Quasistatic delamination problem

Continuum Mechanics and Thermodynamics

Volumn 21, Issue 3, 2009, Pages 223-235

  Roubíček, Tomáš ^a,b   Scardia, Lucia ^c   Zanini, Chiara ^d  

^a CHARLES UNIVERSITY   (Czech Republic)

^b INSTITUTE OF THERMOMECHANICS   (Czech Republic)

^c UNIVERSITY OF BONN   (Germany)

^d UNIVERSITY OF UDINE   (Italy)

Author keywords

convergence; Debonding; Delamination; Energetic formulation; Rate independent processes

Indexed keywords

BODY FORCES; COMPUTER IMPLEMENTATIONS; ELASTIC BODY; ENERGETIC FORMULATION; ENERGETIC SOLUTIONS; EXTERNAL LOADING; QUASI-STATIC; RATE-INDEPENDENT PROCESS; RATE-INDEPENDENT PROCESSES; TIME-DEPENDENT;

DEBONDING; GLUES; GLUING; STEEL SHEET;

DELAMINATION;

EID: 70350566564     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-009-0106-4     Document Type: Article

References (36)

1. Barenblatt, G.: The mathematical theory of equilibrium cracks in brittle fracture. In: Advances in Applied Mechanics, vol. 7, pp. 55-129. Academic Press, New York (1962)
2. E. Bonetti G. Bonfanti R. Rossi 2008 Global existence for a contact problem with adhesion Math. Methods Appl. Sci. 31 1029 1064 1145.35301 10.1002/mma.957 2419088
3. Braides A.: Γ-convergence for beginners volume 22 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford (2002)
4. D. Bucur G. Buttazzo A. Lux 2008 Quasistatic evolution in debonding problems via capacitary methods Arch. Ration. Mech. Anal. 190 2 281 306 1155.74030 10.1007/s00205-008-0166-9 2448320
5. F. Cagnetti 2008 A vanishing viscosity approach to fracture growth in a cohesive zone model with prescribed crack path Math. Models Methods Appl. Sci. 18 1027 1071 1154.49005 10.1142/S0218202508002942 2435184
6. Cagnetti, F., Toader, R.: Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach. ESAIM Control Optim. Calc. Var. (2009) Accepted (SISSA Preprint No. 56/2007/M)
7. J. Cook J. Gordon C. Evans D. Marsh 1964 A mechanism for the control of crack propagation in all-brittle systems Proc. R. Soc. Lond. Ser. A 282 508 520 10.1098/rspa.1964.0248
8. Dacorogna B.: Weak Continuity and Weak Lower Semicontinuity of Nonlinear Functionals. Springer-Verlag, Berlin (1982)
9. Dal Maso G.: An Introduction to Γ-Convergence. Birkhäuser, Boston (1993)
10. G. Dal Maso G. Francfort R. Toader 2005 Quasistatic crack growth in nonlinear elasticity Arch. Ration. Mech. Anal. 176 165 225 1064.74150 10.1007/s00205-004-0351-4 2186036 (Pubitemid 40579676)
11. G. Dal Maso C. Zanini 2007 Quasi-static crack growth for a cohesive zone model with prescribed crack path Proc. R. Soc. Edinburgh Sect. A 137 253 279 1116.74004 10.1017/S030821050500079X 2360770
12. E. De Giorgi 1977 Γ-convergenza e G-convergenza Boll. Unione Mat. Ital., V. Ser. A 14 213 220 0389.49008
13. Fonseca, I., Kružík, M.: Oscillations and concentrations generated by A -free mappings and weak lower semicontinuity of integral functionals. ESAIM Control Optim. Calc. Var. (2009) in print. doi: 10.1051/cocv/2009006
14. I. Fonseca S. Müller 1999 A-quasiconvexity, lower semicontinuity, and Young measures SIAM J. Math. Anal 30 1355 1390 0940.49014 10.1137/S0036141098339885 1718306
15. G. Francfort A. Mielke 2006 Existence results for a class of rate-independent material models with nonconvex elastic energies J. Reine Angew. Math. 595 55 91 1101.74015 2244798
16. Frémond M.: Non-Smooth Thermomechanics. Springer-Verlag, Berlin (2002)
17. A. Griffith 1921 The phenomena of rupture and flow in solids Philos. Trans. R. Soc. Lond. Ser. A. Math. Phys. Eng. Sci. 221 163 198 10.1098/rsta.1921.0006
