This paper presents a computational framework for the simulation of planar crack growth (including kinking) driven by “material forces”. An evolution law for the crack tip position is formulated, which is shown to give rise to different propagation strategies when subjected to certain assumptions on regularity. Three such strategies, that previously have been proposed in the literature in principle: Explicit Proportional Extension (EPE), Implicit Proportional Extension (IPE) and Maximum Parallel Release Rate (MPRR), are outlined and assessed. Based on the results of two numerical examples, it is concluded that the presented propagation strategies produce almost identical results and are robust with respect to time discretization.
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Kuhl E, Menzel A, Steinmann P (2003) Computational modeling of growth. Comput Mech 32: 71–88
Menzel A, Denzer R, Steinmann P (2004) On the comparison of two approaches to compute material forces for inelastic materials. Applicaton to single-slip crystal-plasticity. Comput Methods Appl Mech Eng 193(48–51): 5411–5428
Materna D, Barthold F-J (2009) Goal-oriented r-adaptivity based on variational arguments in the physical and material spaces. Comput Method Appl Mech Eng 198(41–44): 3335–3351
Steinmann P (2008) On boundary potential energies in deformational and configurational mechanics. J Mech Phys Solids 56(3): 772–800
Maugin GA (1995) Material forces: concepts and applications. Appl Mech Rev 48(5): 213–245
Needleman A, Li FZ, Shih CF (1985) A comparison of methods for calculating energy release rates. Eng Fract Mech 21(2): 405–421
Simha NK, Fischer FD, Shan GX, Chen CR, Kolednik O (2008) J-integral and crack driving force in elastic-plastic materials. J Mech Phys Solids 56(9): 2876–2895
Steinmann P (2000) Application of material forces to hyperelastostatic fracture mechanics. i. continuum mechanical setting. Int J Solids Struct 37(48–50): 7371–7391
Steinmann P, Ackermann D, Barth FJ (2001) Application of material forces to hyperelastostatic fracture mechanics. ii. computational setting. Int J Solids Struct 38(32–33): 5509–5526
Nguyen TD, Govindjee S, Klein PA, Gao H (2005) A material force method for inelastic fracture mechanics. J Mech Phys Solids 53(1): 91–121
Tillberg J, Larsson F, Runesson K (2010) On the role of material dissipation for the crack-driving force. Int J Plasticity. doi:10.1016/j.ijplas.2009.12.001
Miehe C, Gurses E (2007) A robust algorithm for configurational-force-driven brittle crack propagation with r-adaptive mesh alignment. Int J Numer Methods Eng 72: 127–155
Denzer R, Barth FJ, Steinmann P (2003) Studies in elastic fracture mechanics based on the material force method. Int J Numer Methods Eng 58: 1817–1835
Schütte H (2009) Curved crack-propagation based on configurational forces. Comp Mater Sci 46: 642–646
Heintz P (2006) On the numerical modelling of quasi-static crack growth in linear elastic fracture mechanics. Int J Numer Methods Eng 65: 174–189
Fagerström M, Larsson R (2008) Approaches to dynamic fracture modeling at finite deformation. J Mech Phys Solids 56: 613–639
Adden S, Merzbacher M, Horst P (2006) Material forces as a simple criterion for the description of crack-turning problems. Aerosp Sci Technol 10: 519–526
Adda-Bedia M (2004) Path prediction of kinked and branched cracks in plane situations. Phys Rev Lett 93(18): 185502-1–185502-4
Broberg KB (1987) On crack paths. Eng Fract Mech 28(5/6): 663–679
Runesson K, Larsson F, Steinmann P (2009) On energetic changes due to configurational motion of standard continua. Int J Solids Struct 46(6): 1464–1475
Chen Y-H, Lu TJ (2004) On the path dependence of the J-integral in notch problems. Int J Solids Struct 41(3–4): 607–618
Bilby BA, Cardew GE (1975) The crack with a kinked tip. Int J Fract 11: 708–712
Hellen TK (1975) On the method of virtual crack extensions. Int J Numer Methods Eng 9: 187–207
Ma L, Korsunsky AM (2005) On the use of vector J-integral in crack growth criteria for brittle solids. Int J Fract 133: L39–L46
Gurtin ME, Podio-Guidugli P (1998) Configurational forces and a constitutive theory for crack propagation that allows for kinking and curving. J Mech Solids 46(8): 1343–1378
Denzer R (2006) Computational configurational mechanics. Dissertation, University of Kaiserslautern
Bittencourt TN, Wawrzynek PA, Ingraffea AR, Sousa JL (1996) Quasi-automatic simulation of crack propagation for 2D lefm problems. Eng Fract Mech 55(2): 321–334
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Brouzoulis, J., Larsson, F. & Runesson, K. Strategies for planar crack propagation based on the concept of material forces. Comput Mech 47, 295–304 (2011) doi:10.1007/s00466-010-0542-9
- Crack propagation
- Crack curving
- Configurational forces