 3, 170–173 (1992).
V. V. Zozulya, “On solving dynamic problems for bodies with cracks using the method of boundary integral equations,” Dokl. AN Ukrainy, 3, 38–43 (1992).
V. V. Zozulya, “Variational principles and algorithms in contact problem with friction,” in: N. Mastorakis, V. Mladenov, R. Suter, and L. J. Wang (eds.), Advances in Scientific Computing, Computational Intelligence and Applications, WSES Press, Danvers (2001), pp. 181–186.
V. V. Zozulya, “Variational principles and algorithms in elastodynamic contact problem with friction,” in: S. N. Atluri, T. Nishioka, and M. Kikuchi (eds.), Advances in Computational and Engineering Sciences, Tech. Science Press, Puerto Vallarta, Mexico (2001).
V. V. Zozulya, “Fracture dynamics with allowance for crack edge contact interaction,” in: C. Constanda, P. Schiavone, and A. Mioduchowski, Integral Methods in Science and Engineering, Birkhauser, Boston (2002), pp. 257–262.
V. V. Zozulya, and N. V. Fenchenko, “Influence of contact interaction between the sides of crack on characteristics of failure mechanics in action of P-and SV-waves,” Int. Appl. Mech., 35, No. 2, 175–180 (1999).
V.V. Zozulya and P. I. Gonzalez-Chi, “Weakly singular, singular, and hypersingular integrals in elasticity and fracture mechanics,” J. Chinese Inst. Eng., 22, No. 6, 763–775 (1999).
V. V. Zozulya and P. I. Gonzalez-Chi, “Application of the BIE with hypersingular integrals in fracture mechanics,” in: C. A. Brebbia (ed.), Boundary Elements XXII, Computational Mechanics Publications, Southampton, UK and Boston, USA (2000), pp. 233–242.
V.V. Zozulya and P. I. Gonzalez-Chi, “Dynamic fracture mechanics with crack edges contact interaction,” Eng. Anal. Bound. Elem., 24, No. 9, 643–659 (2000).
V. V. Zozulya and A. N. Lukin, “Solution of three-dimensional problems in fracture mechanics by the method of boundary integral equations,” Int. Appl. Mech., 34, No. 6, 544–551 (1988).
V. V. Zozulya and V. A. Men'shikov, “Contact interaction between the edges of a crack in a plane under harmonic loading,” Int. Appl. Mech., 30, No. 12, 986–989 (1994).
V. V. Zozulya and V. A. Men'shikov, “Solution of three-dimensional problems of the dynamic theory of elasticity for bodies with cracks using hypersingular integrals,” Int. Appl. Mech., 36, No. 1, 74–81 (2000).
V. V. Zozulya and A. V. Men'shikov, “Contact interaction of the faces of a rectangular crack under normally incident tension-compression waves,” Int. Appl. Mech., 38, No. 3, 302–307 (2002).
V. V. Zozulya and A. V. Men'shikov, “On one contact problem in fracture mechanics for a normally incident tension-compression wave,” Int. Appl. Mech., 38, No. 7, 824–828 (2002).
V. V. Zozulya and O. V. Menshykov, “3-D fracture dynamics with allowance for crack edges contact interaction,” in: Proc. 15th ASCE Engineering Mechanics Division Conference, The Columbia University, New York (2002).
V. V. Zozulya and M. V. Men'shikova, “Study of iterative algorithms for solution of dynamic contact problems for elastic cracked bodies,” Int. Appl. Mech., 38, No. 5, 573–577 (2002).
V. V. Zozulya and M. V. Men'shikova, “Dynamic contact problem for a plane with a finite crack,” (to be published in Int. Appl. Mech., 38, No. 12 (2002)).
V. V. Zozulya, and P. Rivera, “Dynamic fracture mechanics with crack edges contact interaction,” in: A. Kassab, M. Chopra, and C. A. Brebbia (eds.), Boundary Elements XX, Computational Mechanics Publications, Southampton, UK and Boston, New York (1998), pp. 23–32.
V. V. Zozulya, and P. Rivera, “Boundary integral equations and problem of existence in contact problems with friction,” J. Chinese Inst. Eng., 3, No. 3, 313–320 (2000).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Guz, A.N., Zozulya, V.V. Elastodynamic Unilateral Contact Problems with Friction for Bodies with Cracks. International Applied Mechanics 38, 895–932 (2002). https://doi.org/10.1023/A:1021266113662
Issue Date:
DOI: https://doi.org/10.1023/A:1021266113662