Skip to main content
SpringerLink
Log in

Particle methods in the study of fracture

  • Special Invited Article Celebrating IJF at 50
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

This article reviews particle methods in the study of fracture. It focuses on the exact solution of dynamic cracks in an ideal brittle solid. Topics that arise include Cherenkov radiation of phonons, how calculations in a strip let one connect continuum fracture mechanics to atomic solutions, and the use of Wiener-Hopf techniques for analytical results. Then the article discusses molecular dynamics solutions, focusing on how to set them up making use of insights from the exactly solvable models. The particular case of silicon is discussed in detail. Finally there is a brief discussion of mesoscopic particle models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Abraham F, Walkup R, Gao H, Duchaineau M, Rubia TDDL, Seager M (2002) Simulating materials failure by using up to one billion atoms and the world’s fastest computer: brittle fracture. PNAS 99:5777–5782

    Article  Google Scholar 

  • Abraham FF, Bernstein N, Broughton JQ, Hess D (2000) Dynamic fracture of silicon: concurrent simulation of quantum electrons, classical atoms, and the continuum solid. Mater Res Soc Bull 25(5):27–32

    Article  Google Scholar 

  • Abraham FF, Brodbeck D, Rafey RA, Rudge WE (1994) Instability dynamics of fracture: a computer simulation investigation. Phys Rev Lett 73(2):272–275

    Article  Google Scholar 

  • Ashurst WT, Hoover WG (1976) Microscopic fracture studies in the two-dimensional triangular lattice. Phys Rev B 14:1465–1473

    Article  Google Scholar 

  • Atkinson W, Cabrera N (1965) Motion of a Frenkel-Kontorowa dislocation in a one-dimensional crystal. Phys Rev A 138:763

    Article  Google Scholar 

  • Baskes MI (1992) Modified embedded-atom potentials for cubic materials and impurities. Phys Rev B 46:2727–2742

  • Baskes MI, Angelo JE, Bisson CL (1994) Atomistic calculations of composite interfaces. Model Simul Mater Sci Eng 2:505–518

    Article  Google Scholar 

  • Baskes MI, Ortiz M (2015) Scaling laws in the ductile fracture of metallic crystals. J Appl Mech Trans ASME 82. doi:10.1115/1.4030329/1-5

  • Behn C, Marder M (2015) The transition from subsonic to supersonic cracks. Philos Trans A 373:20140122. doi:10.1098/rsta.2014.0122

  • Bernstein N, Hess D (2003) Lattice trapping barriers to brittle fracture. Phys Rev Lett 91:025501/1–025501/4

    Article  Google Scholar 

  • Bobaru F (2015) Why do cracks branch? A peridynamic investigation of dynamic brittle fracture. Int J Fracture. doi:10.1007/s10704-015-0056-8

  • Borysiuk VN, Mochalin VN, Gogotsi Y (2015) Molecular dynamic study of the mechanical properties of two-dimensional titanium carbides Tin+1Cn (MXenes). Nanotechnology 26(26):265705

    Article  Google Scholar 

  • Car R, Parrinello M (1985) Unified approach for molecular dynamics and density-functional theory. Phys Rev Lett 55:2471–2474

    Article  Google Scholar 

  • Cramer T, Wanner A, Gumbsch P (1997) Crack velocities during dynamic fracture of glass and single crystalline silicon. Physica Status Solidi A 164(1):R5–R6

    Article  Google Scholar 

  • Feynman RP (1964) Feynman lectures on phyusics, vol 1. Addison Wesley Longman, Redwood City

    Google Scholar 

  • Fineberg J, Marder M (1999) Instability in dynamic fracture. Phys Rep 313:1–108

    Article  Google Scholar 

  • Frenkel J, Kontorova T (1938) On the theory of plastic deformation and twinning. Physikalische Zeitschrift der Sowjetunion 13:1–10

    Google Scholar 

  • Freund LB (1990) Dynamics fracture mechanics. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Fuller ER, Thomson R (1978) Lattice theories of fracture. In: Bradt RC, Hasselman DPH, Lange FF (eds) Fracture mechanics of ceramics, vol 4. Plenum, New York, pp 507–548

    Google Scholar 

  • Griffith A (1920) The phenomena of rupture and flow in solids. Mech Eng A221:163–198

    Google Scholar 

  • Gumbsch P, Zhou SJ, Holian BL (1997) Molecular dynamics investigation of dynamic crack stability. Phys Rev B 55:3445–3455

    Article  Google Scholar 

  • Guozden TM, Jagla EA, Marder M (2009) Supersonic cracks in lattice models. Int J Fracture 162(1–2):107–125

    Google Scholar 

  • Ha YD, Bobaru F (2010) Studies of dynamic crack propagation and crack branching with peridynamics. Int J Fracture 162(1–2):229–244

    Article  Google Scholar 

  • Hauch J, Holland D, Marder M, Swinney HL (1999) Dynamic fracture in single-crystal silicon. Phys Rev Lett 82:3823–3826

    Article  Google Scholar 

  • Holian BL, Ravelo R (1995) Fracture simulations using large-scale molecular dynamics. Phys Rev B 51:11275–11288

    Article  Google Scholar 

  • Holland D, Marder M (1998a) Erratum: ideal brittle fracture of silicon studied with molecular dynamics. Phys Rev Lett 81:4029

    Article  Google Scholar 

  • Holland D, Marder M (1998b) Ideal brittle fracture of silicon studied with molecular dynamics. Phys Rev Lett 80:746–749

    Article  Google Scholar 

  • Holland D, Marder M (1999) Cracks and atoms. Adv Mater 11:793–806

    Article  Google Scholar 

  • Kulakhmetova SA, Saraikin VA, Slepyan LI (1984) Plane problem of a crack in a lattice. Mech Solids 19:102–108

