Abstract
This contribution presents a comparison between a discrete and a smeared approach to approximate a crack in finite element simulations including the contribution of inertia to the behavior of brittle material under transient loading in the case of fracture. The discrete approximation of a crack is based in this case on a node duplication technique triggered by the evaluation of the so-called “material force” at the crack tip. The smeared approximation of a crack bases on the diffuse description of the crack by a phase-field approach. The governing equations under consideration of transient contributions are shown and the procedure for the finite element implementation is outlined. Numerical simulations investigate the capabilities and limitations of both methods. Firstly, the procedure to introduce initial cracks in a structure and the setup necessary to make them interact with stress waves properly, are under investigation. Moreover, this study deals with the evaluation of the velocity of the crack propagation and its comparison to experimental data. Finally, the phenomenon of crack branching is studied. The presentation and discussion of the results of the simulations provide an overview on the potential of both approaches with respect to an efficient and a realistic simulation of fracture processes in dynamic problems.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Ambati M, Gerasimov T, Lorenzis LD (2015) A review on phase-field models of brittle fracture and a new fast hybrid formulation. Comput Mech 55:383–405
Amor H, Marigo JJ, Maurini C (2009) Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J Mech Phys Solids 57:1209–1229
Arakawa K, Takahashi K (1991) Relationship between fracture parameters and surface roughness of brittle polymers. Int J Fract 48:103–114
Bergkvist H (1974) Some experiments on crack motion and arrest in polymethylmethacrylate. Eng Fract Mech 6:621–626
Borden M (2012) Isogeometric analysis of phase-field model for dynamic brittle and ductile fracture. PhD thesis, The University of Texas at Austin
Borden MJ, Verhoosel CV, Scott MA, Hughes TJR, Landis CM (2012) A phase-field description of dynamic brittle fracture. Comput Methods Appl Mech Eng 217–220:77–95
Bourdin B (2007) The variational formulation of brittle fracture: numerical implementation and extensions. IUTAM Symp Discret Methods Evol Discontin 5:381–393
Bourdin B (2008) The variational approach to fracture. J Elast 91:5–148
Braides A (2002) Gamma-convergence for beginners. Oxford University Press, Oxford
Braun M (1997) Configurational forces induced by finite-element discretization. Proc Estonian Acad Sci Phys Math 35:379–386
Brouzoulis J, Larsson F, Runesson K (2010) Strategies for planar crack propagation based on the concept of material forces. Comput Mech 3:295–304
Dally J (1979) Dynamic photoelastic studies of fracture. Exp Mech 19:349–361
Fineberg J, Gross SP, Marder M, Swinney H (1992) Instability in the propagation of fast cracks. Am Phys Soc 45:5146–5154
Francfort GA, Marigo JJ (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46:1319–1342
Griffith AA (1921) The phenomena of rupture and flow in solids. Philos Trans R Soc London Ser A 221:163–198
Gürses E, Miehe C (2009) A computational framework of three-dimensional configurational-force-driven brittle crack propagation. Comput Methods Appl Mech Eng 198:1413–1428
Gurtin ME (2000) Configurational forces as basic concepts of continuum physics. Springer, New York
Hilber H, Hughes T, Taylor R (1977) Improved numerical dissipation for the time intergration algorithms in structural dynamics. Earthq Eng Struct Dyn 5:283–292
Hofacker M (2013) A thermodynamically consistent phase field approach to fracture. PhD. thesis, Universität Stuttgart
Hofacker M, Miehe C (2013) A phase field model of dynamic fracture: robust field updates for the analysis of complex crack patterns. Int J Numer Methods Eng 93:276–301
Hofacker M, Welschinger F, Miehe C (2009) A variational-based formulation of regularized brittle fracture. Proc Appl Math Mech 9:207–208
Karma A, Kessler DA, Levine H (2001) Phase-field model of mode III dynamic fracture. Phys Rev Lett 87(4):045501
