A hybrid multiscale finite element/peridynamics method
Source abstract
Abstract
A hybrid method is presented that uses a representative volume element-based multiscale finite element technique combined with a peridynamics method for modeling fracture surfaces. The hybrid method dynamically switches from finite element computations to peridynamics based on a damage criterion defined on the peridynamics grid, which is coincident with the nodes of the finite element mesh. Nodal forces are either computed by the finite element method or peridynamics, as appropriate. The multiscale finite element method used here is a representative volume element-based approach so that inhomogeneous local scale material properties can be derived using homogenization. In addition, automatic cohesive zone insertion is used at the local scale to model fracture initiation. Results demonstrate that local scale flaw distributions can alter fracture patterns and initiation times, and the use of cohesive zone insertion can improve accuracy of crack paths.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Numerical methods in engineering · Composite Material Mechanics · Electromagnetic Simulation and Numerical Methods
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References (38)
Show source-provided references
1. Allen DH, Searcy CR (2001) A micromechanical model for a viscoelastic cohesive zone. Int J Fract 107(2):159–17610.1023/A:1007693116116 ↗
2. Allen DH, Yoon C (1998) Homogenization techniques for thermoviscoelastic solids containing cracks. Int J Solids Struct 45:4035–405310.1016/S0020-7683(97)00299-0 ↗
3. Azdoud Y, Han F, Lubineau G (2013) A morphing framework to couple non-local and local anisotropic continua. Int J Solids Struct 50(9):1332–134110.1016/j.ijsolstr.2013.01.016 ↗
4. Azdoud Y, Han F, Lubineau G (2014) The morphing method as a flexible tool for adaptive local/non-local simulation of static fracture. Comput Mech 54(3):711–72210.1007/s00466-014-1023-3 ↗
5. Belytschko T, Moës N, Usui S, Parimi C (2001) Arbitrary discontinuities in finite elements. Int J Numer Methods Eng 50:993–101310.1002/1097-0207(20010210)50:4<993::AID-NME164>3.0.CO;2-M ↗
6. Bobaru F, Duangpanya M (2010) The peridynamic formulation for transient heat conduction. Int J Heat Mass Transf 53(19–20):4047–405910.1016/j.ijheatmasstransfer.2010.05.024 ↗
7. Diehl P, Schweitzer MA (2015) Simulation of wave propagation and impact damage in brittle materials using peridynamics. In: Recent trends in computational engineering-CE2014, pp 251–265. Springer10.1007/978-3-319-22997-3_15 ↗
8. Emmrich E, Weckner O (2006) The peridynamic model in non-local elasticity theory. In: Proceedings in applied mathematics and mechanics, vol 6, pp 155–15610.1002/pamm.200610058 ↗
9. Foster JT, Silling SA, Chen WW (2010) Viscoplasticity using peridynamics. Int J Numer Meth Eng 81(10):1242–125810.1002/nme.2725 ↗
10. Galvanetto U, Mudric T, Shojaei A, Zaccariotto M (2016) An effective way to couple fem meshes and peridynamics grids for the solution of static equilibrium problems. Mech Res Commun 76:41–4710.1016/j.mechrescom.2016.06.006 ↗
11. Gerstle W, Silling S, Read D, Tewary V, Lehoucq R (2008) Peridynamic simulation of electromigration. Science 8(2):75–92
12. Ha YD, Bobaru F (2010) Studies of dynamic crack propagation and crack branching with peridynamics. Int J Fract 162(1–2):229–244
13. Ha YD, Bobaru F (2011) Characteristics of dynamic brittle fracture captured with peridynamics. Eng Fract Mech 78(6):1156–116810.1016/j.engfracmech.2010.11.020 ↗
14. Han F, Lubineau G, Azdoud Y (2016a) Adaptive coupling between damage mechanics and peridynamics: a route for objective simulation of material degradation up to complete failure. J Mech Phys Solids 94:453–47210.1016/j.jmps.2016.05.017 ↗
