Blaise Bourdin,
Gilles A. Francfort,
Jean-Jacques Marigo
Springer Netherlands
0e druk, 2010
9789048176243
The Variational Approach to Fracture
Specificaties
Paperback, 164 blz.
|
Engels
Springer Netherlands |
2010
ISBN13: 9789048176243
Rubricering
Levertijd ongeveer 9 werkdagen
Gratis verzonden
Samenvatting
Presenting original results from both theoretical and numerical viewpoints, this text offers a detailed discussion of the variational approach to brittle fracture. This approach views crack growth as the result of a competition between bulk and surface energy, treating crack evolution from its initiation all the way to the failure of a sample. The authors model crack initiation, crack path, and crack extension for arbitrary geometries and loads.
Specificaties
ISBN13:9789048176243
Taal:Engels
Bindwijze:paperback
Aantal pagina's:164
Uitgever:Springer Netherlands
Druk:0
Inhoudsopgave
1 Introduction;
2 Going variational; 2.1 Griffith’s theory; 2.2 The 1-homogeneous case – A variational equivalence; 2.3 Smoothness – The soft belly of Griffith’s formulation; 2.4 The non 1-homogeneous case – A discrete variational evolution; 2.5 Functional framework – A weak variational evolution; 2.6 Cohesiveness and the variational evolution;
3 Stationarity versus local or global minimality – A comparison; 3.1 1d traction; 3.1.1 The Griffith case – Soft device; 3.1.2 The Griffith case – Hard device; 3.1.3 Cohesive case – Soft device; 3.1.4 Cohesive case – Hard device; 3.2 A tearing experiment;
4 Initiation; 4.1 Initiation – The Griffith case; 4.1.1 Initiation – The Griffith case – Global minimality; 4.1.2 Initiation – The Griffith case – Local minimality; 4.2 Initiation – The cohesive case; 4.2.1 Initiation – The cohesive 1d case – Stationarity; 4.2.2 Initiation – The cohesive 3d case – Stationarity; 4.2.3 Initiation – The cohesive case – Global minimality;
5 Irreversibility; 5.1 Irreversibility – The Griffith case – Well-posedness of the variational evolution; 5.1.1 Irreversibility – The Griffith case – Discrete evolution; 5.1.2 Irreversibility – The Griffith case – Global minimality in the limit; 5.1.3 Irreversibility – The Griffith case – Energy balance in the limit; 5.1.4 Irreversibility – The Griffith case – The time-continuous evolution; 5.2 Irreversibility – The cohesive case;
6 Path;
7 Griffith vs. Barenblatt;
8 Numerics and Griffith; 8.1 Numerical approximation of the energy; 8.1.1 The first time step; 8.1.2 Quasi-static evolution; 8.2 Minimization algorithm; 8.2.1 The alternate minimization algorithm; 8.2.2 The backtracking algorithm; 8.3 Numerical experiments; 8.3.1 The 1D traction (hard device); 8.3.2 The Tearing experiment; 8.3.3 Revisiting the 2D traction experiment on a fiber reinforced matrix;
9 Fatigue; 9.1 Peeling Evolution; 9.2 The limitfatigue law when d tends to 0; 9.3 A variational formulation for fatigue; 9.3.1 Peeling revisited; 9.3.2 Generalization;
Appendix; Glossary; References.
2 Going variational; 2.1 Griffith’s theory; 2.2 The 1-homogeneous case – A variational equivalence; 2.3 Smoothness – The soft belly of Griffith’s formulation; 2.4 The non 1-homogeneous case – A discrete variational evolution; 2.5 Functional framework – A weak variational evolution; 2.6 Cohesiveness and the variational evolution;
3 Stationarity versus local or global minimality – A comparison; 3.1 1d traction; 3.1.1 The Griffith case – Soft device; 3.1.2 The Griffith case – Hard device; 3.1.3 Cohesive case – Soft device; 3.1.4 Cohesive case – Hard device; 3.2 A tearing experiment;
4 Initiation; 4.1 Initiation – The Griffith case; 4.1.1 Initiation – The Griffith case – Global minimality; 4.1.2 Initiation – The Griffith case – Local minimality; 4.2 Initiation – The cohesive case; 4.2.1 Initiation – The cohesive 1d case – Stationarity; 4.2.2 Initiation – The cohesive 3d case – Stationarity; 4.2.3 Initiation – The cohesive case – Global minimality;
5 Irreversibility; 5.1 Irreversibility – The Griffith case – Well-posedness of the variational evolution; 5.1.1 Irreversibility – The Griffith case – Discrete evolution; 5.1.2 Irreversibility – The Griffith case – Global minimality in the limit; 5.1.3 Irreversibility – The Griffith case – Energy balance in the limit; 5.1.4 Irreversibility – The Griffith case – The time-continuous evolution; 5.2 Irreversibility – The cohesive case;
6 Path;
7 Griffith vs. Barenblatt;
8 Numerics and Griffith; 8.1 Numerical approximation of the energy; 8.1.1 The first time step; 8.1.2 Quasi-static evolution; 8.2 Minimization algorithm; 8.2.1 The alternate minimization algorithm; 8.2.2 The backtracking algorithm; 8.3 Numerical experiments; 8.3.1 The 1D traction (hard device); 8.3.2 The Tearing experiment; 8.3.3 Revisiting the 2D traction experiment on a fiber reinforced matrix;
9 Fatigue; 9.1 Peeling Evolution; 9.2 The limitfatigue law when d tends to 0; 9.3 A variational formulation for fatigue; 9.3.1 Peeling revisited; 9.3.2 Generalization;
Appendix; Glossary; References.