    Google Scholar 

  • Liu J, Shen J, Zheng Z, Wu Y, Zhang L (2015) Revealing the toughening mechanism of graphene-polymer nanocomposite through molecular dynamics simulation. Nanotechnology 26(29):291003

    Article  Google Scholar 

  • Marder M (1996) Statistical mechanics of cracks. Phys Rev E 54:3442–3454

    Article  Google Scholar 

  • Marder M (2004) Effect of atoms on brittle fracture. Int J Fracture 130:517–555

    Article  Google Scholar 

  • Marder M (2006) Supersonic rupture of rubber. J Mech Phys Solids 54:491–532

    Article  Google Scholar 

  • Marder M (2010) Condensed matter physics, 2nd edn. Wiley, New York

    Book  Google Scholar 

  • Marder M, Gross S (1995) Origin of crack tip instabilities. J Mech Phys Solids 43:1–48

    Article  Google Scholar 

  • Omeltchenko A, Yu J, Kalia RK, Vashishta P (1997) Crack front propagation and fracture in a graphite sheet: a molecular-dynamics study on parallel computers. Phys Rev Lett 78:2148–2151

    Article  Google Scholar 

  • Pei L, Lu C, Tieu K, Zhao X, Zhang L, Cheng K, Michal G (2015) Brittle versus ductile fracture behaviour in nanotwinned FCC crystals. Mater Lett 152:65–67

    Article  Google Scholar 

  • Petersan PJ, Deegan RD, Marder M, Swinney HL (2004) Cracks in rubber under tension exceed the shear wave speed. Phys Rev Lett 93:015504/1–015504/4

    Article  Google Scholar 

  • Plimpton S (2015), LAMMPS. http://lammps.sandia.gov/

  • Rapaport DC (2004) The art of molecular dynamics simulation, 2nd edn. Cambridge University Press, New York

    Book  Google Scholar 

  • Ravi-Chandar K, Knauss WG (1984) An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching. Int J Fracture 26:141–154

    Article  Google Scholar 

  • Shenoy VB, Miller R, Tadmor EB, Phillips R (1998) Quasicontinuum models of interfacial structure and deformation. Phys Rev Lett 80:742–745

    Article  Google Scholar 

  • Shenoy VB, Miller R, Tadmor EB, Rodney D, Phillips R, Ortiz M (1999) An adaptive finite element approach to atomic-scale mechanics—the quasicontinuum method. J Mech Phys Solids 47(3):611–642

  • Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48:175–209

    Article  Google Scholar 

  • Silling SA, Bobaru F (2005) Peridynamic modeling of membranes and fibers. Int J Non-Linear Mech 40:395–409

    Article  Google Scholar 

  • Silling SA, Lehoucq RB (2010) Peridynamic theory of solid mechanics. Adv Appl Mech 44:73–168

    Article  Google Scholar 

  • Slepyan L (1981) Dynamics of a crack in a lattice. Sov Phys Doklady 26:538–540

    Google Scholar 

  • Slepyan LI (2002) Models and phenomena in fracture mechanics. Springer, Berlin

    Book  Google Scholar 

  • Slepyan LI, Fishkov AL (1981) The problem of the propagation of a cut at transonic velocity. Doklady Akademii Nauk SSSR 26:1192–1193

    Google Scholar 

  • Stillinger FH, Weber TA (1985) Computer simulation of local order in condensed phases of silicon. Phys Rev B 31:5262

    Article  Google Scholar 

  • Swadener J, Baskes M, Nastasi M (2002) Molecular dynamics simulation of brittle fracture in silicon. Phys Rev Lett 89(8):085503/1–085503/4

    Article  Google Scholar 

  • Tabarraei A, Wang X (2015) A molecular dynamics study of nanofracture in monolayer boron nitride. Mater Sci Eng A Struct Mater Prop Microstruct Process 641:225–230

    Article  Google Scholar 

  • Tadmor EB, Ortiz M, Phillips R (1996) Quasicontinuum analysis of defects in solids. Philos Mag A 73:1529–1563

    Article  Google Scholar 

  • Tadmore EB, Miller RE (2011) Modeling materials: continuum, atomistic, and multiscale techniques. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Thomson R (1986) The physics of fracture. Solid State Phys 39:1–129

    Google Scholar 

  • Thomson R, Hsieh C, Rana V (1971) Lattice trapping of fracture cracks. J Appl Phys 42(8):3154–3160

    Article  Google Scholar 

  • Tian Y, Xu B, Yu D, Ma Y, Wang Y, Jiang Y, Hu W, Tang C, Gao Y, Luo K, Zhao Z, Wang L-M, Wen B, He J, Liu Z (2013) Ultrahard nanotwinned cubic boron nitride. Nature 493(7432):385–388

    Article  Google Scholar 

  • Verlet L (1967) Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys Rev 159:98

    Article  Google Scholar 

  • Wang X, Wang L, Guo L (2015) Fracture behavior of functionally graded joint interfaces between copper and aluminum at nano-scale. J Comput Theor Nanosci 12(8):1944–1950

    Article  Google Scholar 

  • Xu GQ, Demkowicz MJ (2013) Healing of nanocracks by disclinations. Phys Rev Lett 111(14):145501

    Article  Google Scholar 

Download references

Acknowledgments

This work was partially supported by the Condensed Matter and Materials Theory Program of the National Science Foundation, DMR-1002428.

Author information

Authors and Affiliations

  1. Department of Physics, The University of Texas at Austin, Austin, TX, USA

    M. Marder

Authors
  1. M. Marder
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Marder.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Marder, M. Particle methods in the study of fracture. Int J Fract 196, 169–188 (2015). https://doi.org/10.1007/s10704-015-0070-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-015-0070-x

Keywords

Search

Navigation