Quasistatic fracture evolution using a nonlocal cohesive model
Source abstract
Abstract
We introduce a nonlocal model of peridynamic type for fracture evolution in the quasistatic regime. Nonlocal quasistatic fracture evolution is developed and supporting numerical examples are presented. The approach is implicit and is based on local stationary and fixed point methods. Here a smooth cohesive force-strain model is used. Initially the force increases with strain then softens and decreases to zero. It is proved that the fracture evolution decreases stored elastic energy with each displacement step as the cracks advance; provided the displacement increments are chosen sufficiently small. These results apply to any system of multiple cracks. This is also seen in the numerical examples. The numerical examples include evolution of a straight crack, a crack propagating inside an L-shaped domain, and two offset inward propagating cracks.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Numerical methods in engineering · Geotechnical Engineering and Underground Structures · Rock Mechanics and Modeling
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (54)
Show source-provided references
1. Anderson TL (2017) Fracture mechanics: fundamentals and applications. CRC Press, Boca Raton10.1201/9781315370293 ↗
2. Bhattacharya D, Lipton R (2023) Quasistatic evolution with unstable forces. Multiscale Model Simul. https://doi.org/10.1137/22M148964210.1137/22M1489642 ↗
3. Bhattacharya D, Diehl P, Lipton RP (2021) Peridynamics for quasistatic fracture modeling. In: ASME International Mechanical Engineering Congress and Exposition, vol. 85680, p. V012T12A041. American Society of Mechanical Engineers10.1115/IMECE2021-70793 ↗
4. Bobaru F, Foster JT, Geubelle PH, Silling SA (2016) Handbook of peridynamic modeling. CRC Press, Boca Raton10.1201/9781315373331 ↗
5. Bourdin B, Francfort G, Marigo JJ (2008) The variational approach to fracture. J Elast 91:5–14810.1007/s10659-007-9107-3 ↗
6. Breitenfeld M (2014) Quasi-static non-ordinary state-based peridynamics for the modeling of 3d fracture. Ph.D. thesis, University of Illinois at Urbana-Champaign, Champaign, IL
7. Diehl P, Lipton R (2022) Quasistatic fracture using nonlinear-nonlocal elastostatics with explicit tangent stiffness matrix. Int J Numer Methods Eng 123(18):4183–420810.1002/nme.7005 ↗
8. Diehl P, Lipton R, Schweitzer MA (2016) A numerical verification of a bond-based softening peridynamic model for small displacements: Deducing material parameters from classical linear theory. In: Institute for Numerical Simulation, Universität Bonn preprint series, vol. I.N.S. preprint 1630
9. Diehl P, Prudhomme S, Lévesque M (2019) A review of benchmark experiments for the validation of peridynamics models. J Peridynamics Nonlocal Model 1(1):14–3510.1007/s42102-018-0004-x ↗
10. Diehl P, Lipton R, Wick T, Tyagi M (2022) A comparative review of peridynamics and phase-field models for engineering fracture mechanics. Computational Mechanics 1–3510.31224/osf.io/gty2b ↗
11. Du Q, Gunzburger M, Lehoucq RB, Zhou K (2013) Analysis of the volume-constrained peridynamic navier equation of linear elasticity. J Elast 113:193–21710.1007/s10659-012-9418-x ↗
12. Freimanis A, Paeglitis A (2017) Mesh sensitivity in peridynamic quasi-static simulations. Procedia Eng 172:284–29110.1016/j.proeng.2017.02.116 ↗
13. Freund B (1972) Energy flux into the tip of an extending crack in an elastic solid. J. Elast. 2:341–34910.1007/BF00045718 ↗
