journal article·2017-05

Experimental validation of a phase-field model for fracture

K. H. Pham, K. Ravi-Chandar, C. M. Landis

International Journal of Fracture· Volume 205· Issue 1
Publisher page

Abstract

Simulations from a numerical implementation of the phase-field model for brittle fracture are compared against analytical and experimental results in order to explore the verification and validation of the method. It is found that while the intrinsic length scale associated with the phase-field model can be set arbitrarily, the scale of the fracture process zone, and the scale at which the elastic field attains the corresponding analytical brittle fracture limit could be substantially larger than this intrinsic length. It is demonstrated that with a suitable choice of this length scale, phase-field simulations can provide valid predictions of the growth of cracks in quasi-static brittle fracture.
Source: openaire · Quality: candidate unverified · Source record ↗

Research context

OpenAlex topics: Numerical methods in engineering · Ultrasonics and Acoustic Wave Propagation · Fatigue and fracture mechanics

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (24)

Show source-provided references
1. Ambati M, Gerasimov T, De Lorenzis L (2015) A review on phase-field models of brittle fracture and a new fast hybrid formulation. Comput Mech 55:383–40510.1007/s00466-014-1109-y ↗
2. Ambrosio L, Tortorelli VM (1990) Approximation of functionals depending on jumps by elliptic functionals via $$\Gamma $$ Γ -convergence. Commun Pure Appl Math 43(8):999–103610.1002/cpa.3160430805 ↗
3. Ambrosio L, Tortorelli VM (1992) On the approximation of free discontinuity problems. Boll Un Mat Ital B (7) 6(1):105–123
4. Amor H, Marigo JJ, Maurini C (2009) Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J Mech Phys Solids 57:1209–122910.1016/j.jmps.2009.04.011 ↗
5. Balay S et al (2014) PETSc users manual. ANL-95/11—Revision 3.5. Argonne National Laboratory, Chicago
6. Borden MJ et al (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217:77–9510.1016/j.cma.2012.01.008 ↗
7. Bourdin B (1999) Image segmentation with a finite element method. M2AN Math Model Numer Anal 33(2):229–24410.1051/m2an:1999114 ↗
8. Bourdin B, Francfort GA, Marigo JJ (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48(4):797–82610.1016/S0022-5096(99)00028-9 ↗
9. Bourdin B, Francfort GA, Marigo J (2008) The variational approach to fracture. J Elast 91:5–14810.1007/s10659-007-9107-3 ↗
10. Braides A (1998) Approximation of free-discontinuity problems. Number 1694 in Lecture Notes in Mathematics. Springer, Berlin10.1007/BFb0097344 ↗
11. Chambolle A (2004) An approximation result for special functions with bounded variations. J Math Pure Appl 83:929–954 200410.1016/j.matpur.2004.02.004 ↗
12. Chambolle A (2005) Addendum to an approximation result for special functions with bounded deformation [J Math Pure Appl (9) 83 (7) (2004) 929–954]: the n-dimensional case. J Math Pure Appl 84:137–14510.1016/j.matpur.2004.11.001 ↗
13. Erdogan F, Sih GC (1963) On the crack extension in plates under plane loading and transverse shear. J Basic Eng 85:519–52510.1115/1.3656897 ↗
14. Giacomini A (2005) Ambrosio–Tortorelli approximation of quasi-static evolution of brittle fractures. Calc Var Partial Differ Equ 22(2):129–17210.1007/s00526-004-0269-6 ↗
15. Goldstein RV, Salganik RL (1974) Brittle fracture of solids with arbitrary cracks. Int J Fract 10:507–52310.1007/BF00155254 ↗
16. Karma A, Kessler DA, Levine H (2001) Phase-field model of mode III dynamic fracture. Phys Rev Lett 87:04550110.1103/PhysRevLett.87.045501 ↗
17. Karypis G, Kumar V (1999) A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J Sci Comput 20:359–39210.1137/S1064827595287997 ↗
18. Leblond JB (1999) Crack paths in three-dimensional elastic solids. I: two-term expansion of the stress intensity factors-application to crack path stability in hydraulic fracturing. Int J Solids Struct 36:79–10310.1016/S0020-7683(97)00276-X ↗
19. Miehe C, Hofacker M, Welschinger F (2010) A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199:2765–277810.1016/j.cma.2010.04.011 ↗
20. Murakami Y et al (1987) Stress intensity factors handbook, vol 1. Pergamon Press, New York
21. Ortiz M (1985) A constitutive theory for the inelastic behavior of concrete. Mech Mater 4:67–9310.1016/0167-6636(85)90007-9 ↗
22. Pham K, Amor H, Marigo JJ, Maurini C (2011) Gradient damage models and their use to approximate brittle fracture. Int J Damage Mech 20(4, SI):618–65210.1177/1056789510386852 ↗
23. Pham K, Marigo JJ, Maurini C (2011) The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models. J Mech Phys Solids 59(6):1163–119010.1016/j.jmps.2011.03.010 ↗
24. Rubinstein AA (1985) Macrocrack interaction with semi-infinite microcrack array. Int J Fract 27:113–11910.1007/BF00040390 ↗