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Effect of random defects on dynamic fracture in quasi-brittle materials

  • IUTAM Baltimore
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Abstract

We propose an asynchronous spacetime discontinuous Galerkin (aSDG) method combined with a novel rate-dependent interfacial damage model as a means to simulate crack nucleation and propagation in quasi-brittle materials. Damage acts in the new model to smoothly transition the aSDG jump conditions on fracture surfaces between Riemann solutions for bonded and debonded conditions. We use the aSDG method’s powerful adaptive meshing capabilities to ensure solution accuracy without resorting to crack-tip enrichment functions and extend those capabilities to support fracture nucleation, extension and intersection. Precise alignment of inter-element boundaries with flaw orientations and crack-propagation directions ensures mesh-independent crack-path predictions. We demonstrate these capabilities in a study of crack-path convergence as adaptive error tolerances tend to zero. The fracture response of quasi-brittle materials is highly sensitive to the presence and properties of microstructural defects. We propose two approaches to model these inhomogeneities. In the first, we represent defects explicitly as crack-like features in the analysis domain’s geometry with random distributions of size, location, and orientation. In the second, we model microscopic flaws implicitly, with probabilistic distributions of strength and orientation, to drive nucleation of macroscopic fractures. Crack-path oscillation, microcracking, and crack branching make numerical simulation of dynamic fracture particularly challenging. We present numerical examples that explore the influence of model parameters and inhomogeneities on fracture patterns and the aSDG model’s ability to capture complex fracture patterns and interactions.

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Notes

  1. Abedi (2010) uses a crack-tracking scheme, so his method would not suffer artificial compliance even if he chose an interfacial damage model with finite initial compliance.

References

  • Abedi R (2010) Spacetime damage-based cohesive model for elastodynamic fracture with dynamic contact. Ph.D. thesis, Department of Theoretical and Applied Mechanics, University of Illinois at Urbana–Champaign

  • Abedi R, Haber R (2011) Spacetime dimensional analysis and self-similar solutions of linear elastodynamics and cohesive dynamic fracture. Int J Solids Struct 48(13):2076–2087

    Article  Google Scholar 

  • Abedi R, Haber RB (2014) Riemann solutions and spacetime discontinuous Galerkin method for linear elastodynamic contact. Comput Methods Appl Mech Eng 270:150–177

    Article  Google Scholar 

  • Abedi R, Chung SH, Erickson J, Fan Y, Garland M, Guoy D, Haber R, Sullivan JM, Thite S, Zhou Y (2004) Spacetime meshing with adaptive refinement and coarsening. In: Proceedings of the twentieth annual symposium on computational geometry, ACM, SCG ’04, pp 300–309

  • Abedi R, Haber RB, Petracovici B (2006a) A spacetime discontinuous Galerkin method for elastodynamics with element-level balance of linear momentum. Comput Methods Appl Mech Eng 195:3247–3273

    Article  Google Scholar 

  • Abedi R, Haber RB, Thite S, Erickson J (2006b) An \(h\)-adaptive spacetime-discontinuous Galerkin method for linearized elastodynamics. Revue Européenne de Mécanique Numérique (Eur J Comput Mech) 15(6):619–642

    Google Scholar 

  • Abedi R, Hawker MA, Haber RB, Matouš K (2009) An adaptive spacetime discontinuous Galerkin method for cohesive models of elastodynamic fracture. Int J Numer Methods Eng 1:1–42

    Google Scholar 

  • Alfano G, Sacco E (2006) Combining interface damage and friction in a cohesive-zone model. Int J Numer Methods Eng 68(5):542–582

    Article  Google Scholar 

  • Allix O, Corigliano A (1996a) Modeling and simulation of crack propagation in mixed modes interlaminar fracture. Int J Fract 77:111–140

    Article  Google Scholar 

  • Allix O, Corigliano A (1996b) Modeling and simulation of crack propagation in mixed modes interlaminar fracture. Int J Fract 77:111–140

    Article  Google Scholar 

  • Allix O, Feissel P, Thevenet P (2003) A delay damage mesomodel of laminates under dynamic loading: basic aspects and identification issues. Comput Struct 81(12):1177–1191

    Article  Google Scholar 

  • 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 55:383–405

    Article  Google Scholar 

  • Barenblatt GI (1962) The mathematical theory of equilibrium of cracks in brittle fracture. Adv Appl Mech 7:55–129

    Article  Google Scholar 

  • Baxter S, Graham L (2000) Characterization of random composites using moving-window technique. J Eng Mech 126(4):389–397