18. I. Hlaváček J. Nečas 1970 On inequalities of Korn's type Arch. Ration. Mech. Anal. 36 305 334 0193.39001 10.1007/BF00249518
19. D. Knees A. Mielke C. Zanini 2008 On the inviscid limit of a model for crack propagation Math. Models Methods Appl. Sci. 18 1529 1569 1151.49014 10.1142/S0218202508003121 2446401
20. Knees, D., Zanini, C., Mielke, A.: Crack growth in polyconvex materials. Phys. D (2009, in print). doi: 10.1016/j.physd.2009.02.008
21. M. Kočvara A. Mielke T. Roubíček 2006 A rate-independent approach to the delamination problem Math. Mech. Solids 11 423 447 1133.74038 10.1177/1081286505046482 2245202 (Pubitemid 44070515)
22. D. Leguillon 2002 Strengh or toughness? A criterion for crack onset at a notch Eur. J. Mech. A/Solids 21 61 72 1061.74047 10.1016/S0997-7538(01)01184-6 (Pubitemid 34237283)
23. V.I. Levitas 1995 The postulate of realizability: formulation and applications to the post-bifurcation behaviour and phase transitions in elastoplastic materials. I, II Int. J. Eng. Sci. 33 7 921 945 0899.73132 10.1016/0020-7225(94)00117-3 1324158 947-971
24. A. Mainik A. Mielke 2005 Existence results for energetic models for rate-independent systems Calc. Var. Partial Differ. Equ. 22 73 99 1161.74387 2105969
25. V. Mantič 2009 Interface crack onset at a circular cylindrical inclusion under a remote transverse tension. Application of a coupled stress and energy criterion Int. J. Solids Struct. 46 1287 1304 10.1016/j.ijsolstr.2008. 10.036
26. Mielke A.: Evolution in rate-independent systems. In: Dafermos, C., Feireisl, E. (eds) Handbook of Differential Equations, Evolutionary Equations, vol. 2, pp. 461-559. Elsevier, Amsterdam (2005)
27. A. Mielke T. Roubíček 2009 Numerical approaches to rate-independent processes and applications in inelasticity M2AN Math. Model. Numer. Anal. 43 399 428 10.1051/m2an/2009009 05574325 10.1051/m2an/2009009
28. A. Mielke T. Roubíček U. Stefanelli 2008 Γ-limits and relaxations for rate-independent evolutionary problems Calc. Var. Partial Differ. Equ. 31 387 416 05236593 10.1007/s00526-007-0119-4
29. Mielke A., Theil F.: A mathematical model for rate-independent phase transformations with hysteresis. In: Alber, H.-D., Balean, R., Farwig, R. (eds) Proceedings of the Workshop on Models of Continuum Mechanics in Analysis and Engineering, pp. 117-129. Shaker-Verlag, Aachen (1999)
30. A. Mielke F. Theil 2004 On rate-independent hysteresis models Nonlinear Differ. Equ. Appl. 1 151 189 2210284 (Accepted July 2001)
31. A. Mielke F. Theil V. Levitas 2002 A variational formulation of rate-independent phase transformations using an extremum principle Arch. Ration. Mech. Anal. 162 137 177 1012.74054 10.1007/s002050200194 1897379 (Pubitemid 36195114)
32. M. Negri C. Ortner 2008 Quasi-static crack propagation by Griffith's criterion Math. Models Methods Appl. Sci. 18 1895 1925 1155.74035 10.1142/S0218202508003236 2472402
33. N. Point 1988 Unilateral contact with adherence Math. Methods Appl. Sci. 10 367 381 0656.73052 10.1002/mma.1670100403 958479
34. N. Point E. Sacco 1996 A delamination model for laminated composites Math. Methods Appl. Sci. 33 483 509 0902.73054
35. N. Point E. Sacco 1998 Mathematical properties of a delamination model Math. Comput. Model. 28 359 371 1126.74359 10.1016/S0895-7177(98)00127-7 1648761 (Pubitemid 28448171)
36. R. Toader C. Zanini 2009 An artificial viscosity approach to quasistatic crack growth Boll. Unione Mat. Ital. (9) 2 1 1 35 05572795 2493642