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Micromechanics of Fracture and Damage [Kõva köide]

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  • Formaat: Hardback, 334 pages, kõrgus x laius x paksus: 241x163x25 mm, kaal: 649 g
  • Ilmumisaeg: 08-Apr-2016
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 184821863X
  • ISBN-13: 9781848218635
Teised raamatud teemal:
Micromechanics of Fracture and DamageSuurem pilt
  • Formaat: Hardback, 334 pages, kõrgus x laius x paksus: 241x163x25 mm, kaal: 649 g
  • Ilmumisaeg: 08-Apr-2016
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 184821863X
  • ISBN-13: 9781848218635
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781848218635.html
Märksõnad:
This book deals with the mechanics and physics of fractures at various scales. Based on advanced continuum mechanics of heterogeneous media, it develops a rigorous mathematical framework for single macrocrack problems as well as for the effective properties of microcracked materials. In both cases, two geometrical models of cracks are examined and discussed: the idealized representation of the crack as two parallel faces (the Griffith crack model), and the representation of a crack as a flat elliptic or ellipsoidal cavity (the Eshelby inhomogeneity problem).

The book is composed of two parts:





The first part deals with solutions to 2D and 3D problems involving a single crack in linear elasticity. Elementary solutions of cracks problems in the different modes are fully worked. Various mathematical techniques are presented, including Neuber-Papkovitch displacement potentials, complex analysis with conformal mapping and Eshelby-based solutions. The second part is devoted to continuum micromechanics approaches of microcracked materials in relation to methods and results presented in the first part. Various estimates and bounds of the effective elastic properties are presented. They are considered for the formulation and application of continuum micromechanics-based damage models.
Notations xiii
Preface xv
Part
1. Elastic Solutions to Single Crack Problems		 1(172)
Chapter 1 Fundamentals of Plane Elasticity
3(30)
1.1 Complex representation of Airy's biharmonic stress function
3(4)
1.2 Force acting on a curve or an element of arc
7(2)
1.3 Derivation of stresses
9(2)
1.4 Derivation of displacements
11(1)
1.5 General form of the potentials φ and ψ
12(3)
1.6 Examples
15(3)
1.6.1 Circular cavity under pressure
15(1)
1.6.2 Circular cavity in a plane subjected to uniaxial traction at infinity
16(2)
1.7 Conformal mapping
18(8)
1.7.1 Application of conformal mapping to plane elasticity problems
18(2)
1.7.2 The domain σ is the unit disc |ζ| < 1
20(3)
1.7.3 The domain σ is the complement σ- of the unit disc
23(3)
1.8 The anisotropic case
26(3)
1.8.1 General features
26(2)
1.8.2 Stresses, displacements and boundary conditions
28(1)
1.9 Appendix: mathematical tools
29(4)
1.9.1 Theorem 1
30(1)
1.9.2 Theorem 2
31(1)
1.9.3 Theorem 3
31(2)
Chapter 2 Fundamentals of Elasticity in View of Homogenization Theory
33(38)
2.1 Green's function concept
33(1)
2.2 Green's function in two-dimensional conditions
34(4)
2.2.1 The general anisotropic case
34(1)
2.2.2 The isotropic case
35(3)
2.3 Green's function in three-dimensional conditions
38(3)
2.3.1 The general anisotropic case
38(1)
2.3.2 The isotropic case
39(2)
2.4 Eshelby's problems in linear microelasticity
41(13)
2.4.1 The (elastic) inclusion problem
41(3)