Kienzler R, Herrmann G (2000) Mechanics in material space: with applications to defect and fracture mechanics. Springer, Berlin
Kobayashi AS, Mall S (1978) Dynamic fracture toughness of homalite-100. Exp Mech 18:11–18
Kobayashi AS, Wade BG, Bradley WB, Chiu ST (1972) Crack branching in homalite-100 sheets. Off Nav Res 13:1–29
Kuhn C, Müller R (2010) A continuum phase field model for fracture. Eng Fract Mech 77:3625–3634
Kuhn C, Müller R (2011) A new finite element technique for a phase field model of brittle fracture. J Theor Appl Mech 49:1115–1133
Maugin GA (2010) Configurational forces: thermomechanics, physics, mathematics, and numerics. CRC Press, Boca Raton
Maugin GA, Trimarco C (1992) Pseudomomentum and material forces in nonlinear elasticity: variational formulations and application to brittle fracture. Acta Mech 94:1–28
Menzel A, Denzer R, Steinmann P (2004) On the comparison of two approaches to compute material forces for inelastic materials. Application to single-slip crystal-plasticity. Comput Meth Appl Mech Eng 193:5411–5428
Meyers MA (1994) Dynamic behavior of materials. Wiley, New York
Miehe C, Gürses 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
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 199:2765–2778
Miehe C, Welschinger F, Hofacker M (2010) Thermodynamically consistent phase-field models of fracture: variational principles and multi-field fe implementations. Int J Numer Methods Eng 83:1273–1311
Müller R, Maugin GA (2002) On material forces and finite element discretizations. Comput Mech 29:52–60
Näser B, Kaliske M, Dal H, Netzker C (2009) Fracture mechanical behaviour of visco-elastic materials: application to the so-called dwell-effect. Z Angew Math Mech 89:677–686
Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44:1267–1282
Özenç K, Kaliske M (2014) An implicit adaptive node-splitting algorithm to assess the failure mechanism of inelastic elastomeric continua. Int J Numer Meth Eng 100:669–688
Özenç K, Kaliske M, Lin G, Bashyam G (2014) Evaluation of energy contributions in elasto-plastic fracture: a review of the configurational force approach. Eng Fract Mech 115:137–153
Özenç K, Chinaryan G, Kaliske M (2016) A configurational force approach to model the branching phenomenon in dynamic brittle fracture. Eng Fract Mech 157:26–42
Pandolfi A, Ortiz M (2002) An efficient adaptive procedure for three-dimensional fragmentation simulations. Eng Comput 18:148–159
Ramulu M, Kobayashi AS (1985) Mechanics of crack curving and branching—a dynamic fracture analysis. Int J Fract 27:187–201
Ravi-Chandar K, Knauss W (1984) An experimental investigation into dynamic fracture: III. On steady-state crack propagation and branching. Int J Fract 26:141–154
Rice JR (1968) Mathematical analysis in the mechanics of fracture, vol 2. Academic Press, New York
Schlüter A, Willenbücher A, Kuhn C, Müller R (2014) Phase field approximation of dynamic brittle fracture. Comput Mech 54:1141–1161
Schütte H (2009) Curved crack-propagation based on configurational forces. Comput Mater Sci 46:642–646
Sharon E, Gross SP, Fineberg J (1996) Energy dissipation in dynamic fracture. Phys Rev Lett 76:2117–2120
Simha N, Fischer F, Shan G, Chene C, Kolednikf O (2008) J-integral and crack driving force in elastic-plastic materials. J Mech Phys Solids 56:2876–2895
Steinmann P (2000) Application of material forces to hyperelastostatic fracture mechanics. I. Continuum mechanical setting. Int J Solids Struct 37:7371–7391
Acknowledgments
The authors would like to acknowledge the financial support of “Deutsche Forschungsgemeinschaft” under grant KA 1163/19-1 and as well the technical support of the center for information services and high performance computing of the TU Dresden for providing access to the Bull HPC-Cluster. Moreover, we would like to thank ANSYS, Inc. for supporting Kaan Özenç.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Steinke, C., Özenç, K., Chinaryan, G. et al. A comparative study of the r-adaptive material force approach and the phase-field method in dynamic fracture. Int J Fract 201, 97–118 (2016). https://doi.org/10.1007/s10704-016-0125-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-016-0125-7