14. Gragg W, Tapia R (1974) Optimal error bounds for the newton-Kantorovitch theorem. SIAM J. Numer. Anal. 11(1):10–1310.1137/0711002 ↗
15. Hu Y, Madenci E (2016) Bond-based peridynamic modeling of composite laminates with arbitrary fiber orientation and stacking sequence. Composite Struct 153:139–17510.1016/j.compstruct.2016.05.063 ↗
16. Hu Y, Chen H, Spencer BW, Madenci E (2018) Thermomechanical peridynamic analysis with irregular non-uniform domain discretization. Eng Fract Mech 197:92–11310.1016/j.engfracmech.2018.02.006 ↗
17. Huang D, Lu G, Qiao P (2015) An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis. Int J Mech Sci 94:111–12210.1016/j.ijmecsci.2015.02.018 ↗
18. Isiet M, Mišković I, Mišković S (2021) Review of peridynamic modelling of material failure and damage due to impact. Int J Impact Eng 147:10374010.1016/j.ijimpeng.2020.103740 ↗
19. Jafarzadeh S, Mousavi F, Larios A, Bobaru F (2022) A general and fast convolution-based method for peridynamics: applications to elasticity and brittle fracture. Comput Methods Appl Mech Eng 392:11466610.1016/j.cma.2022.114666 ↗
20. Javili A, Morasata R, Oterkus E, Oterkus S (2019) Peridynamics review. Math Mech Solids 24(11):3714–373910.1177/1081286518803411 ↗
21. Jha PK, Lipton R (2020) Kinetic relations and local energy balance for LEFM from a nonlocal peridynamic model. Int J Fract 226(1):81–9510.1007/s10704-020-00480-0 ↗
22. Kantorovich L, Akilov P (1964) Functional analysis in normed spaces. Pergamon, New York
23. Kilic B, Madenci E (2010) An adaptive dynamic relaxation method for quasi-static simulations using the peridynamic theory. Theor Appl Fract Mech 53(3):194–20410.1016/j.tafmec.2010.08.001 ↗
24. Li Q, Bobaru F (2016) Surface corrections for peridynamic models in elasticity and fracture. Comput Mech 61:499–518
25. Lipton R (2014) Dynamic brittle fracture as a small horizon limit of peridynamics. J Elast 117(1):21–5010.1007/s10659-013-9463-0 ↗
26. Lipton R (2016) Cohesive dynamics and brittle fracture. J Elast 124(2):143–19110.1007/s10659-015-9564-z ↗
27. Lipton RP, Jha PK (2021) Nonlocal elastodynamics and fracture. Nonlinear Differ Equ Appl. https://doi.org/10.1007/s00030-021-00683-x10.1007/s00030-021-00683-x ↗
28. Lipton R, Said E, Jha P (2018) Free damage propagation with memory. J Elast 133(2):129–15310.1007/s10659-018-9672-7 ↗
29. Lipton RP, Lehoucq RB, Jha PK (2019) Complex fracture nucleation and evolution with nonlocal elastodynamics. J Peridynamics Nonlocal Model 1(2):122–13010.1007/s42102-019-00010-0 ↗
30. Mehrmashhadi J, Chen Z, Zhao J, Bobaru F (2019) A stochastically homogenized peridynamic model for intraply fracture in fiber-reinforced composites. Compos Sci Technol 182:10777010.1016/j.compscitech.2019.107770 ↗
31. Mengesha T, Du Q (2013) Analysis of a scalar nonlocal peridynamic model with a sign changing kernel. Discrete Continuous Dyn Syst B 18(5):1415–143710.3934/dcdsb.2013.18.1415 ↗
32. Mengesha T, Du Q (2014) Nonlocal constrained value problems for a linear peridynamic Navier equation. J Elast 116(1):27–51. https://doi.org/10.1007/s10659-013-9456-z10.1007/s10659-013-9456-z ↗
33. Mikata Y (2012) Analytical solutions of peristatic and peridynamic problems for a 1d infinite rod. Int J Solids Struct 49(21):2887–289710.1016/j.ijsolstr.2012.02.012 ↗
34. Ni T, Zaccariotto M, Zhu Q, Galvanetto U (2018) Static solution of crack propagation problems in peridynamics. Comput Methods Appl Mech Eng. https://doi.org/10.1016/j.cma.2018.11.02810.1016/j.cma.2018.11.028 ↗
