Elastodynamic Unilateral Contact Problems with Friction for Bodies with Cracks

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.

[1]  D. Rooke,et al.  Numerical Fracture Mechanics , 1990 .

[2]  C. Brebbia,et al.  Boundary Elements IX , 1987 .

[3]  A. N. Guz On Foundation of Non-Destructive Method of Determination of Three-Axial Stresses in Solids , 2001 .

[4]  A. N. Guz,et al.  Fracture Dynamics with Allowance for Crack Edge Contact Interaction , 2001 .

[5]  I. Ekeland,et al.  Convex analysis and variational problems , 1976 .

[6]  V. V. Zozulya Investigation of the contact of edges of cracks interacting with a plane, longitudinal, harmonic wave , 1991 .

[7]  V. V. Zozulya,et al.  Dynamic Fracture Mechanics With Crack Edges Contact Interaction , 1998 .

[8]  J. Achenbach I – Dynamic Effects in Brittle Fracture , 1974 .

[9]  Dimitri E. Beskos,et al.  Boundary Element Methods in Dynamic Analysis: Part II (1986-1996) , 1997 .

[10]  John W. Hutchinson,et al.  Dynamic Fracture Mechanics , 1990 .

[11]  P. D. Panagiotopoulos,et al.  The Boundary Integral Approach to Static and Dynamic Contact Problems: Equality and Inequality Methods , 1992 .

[12]  T. Cruse Boundary Element Analysis in Computational Fracture Mechanics , 1988 .

[13]  P. Panagiotopoulos,et al.  On the consideration of unilateral contact and friction in cracks the boundary integral method , 1992 .

[14]  A. Guz Formulation of problems in dynamic fracture mechanics , 1999 .

[15]  K. Washizu Variational Methods in Elasticity and Plasticity , 1982 .

[16]  J. Domínguez Boundary elements in dynamics , 1993 .

[17]  R. Glowinski,et al.  Numerical Analysis of Variational Inequalities , 1981 .

[18]  Contact Interaction of the Faces of a Rectangular Crack under Normally Incident Tension–Compression Waves , 2002 .

[19]  J. Hadamard,et al.  Lectures on Cauchy's Problem in Linear Partial Differential Equations , 1924 .

[20]  D. Beskos,et al.  Boundary Element Methods in Elastodynamics , 1988 .

[21]  V. V. Zozulya,et al.  Dynamic Contact Problem for a Plane with a Finite Crack , 2002 .

[22]  Heinz Antes,et al.  Time domain boundary element method approaches in elastodynamics: a comparative study , 1986 .

[23]  B. Steverding,et al.  Dynamics of brittle fracture , 1972 .

[24]  Dietmar Gross,et al.  On Wave Propagation in Elastic Solids with Cracks , 1997 .

[25]  V. Z. Parton Dynamic fracture mechanics , 1989 .

[26]  M. Aliabadi Boundary Element Formulations in Fracture Mechanics , 1997 .

[27]  Dimitri E. Beskos,et al.  Boundary Element Methods in Dynamic Analysis , 1987 .

[28]  J. Sládek,et al.  Regularization Techniques Applied to Boundary Element Methods , 1994 .

[29]  Panagiotis D. Panagiotopoulos,et al.  Hemivariational Inequalities: Applications in Mechanics and Engineering , 1993 .

[30]  V. V. Mikhas’kiv Opening-Function Simulation of the Three-Dimensional Nonstationary Interaction of Cracks in an Elastic Body , 2001 .

[31]  V. V. Zozulya,et al.  Dynamic fracture mechanics with contact interaction at the crack edges , 2000 .

[32]  J. Hadamard,et al.  Lectures on Cauchy's Problem in Linear Partial Differential Equations , 1924 .

[33]  G. A. Watson A treatise on the theory of Bessel functions , 1944 .

[34]  E. Sternberg,et al.  Three-Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity , 1980 .

[35]  S. L. Sobolev,et al.  Applications of functional analysis in mathematical physics , 1963 .

[36]  A. N. Guz,et al.  Contact interaction between crack edges under a dynamic load , 1992 .

[37]  V. V. Zozulya,et al.  Solution of three-dimensional problems of the dynamic theory of elasticity for bodies with cracks using hypersingular integrals , 2000 .

[38]  P. Panagiotopoulos Inequality Problems in Mechanics and Applications: Convex and Nonconvex Energy Functions , 1985 .

[39]  G. Fichera Boundary Value Problems of Elasticity with Unilateral Constraints , 1973 .

[40]  W. C. Cooley,et al.  Mechanics of Brittle Fracture , 1982 .

[41]  V. V. Zozulya,et al.  Weakly singular, singular and hypersingular integrals in 3-D elasticity and fracture mechanics , 1999 .

[42]  G. P. Cherepanov,et al.  Fracture : a topical encyclopedia of current knowledge , 1998 .

[43]  Vladimir Sladek,et al.  Stress analysis by boundary element methods , 1989 .

[44]  George D. Manolis,et al.  A comparative study on three boundary element method approaches to problems in elastodynamics , 1983 .

[45]  Georgios E. Stavroulakis,et al.  Transient elastodynamics around cracks including contact and friction , 1999 .

[46]  A. N. Guz,et al.  Description and Study of Some Nonclassical Problems of Fracture Mechanics and Related Mechanisms , 2000 .

[47]  G. Tolstov Fourier Series , 1962 .

[48]  J. Oden,et al.  Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods , 1987 .

[49]  A. N. Guz',et al.  Diffraction of elastic waves , 1978 .

[50]  J. Haslinger,et al.  Solution of Variational Inequalities in Mechanics , 1988 .

[51]  H. Hong,et al.  Review of Dual Boundary Element Methods With Emphasis on Hypersingular Integrals and Divergent Series , 1999 .

[52]  V. V. Zozulya,et al.  Influence of contact interaction between the sides of crack on characteristics of failure mechanics in action ofP- andSV-waves , 1999 .

[53]  V.V. Zozulya,et al.  Boundary integral equation and the existence theorems in contact problems with friction , 2000 .

[54]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[55]  A. N. Guz',et al.  The Physical Fundamentals of the Ultrasonic Nondestructive Stress Analysis of Solids , 2000 .

[56]  A. Mal Interaction of elastic waves with a Griffith crack , 1970 .