    Article  Google Scholar 

  • Bazant ZP, Belytschko TB, Chang TP (1984) Continuum theory for strain-softening. J Eng Mech 110(12):1666–1692

    Article  Google Scholar 

  • Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45:601–620

    Article  Google Scholar 

  • Blal N, Daridon L, Monerie Y, Pagano S (2012) Artificial compliance inherent to the intrinsic cohesive zone models: criteria and application to planar meshes. Int J Fract 178(1):71–83. doi:10.1007/s10704-012-9734-y

    Article  Google Scholar 

  • Bourdin B, Larsen CJ, Richardson CL (2011) A time-discrete model for dynamic fracture based on crack regularization. Int J Fract 168(2):133–143. doi:10.1007/s10704-010-9562-x

    Article  Google Scholar 

  • Camacho GT, Ortiz M (1996) Computational modeling of impact damage in brittle materials. Int J Solids Struct 33:2899–2938

    Article  Google Scholar 

  • Cazes F, Moës N (2015) Comparison of a phase-field model and of a thick level set model for brittle and quasi-brittle fracture. Int J Numer Methods Eng 103(2):114–143. doi:10.1002/nme.4886

    Article  Google Scholar 

  • Corigliano A, Ricci M (2001) Rate-dependent interface models: formulation and numerical applications. Int J Solids Struct 38:547–576

    Article  Google Scholar 

  • Dolbow J, Moes N, Belytschko T (2000) Discontinuous enrichment in finite elements with a partition of unity method. Int J Numer Methods Eng 36(3):235–260

    Google Scholar 

  • Duarte CA, Babuška I, Oden JT (2000) Generalized finite element methods for three-dimensional structural mechanics problems. Comput Struct 77(2):215–232

    Article  Google Scholar 

  • Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8:100–104

    Article  Google Scholar 

  • Evangelatos GI, Spanos PD (2012) A collocation approach for spatial discretization of stochastic peridynamic modeling of fracture. J Mech Mater Struct 6(7–8):1171–1195

    Google Scholar 

  • Genet M, Couegnat G, Tomsia A, Ritchie R (2014) Scaling strength distributions in quasi-brittle materials from micro- to macro-scales: a computational approach to modeling nature-inspired structural ceramics. J Mech Phys Solids 68(1):93–106

    Article  Google Scholar 

  • Grady D, Kipp M (1980) Continuum modeling of explosive fracture in oil shale. Int J Rock Mech Mining Sci Geomech Abstr 17(3):147–157

    Article  Google Scholar 

  • Ibrahimbegovic A, Delaplace A (2003) Microscale and mesoscale discrete models for dynamic fracture of structures built of brittle material. Comput Struct 81(12):1255–65

    Article  Google Scholar 

  • Karnopp D (1985) Computer simulation of stick-slip friction in mechanical dynamic systems. J Dyn Syst Meas Control Trans ASME 107(1):100–103

    Article  Google Scholar 

  • Koyama T, Jing L (2007) Effects of model scale and particle size on micro-mechanical properties and failure processes of rocks—a particle mechanics approach. Eng Anal Bound Elements 31(5):458–472

    Article  Google Scholar 

  • Levy S, Molinari J, Radovitzky R (2012) Dynamic fragmentation of a brittle plate under biaxial loading: strength or toughness controlled? Int J Fract 174(2):203–15

    Article  Google Scholar 

  • Li H, Bai Y, Xia M, Ke F, Yin X (2000) Damage localization as a possible precursor of earthquake rupture. Pure Appl Geophys 157(11):1929–1943

    Article  Google Scholar 

  • Li T, Marigo JJ, Guilbaud D, Potapov S (2016) Gradient damage modeling of brittle fracture in an explicit dynamics context. Int J Numer Methods Eng 108(11):1381–1405. doi:10.1002/nme.5262

    Article  Google Scholar 

  • Meguid S, Czekanski A (2008) Advances in computational contact mechanics. Int J Mech Mater Des 4(4):419–443

    Article  Google Scholar 

  • Mergheim J, Kuhl E, Steinmann P (2005) A finite element method for the computational modeling of cohesive cracks. Int J Numer Methods Eng 63:276–289

    Article  Google Scholar 

  • Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150

    Article  Google Scholar 

  • Mostaghel N, Davis T (1997) Representations of Coulomb friction for dynamic analysis. Earthq Eng Struct Dyn 26(5):541–548

    Article  Google Scholar 

  • Needleman A (1988) Material rate dependence and mesh sensitivity in localization problems. Comput Methods Appl Mech Eng 67(1):69–85