35. Niazi S, Chen Z, Bobaru F (2021) Crack nucleation in brittle and quasi-brittle materials: a peridynamic analysis. Theor Appl Fract Mech 112:102855. https://doi.org/10.1016/j.tafmec.2020.10285510.1016/j.tafmec.2020.102855 ↗
36. Ortega J (1968) The newton-kantorovich theorem. The American Math Monthly 658–66010.2307/2313800 ↗
37. Prakash N, Stewart RJ (2020) A multi-threaded method to assemble a sparse stiffness matrix for quasi-static solutions of linearized bond-based peridynamics. J Peridynamics Nonlocal Model 3(2):113–14710.1007/s42102-020-00041-y ↗
38. Rabczuk T, Ren H (2017) A peridynamics formulation for quasi-static fracture and contact in rock. Eng Geol 225:42–4810.1016/j.enggeo.2017.05.001 ↗
39. Sheikhbahaei P, Mossaiby F, Shojaei A (2023) An efficient peridynamic framework based on the arc-length method for fracture modeling of brittle and quasi-brittle problems with snapping instabilities. Comput Math Appl 136:165–19010.1016/j.camwa.2023.02.020 ↗
40. Shiihara Y, Tanaka S, Yoshikawa N (2019) Fast quasi-implicit nosb peridynamic simulation based on fire algorithm. Mech Eng J10.1299/mej.18-00363 ↗
41. Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48(1):175–20910.1016/S0022-5096(99)00029-0 ↗
42. Silling S, Ascari E (2005) A mesh free method based on the peridynamic model of solid mechanics. Comput Struct 83:1526–153610.1016/j.compstruc.2004.11.026 ↗
43. Silling S, Lehoucq R (2008) Convergence of peridynamics to classical elasticity theory. J Elast 93:13–3710.1007/s10659-008-9163-3 ↗
44. Silling SA, Epton M, Weckner O, Xu J, Askari E (2007) Peridynamic states and constitutive modeling. J Elast 88(2):151–18410.1007/s10659-007-9125-1 ↗
45. Silling SA, Weckner O, Askari E, Bobaru F (2010) Crack nucleation in a peridynamic solid. Int J Fract 162(1–2):219–22710.1007/s10704-010-9447-z ↗
46. Wang H, Tian H (2012) A fast galerkin method with efficient matrix assembly and storage for a peridynamic model. J Comput Phys 231(23):7730–773810.1016/j.jcp.2012.06.009 ↗
47. Wang F, Ma Y, Guo Y, Huang W (2019) Studies on quasi-static and fatigue crack propagation behaviours in friction stir welded joints using peridynamic theory. Adv Mater Sci Eng10.1155/2019/5105612 ↗
48. Willis J (1975) Equations of motion for propagating cracks. The Mechanics and Physics of Fracture. Met Soc 4:57–67
49. Winkler B (2001) Traglastuntersuchungen von unbewehrten und bewehrten Betonstrukturen auf der Grundlage eines objektiven Werkstoffgesetzes für Beton. University of Innsbruck, Austria
50. Wu P, Zhao J, Chen Z, Bobaru F (2020) Validation of a stochastically homogenized peridynamic model for quasi-static fracture in concrete. Eng Fract Mech 237:10729310.1016/j.engfracmech.2020.107293 ↗
51. Yaghoobi A, Chorzepa MG, Kim SS, Durham SA (2017) Mesoscale fracture analysis of multiphase cementitious composites using peridynamics. Materials 10(2):162. https://doi.org/10.3390/ma1002016210.3390/ma10020162 ↗
52. Zaccaritto M, Luongo F, Sargeo G, Galvanetto U (2015) Examples of applications of the peridynamic theory to the solution of static equilibrium problems. Aeronaut J 119:677–70010.1017/S0001924000010770 ↗
53. Zhang G, Le Q, Loghin A, Subramaniyan A, Bobaru F (2016) Validation of a peridynamic model for fatigue cracking. Eng Fract Mech 162:76–9410.1016/j.engfracmech.2016.05.008 ↗
54. Zhao J, Tang H, Xue S (2018) Peridynamics versus xfem: a comparative study for quasi-static crack problems. Front Struct Civil Eng 12(4):548–55710.1007/s11709-017-0434-6 ↗