2.4.2 The Green operator of the infinite space
44(4)
2.4.3 The Green operator of a finite domain
48(2)
2.4.4 The inhomogeneity problem
50(1)
2.4.5 The inhomogeneity problem with stress boundary conditions
51(1)
2.4.6 The infinite heterogeneous elastic medium
52(2)
2.5 Hill tensor for the elliptic inclusion
54(6)
2.5.1 Properties of the logarithmic potential
54(3)
2.5.2 Integration of the r,ir,l term
57(2)
2.5.3 Components of the Hill tensor
59(1)
2.6 Hill's tensor for the spheroidal inclusion
60(5)
2.6.1 Components of the Hill tensor
63(1)
2.6.2 Series expansions of the components of the Hill tensor for flat spheroids
64(1)
2.7 Appendix
65(2)
2.8 Appendix: derivation of the χij
67(4)
Chapter 3 Two-dimensional Griffith Crack
71(32)
3.1 Stress singularity at crack tip
72(8)
3.1.1 Stress singularity in plane elasticity: modes I and II
73(5)
3.1.2 Stress singularity in antiplane problems in elasticity: mode III
78(2)
3.2 Solution to mode I problem
80(12)
3.2.1 Solution of PI
82(8)
3.2.2 Solution of PI
90(1)
3.2.3 Displacement jump across the crack surfaces
91(1)
3.3 Solution to mode II problem
92(6)
3.3.1 Solution of P'II
93(3)
3.3.2 Solution of PII
96(1)
3.3.3 Displacement jump across the crack surfaces
97(1)
3.4 Appendix: Abel's integral equation
98(3)
3.5 Appendix: Neuber—Papkovitch displacement potentials
101(2)
Chapter 4 The Elliptic Crack Model in Plane Strains
103(34)
4.1 The infinite plane with elliptic hole
103(9)
4.1.1 Fx = Fy = Γ = Γ' = 0
104(2)
4.1.2 Fx, Fy, Γ, Γ' is not = to 0
106(1)
4.1.3 Elliptic cavity in a plane subjected to a remote stress state at infinity
107(1)
4.1.4 Stress intensity factors
108(3)
4.1.5 Some remarks on unilateral contact
111(1)
4.2 Infinite plane with elliptic hole: the anisotropic case
112(18)
4.2.1 General properties
112(3)
4.2.2 Complex potentials for an elliptic cavity in the presence of traction at infinity
115(1)
4.2.3 Complex potentials for an elliptic cavity in the case of shear at infinity
116(1)
4.2.4 Stresses in the limit case b -> 0 (crack)
117(4)
4.2.5 Displacement discontinuities
121(2)
4.2.6 Closed cracks
123(7)
4.3 Eshelby approach
130(7)
4.3.1 Mode I
130(3)
4.3.2 Mode II
133(4)
Chapter 5 Griffith Crack in 3D
137(18)
5.1 Griffith circular (penny-shaped) crack in mode I
138(6)
5.1.1 Solution of P'I
139(4)
5.1.2 Solution of PI
143(1)
5.2 Griffith circular (penny-shaped) crack under shear loading
144(11)
5.2.1 Solution of P'II-
146(5)
5.2.2 Solution of PII
151(4)
Chapter 6 Ellipsoidal Crack Model: the Eshelby Approach
155(8)
6.1 Mode I
156(3)
6.2 Mode II
159(4)
Chapter 7 Energy Release Rate and Conditions for Crack Propagation
163(10)
7.1 Driving force of crack propagation
163(4)
7.2 Stress intensity factor and energy release rate
167(6)
Part
2. Homogenization of Microcracked Materials		 173(132)
Chapter 8 Fundamentals of Continuum Micromechanics
175(22)
8.1 Scale separation
175(2)
8.2 Inhomogeneity model for cracks
177(10)
8.2.1 Uniform strain boundary conditions
177(4)
8.2.2 Uniform stress boundary conditions
181(1)
8.2.3 Linear elasticity with uniform strain boundary conditions
182(3)
8.2.4 Linear elasticity with uniform stress boundary conditions
185(2)
8.3 General results on homogenization with Griffith cracks
187(10)
8.3.1 Hill's lemma with Griffith cracks
187(1)
8.3.2 Uniform strain boundary conditions
188(2)
8.3.3 Uniform stress boundary conditions
190(1)
8.3.4 Derivation of effective properties in linear elasticity: principle of the approach
190(4)