    Article  Google Scholar 

  • Ostoja-Starzewski M (2002) Microstructural randomness versus representative volume element in thermomechanics. J Appl Mech Trans ASME 69(1):25–35

    Article  Google Scholar 

  • Pandolfi A, Ortiz M (2002) An efficient adaptive procedure for three-dimensional fragmentation simulations. Eng Comput 18:148–159

    Article  Google Scholar 

  • Parrinello F, Failla B, Borino G (2009) Cohesive-frictional interface constitutive model. Int J Solids Struct 46(13):2680–2692

    Article  Google Scholar 

  • Pramanik R, Deb D (2014) Implementation of smoothed particle hydrodynamics for detonation of explosive with application to rock fragmentation. Rock Mech Rock Eng 48(4):1683–1698

    Article  Google Scholar 

  • Quinn DD (2004) A new regularization of Coulomb friction. J Vib Acoust Trans ASME 126(3):391–397

    Article  Google Scholar 

  • Radovitzky R, Seagraves A, Tupek M, Noels L (2011) A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element method. Comput Methods Appl Mech Eng 200(1–4):326–344

    Article  Google Scholar 

  • Rangarajan R, Lew AJ (2014) Universal meshes: A method for triangulating planar curved domains immersed in nonconforming meshes. Int J Numer Methods Eng 98(4):236–264

    Article  Google Scholar 

  • Rangarajan R, Chiaramonte MM, Hunsweck MJ, Shen Y, Lew AJ (2015) Simulating curvilinear crack propagation in two dimensions with universal meshes. Int J Numer Methods Eng 102(3–4):632–670

    Article  Google Scholar 

  • Remmers JJC, de Borst R, Needleman A (2003) A cohesive segments method for the simulation of crack growth. Comput Mech 31:69–77

    Article  Google Scholar 

  • Sakata S, Ashida F, Enya K (2012) A microscopic failure probability analysis of a unidirectional fiber reinforced composite material via a multiscale stochastic stress analysis for a microscopic random variation of an elastic property. Comput Mater Sci 62:35–46

    Article  Google Scholar 

  • Schlangen E, Garboczi E (1997) Fracture simulations of concrete using lattice models: computational aspects. Eng Fract Mech 57(23):319–332

    Article  Google Scholar 

  • Shao J, Rudnicki J (2000) A microcrack-based continuous damage model for brittle geomaterials. Mech Mater 32(10):607–619

    Article  Google Scholar 

  • Spring DW, Leon SE, Paulino GH (2014) Unstructured polygonal meshes with adaptive refinement for the numerical simulation of dynamic cohesive fracture. Int J Fract 189(1):33–57. doi:10.1007/s10704-014-9961-5 adaptive refinement;Cohesive model;Cohesive zone element;Dynamic fractures;Polygonal meshes

    Article  Google Scholar 

  • Strouboulis T, Babuška I, Copps K (2000) The design and analysis of the generalized finite element method. Comput Methods Appl Mech Eng 181:43–69

    Article  Google Scholar 

  • Strouboulis T, Copps K, Babuška I (2001) The generalized finite element method. Comput Methods Appl Mech Eng 190:4081–4193

    Article  Google Scholar 

  • Versino D, Mourad HM, Davila CG, Addessio FL (2015) A thermodynamically consistent discontinuous galerkin formulation for interface separation. Compos Struct 133:595–606

    Article  Google Scholar 

  • Weibull W (1939) A statistical theory of the strength of materials. R Swed Inst Eng Res p Res 151:1–45

  • Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech 18:293–297

    Google Scholar 

  • Xu XP, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42:1397–1434

    Article  Google Scholar 

  • Zhang Z, Peng S, Ghassemi A, Ge X (2015) Lattice bond cell modeling of dynamic hydraulic fracture. In: The 49th US rock mechanics/geomechanics symposium, June 28–July 1, San Francisco, CA, USA, ARMA 15–258

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Acknowledgements

This material is partially based upon work supported by the National Science Foundation under Grant No. 1538332.

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Authors and Affiliations

  1. Department of Mechanical Aerospace and Biomedical Engineering, University of Tennessee Space Institute, 411 B.H. Goethert Parkway, Tullahoma, TN, 37388, USA

    Reza Abedi & Philip L. Clarke

  2. Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green St., Urbana, IL, 61801, USA

    Robert B. Haber

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  1. Reza Abedi
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  2. Robert B. Haber
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Correspondence to Reza Abedi.

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Abedi, R., Haber, R.B. & Clarke, P.L. Effect of random defects on dynamic fracture in quasi-brittle materials. Int J Fract 208, 241–268 (2017). https://doi.org/10.1007/s10704-017-0243-x

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