15. Han F, Lubineau G, Azdoud Y, Askari A (2016b) A morphing approach to couple state-based peridynamics with classical continuum mechanics. Comput Methods Appl Mech Eng 301:336–35810.1016/j.cma.2015.12.024 ↗
16. Hill R (1967) The essential structure of constitutive laws for metal composites and polycrystals. J Mech Phys Solids 15:79–9510.1016/0022-5096(67)90018-X ↗
17. Kalthoff J, Winkler S (1988) Failure mode transition at high rates of shear loading. In: Impact loading and dynamic behavior of materials, vol 1. DGM Informationsgesellschaft mbH, Oberursel, pp 185–195
18. Katiyar A, Foster JT, Ouchi H, Sharma MM (2014) A peridynamic formulation of pressure driven convective fluid transport in porous media. J Comput Phys 261:209–22910.1016/j.jcp.2013.12.039 ↗
19. Kobayashi A, Ramulu M (1985) Dynamic fracture analysis of crack curving and branching. J Phys Colloq 46:197–206
20. Liu W, Hong J-W (2012) A coupling approach of discretized peridynamics with finite element method. Comput Methods Appl Mech Eng 245:163–17510.1016/j.cma.2012.07.006 ↗
21. Lubineau G, Azdoud Y, Han F, Rey C, Askari A (2012) A morphing strategy to couple non-local to local continuum mechanics. J Mech Phys Solids 60(6):1088–110210.1016/j.jmps.2012.02.009 ↗
22. Madenci E, Oterkus E (2014) Peridynamic theory and its applications, vol 17. Springer, Berlin10.1007/978-1-4614-8465-3 ↗
23. Oterkus S, Madenci E, Agwai A (2014) Peridynamic thermal diffusion. J Comput Phys 265:71–9610.1016/j.jcp.2014.01.027 ↗
24. Seleson P, Beneddine S, Prudhomme S (2013) A force-based coupling scheme for peridynamics and classical elasticity. Comput Mater Sci 66:34–4910.1016/j.commatsci.2012.05.016 ↗
25. Shojaei A, Mudric T, Zaccariotto M, Galvanetto U (2016) A coupled meshless finite point/peridynamic method for 2d dynamic fracture analysis. Int J Mech Sci 119:419–43110.1016/j.ijmecsci.2016.11.003 ↗
26. Silling S (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 ↗
27. Silling SA (2002) Peridynamic modeling of the Kalthoff–Winkler experiment. Technical report submission for the 2001 Sandia Prize in Computational Science, Sandia National Laboratories
28. Silling S, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83(17–18):1526–153510.1016/j.compstruc.2004.11.026 ↗
29. 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 ↗
30. Souza FV (2009) Multiscale modeling of impact on heterogeneous viscoelastic solids with evolving microcracks. Ph.D. thesis, University of Nebraska, Lincoln, NE10.1002/nme.2773 ↗
31. Souza FV (2016) Multimech http://www.multimechanics.com/ . Accessed 7 Dec 2016
32. Souza FV, Allen DH (2010a) Modeling failure of heterogeneous viscoelastic solids under dynamic/impact loading due to multiple evolving cracks using a two-way coupled multiscale model. Mech Time Depend Mater 14:125–15110.1007/s11043-009-9099-4 ↗
33. Souza FV, Allen DH (2010b) Multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks. Int J Numer Methods Eng 82:464–50410.1002/nme.2773 ↗
34. Souza FV, Allen DH (2011) Modeling the transition of microcracks into macrocracks in heterogeneous viscoelastic media using a two-way coupled multiscale model. Int J Solids Struct 48:3160–317510.1016/j.ijsolstr.2011.07.010 ↗
35. Souza FV, Allen DH (2013) Verification of a two-way coupled multiscale finite element code for dynamic/impact problems. Mech Adv Mater Struct 20(1):74–9010.1080/15376494.2011.581416 ↗
36. Wildman RA, Gazonas GA (2013) A perfectly matched layer for peridynamics in two dimensions. J Mech Mater Struct 7(8):765–781
37. Wildman RA, Gazonas GA (2014) A finite difference-augmented peridynamics method for reducing wave dispersion. Int J Fract 190(1–2):39–5210.1007/s10704-014-9973-1 ↗
38. Zhang Z, Paulino GH, Celes W (2008) Cohesive modeling of dynamic crack growth in homogeneous and functionally graded materials. Multiscale Funct Grad Mater 973:562–567