8.3.5 Appendix
194(3)
Chapter 9 Homogenization of Materials Containing Griffith Cracks
197(16)
9.1 Dilute estimates in isotropic conditions
197(9)
9.1.1 Stress-based dilute estimate of stiffness
199(3)
9.1.2 Stress-based dilute estimate of stiffness with closed cracks
202(2)
9.1.3 Strain-based dilute estimate of stiffness with opened cracks
204(1)
9.1.4 Strain-based dilute estimate of stiffness with closed cracks
205(1)
9.2 A refined strain-based scheme
206(2)
9.3 Homogenization in plane strain conditions for anisotropic materials
208(5)
9.3.1 Opened cracks
208(3)
9.3.2 Closed cracks
211(2)
Chapter 10 Eshelby-based Estimates of Strain Concentration and Stiffness
213(22)
10.1 Dilute estimate of the strain concentration tensor: general features
213(2)
10.1.1 The general case
213(2)
10.2 The particular case of opened cracks
215(5)
10.2.1 Spheroidal crack
215(1)
10.2.2 Elliptic crack
216(2)
10.2.3 Crack opening change
218(2)
10.3 Dilute estimates of the effective stiffness for opened cracks
220(6)
10.3.1 Opened parallel cracks
222(2)
10.3.2 Opened randomly oriented cracks
224(2)
10.4 Dilute estimates of the effective stiffness for closed cracks
226(3)
10.4.1 Closed parallel cracks
228(1)
10.4.2 Closed randomly oriented cracks
228(1)
10.5 Mori—Tanaka estimate of the effective stiffness
229(6)
10.5.1 Opened cracks
231(2)
10.5.2 Closed cracks
233(2)
Chapter 11 Stress-based Estimates of Stress Concentration and Compliance
235(16)
11.1 Dilute estimate of the stress concentration tensor
235(1)
11.2 Dilute estimates of the effective compliance for opened cracks
236(4)
11.2.1 Opened parallel cracks
237(2)
11.2.2 Opened randomly oriented cracks
239(1)
11.2.3 Discussion
239(1)
11.3 Dilute estimate of the effective compliance for closed cracks
240(4)
11.3.1 3D case
241(1)
11.3.2 2D case
242(1)
11.3.3 Stress concentration tensor
243(1)
11.3.4 Comparison with other estimates
244(1)
11.4 Mori—Tanaka estimates of effective compliance
244(2)
11.4.1 Opened cracks
246(1)
11.4.2 Closed cracks
246(1)
11.5 Appendix: algebra for transverse isotropy and applications
246(5)
Chapter 12 Bounds
251(22)
12.1 The energy definition of the homogenized stiffness
252(3)
12.2 Hashin—Shtrikman's bound
255(18)
12.2.1 Hashin—Shtrikman variational principle
255(4)
12.2.2 Piecewise constant polarization field
259(2)
12.2.3 Random microstructures
261(9)
12.2.4 Application of the Ponte-Castaneda and Willis (PCW) bound to microcracked media
270(3)
Chapter 13 Micromechanics-based Damage Constitutive Law and Application
273(32)
13.1 Formulation of damage constitutive law
273(4)
13.1.1 Description of damage level by a single scalar variable
274(2)
13.1.2 Extension to multiple cracks
276(1)
13.2 Some remarks concerning the loss of uniqueness of the mechanical response in relation to damage
277(3)
13.3 Mechanical fields and damage in a hollow sphere subjected to traction
280(16)
13.3.1 General features
280(4)
13.3.2 Case of damage model based on the dilute estimate
284(1)
13.3.3 Complete solution in the case of the damage model based on PCW estimate
285(11)
13.4 Stability of the solution to damage evolution in a hollow sphere
296(9)
13.4.1 The MT damage model
298(2)
13.4.2 The general damage model [ 13.44]
300(5)
Bibliography 305(4)
Index 309
Luc Dormieux is Professor at Ecole Nationale des Ponts et Chaussées (Laboratoire NAVIER) in Marne-la-Vallée, France.

Djimédo Kondo is Professor at Sorbonne University (UPMC, Institut D'Alembert) in Paris, France.