The Griffith formula and J-integral for elastic bodies with Timoshenko inclusions

被引：24

作者：

Shcherbakov, V. V. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Lavrentyev Inst Hydrodynam, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Novosibirsk 630090, Russia

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2016年 / 96卷 / 11期

基金：

俄罗斯科学基金会;

关键词：

Timoshenko beam; thin elastic inclusion; crack; nonpenetration conditions; variational inequality; Griffith formula; J-integral; SHAPE SENSITIVITY-ANALYSIS; RIGID INCLUSION; INVARIANT INTEGRALS; ASYMPTOTIC-BEHAVIOR; CURVILINEAR CRACKS; INTERFACE CRACK; BODY; BOUNDARY; NONPENETRATION; PLATE;

D O I：

10.1002/zamm.201500145

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The paper contains an analysis of a two-dimensional equilibrium problem for an elastic body with a thin elastic inclusion. The thin elastic inclusion is modeled within the framework of Timoshenko beam theory. There is a crack on the interface between two media, displacements of the opposite crack faces are constrained with nonpenetration conditions. We derive the Griffith formula, which gives the first derivative of the energy functional with respect to the crack length. It is proved that the formula for the derivative can be represented as a path-independent integral along a smooth curve surrounding the crack tip. The invariant integral consists of a regular part and a singular part and is an analogue of the classical Eshelby-Cherepanov-Rice J-integral. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

引用

页码：1306 / 1317

页数：12

共 40 条

[1]

[Anonymous], 1998, PARTIAL DIFFERENTIAL

[2]

Bach M, 2000, MATH METHOD APPL SCI, V23, P515, DOI 10.1002/(SICI)1099-1476(200004)23:6<515::AID-MMA122>3.0.CO

[3]

2-S

[4]

BUDIANSKY B, 1973, J APPL MECH-T ASME, V40, P201, DOI 10.1115/1.3422926

[5] CONSERVATION LAWS IN ELASTICITY OF J-INTEGRAL TYPE [J].

CHEN, FHK ;

SHIELD, RT .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1977, 28 (01) :1-22

[6] CRACK PROPAGATION IN CONTINUOUS MEDIA [J].

CHEREPANOV, GP .

JOURNAL OF APPLIED MATHEMATICS AND MECHANICS-USSR, 1967, 31 (03) :503-+

[7]

Destuynder P., 1981, Math. Meth. Appl. Sci., V3, P70, DOI [DOI 10.1002/MMA.1670030106, 10.1002/mma.1670030106]

[8]

Griffith G.-A., 1921, Philos. Trans. R. Soc. London, V221, P163, DOI [10.1098/rsta.1921.0006, DOI 10.1098/RSTA.1921.0006]

[9]

GRISVARD P, 1991, SINGULARITIES BOUNDA

[10] THE DISPLACEMENT FIELD DUE TO AN INTERFACE CRACK ALONG AN ELASTIC INCLUSION IN A DIFFERING ELASTIC MATRIX [J].

HERRMANN, JM .

ACTA MECHANICA, 1994, 105 (1-4) :207-226

← 1 2 3 4 →