# Three-dimensional problems in the dynamic fracture mechanics of materials with interface cracks (review)

A N Guz, I A Guz, A V Menshykov, V A Menshykov

Research output: Contribution to journalArticle

24 Citations (Scopus)

### Abstract

Three-dimensional problems in the dynamic fracture mechanics of materials with interface cracks are considered as nonclassical problems of fracture mechanics. Physically correct results in fracture mechanics in the case where the interaction of the crack edges must be taken into account are analyzed. The linear (classical) and nonlinear (nonclassical) problems of dynamic fracture mechanics for materials with interface cracks are formulated using the above approaches. A method for solving three-dimensional linear dynamic problems based on boundary integral equations for piecewise-homogeneous materials and the boundary-element method is outlined. This method can be used for incremental solution of nonlinear problems. The method involves the regularization of hypersingular integrals. New classes of three-dimensional linear dynamic problems for circular and elliptic interface cracks are solved. Numerical values of stress intensity factors obtained with the linear problem formulation are the first step toward calculating them in the nonlinear formulation. The first results obtained in solving nonlinear dynamic problems for interface cracks with interacting faces are briefly analyzed
Original language English 1-61 61 International Applied Mechanics 49 1 https://doi.org/10.1007/s10778-013-0551-4 Published - Jan 2013

### Fingerprint

Fracture mechanics
Cracks
Boundary integral equations
Boundary element method
Stress intensity factors

### Keywords

• nonclassical problems of fracture mechanics
• physically incorrect results
• interaction of crack edges
• spatial dynamic problems
• interface cracks
• boundary integral equations
• BEM
• penny-shaped and elliptic cracks

### Cite this

In: International Applied Mechanics, Vol. 49, No. 1, 01.2013, p. 1-61.

Research output: Contribution to journalArticle

@article{e53ac9b433b3406ca450e3edee165643,
title = "Three-dimensional problems in the dynamic fracture mechanics of materials with interface cracks (review)",
abstract = "Three-dimensional problems in the dynamic fracture mechanics of materials with interface cracks are considered as nonclassical problems of fracture mechanics. Physically correct results in fracture mechanics in the case where the interaction of the crack edges must be taken into account are analyzed. The linear (classical) and nonlinear (nonclassical) problems of dynamic fracture mechanics for materials with interface cracks are formulated using the above approaches. A method for solving three-dimensional linear dynamic problems based on boundary integral equations for piecewise-homogeneous materials and the boundary-element method is outlined. This method can be used for incremental solution of nonlinear problems. The method involves the regularization of hypersingular integrals. New classes of three-dimensional linear dynamic problems for circular and elliptic interface cracks are solved. Numerical values of stress intensity factors obtained with the linear problem formulation are the first step toward calculating them in the nonlinear formulation. The first results obtained in solving nonlinear dynamic problems for interface cracks with interacting faces are briefly analyzed",
keywords = "nonclassical problems of fracture mechanics, physically incorrect results, interaction of crack edges, spatial dynamic problems, interface cracks, boundary integral equations, BEM, penny-shaped and elliptic cracks",
author = "Guz, {A N} and Guz, {I A} and Menshykov, {A V} and Menshykov, {V A}",
year = "2013",
month = "1",
doi = "10.1007/s10778-013-0551-4",
language = "English",
volume = "49",
pages = "1--61",
journal = "International Applied Mechanics",
issn = "1063-7095",
publisher = "Springer New York",
number = "1",

}

TY - JOUR

T1 - Three-dimensional problems in the dynamic fracture mechanics of materials with interface cracks (review)

AU - Guz, A N

AU - Guz, I A

AU - Menshykov, A V

AU - Menshykov, V A

PY - 2013/1

Y1 - 2013/1

N2 - Three-dimensional problems in the dynamic fracture mechanics of materials with interface cracks are considered as nonclassical problems of fracture mechanics. Physically correct results in fracture mechanics in the case where the interaction of the crack edges must be taken into account are analyzed. The linear (classical) and nonlinear (nonclassical) problems of dynamic fracture mechanics for materials with interface cracks are formulated using the above approaches. A method for solving three-dimensional linear dynamic problems based on boundary integral equations for piecewise-homogeneous materials and the boundary-element method is outlined. This method can be used for incremental solution of nonlinear problems. The method involves the regularization of hypersingular integrals. New classes of three-dimensional linear dynamic problems for circular and elliptic interface cracks are solved. Numerical values of stress intensity factors obtained with the linear problem formulation are the first step toward calculating them in the nonlinear formulation. The first results obtained in solving nonlinear dynamic problems for interface cracks with interacting faces are briefly analyzed

AB - Three-dimensional problems in the dynamic fracture mechanics of materials with interface cracks are considered as nonclassical problems of fracture mechanics. Physically correct results in fracture mechanics in the case where the interaction of the crack edges must be taken into account are analyzed. The linear (classical) and nonlinear (nonclassical) problems of dynamic fracture mechanics for materials with interface cracks are formulated using the above approaches. A method for solving three-dimensional linear dynamic problems based on boundary integral equations for piecewise-homogeneous materials and the boundary-element method is outlined. This method can be used for incremental solution of nonlinear problems. The method involves the regularization of hypersingular integrals. New classes of three-dimensional linear dynamic problems for circular and elliptic interface cracks are solved. Numerical values of stress intensity factors obtained with the linear problem formulation are the first step toward calculating them in the nonlinear formulation. The first results obtained in solving nonlinear dynamic problems for interface cracks with interacting faces are briefly analyzed

KW - nonclassical problems of fracture mechanics

KW - physically incorrect results

KW - interaction of crack edges

KW - spatial dynamic problems

KW - interface cracks

KW - boundary integral equations

KW - BEM

KW - penny-shaped and elliptic cracks

U2 - 10.1007/s10778-013-0551-4

DO - 10.1007/s10778-013-0551-4

M3 - Article

VL - 49

SP - 1

EP - 61

JO - International Applied Mechanics

JF - International Applied Mechanics

SN - 1063-7095

IS - 1

ER -