×

A numerical study of the jerky crack growth in elastoplastic materials with localized plasticity. (English) Zbl 1471.65183

The authors present a numerical implementation of a model of quasi-static crack growth in linearly elastic-perfectly plastic materials. By assuming that the displacement is antiplane, and that the cracks and the plastic slips are localized on a prescribed path, a numerical evidence of the fact that the crack growth is intermittent, with jump characteristics that depend on the material properties, is provided.

MSC:

65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations
74A45 Theories of fracture and damage
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74B10 Linear elasticity with initial stresses
74R10 Brittle fracture

Software:

deal2lkit; deal.ii
PDF BibTeX XML Cite
Full Text: arXiv Link

References:

[1] D. Arndt, W. Bangerth, T. C. Clevenger, D. Davydov, M. Fehling, D. Garcia-Sanchez, G. Harper, T. Heister, L. Heltai, M. Kronbichler, R. Maguire Kynch, M. Maier, J. P. Pelteret, B. Turcksin, D. Wells:The deal.II library, Version 9.1, J. Numer. Math. 27/4 (2019) 203-213. · Zbl 1435.65010
[2] D. Arndt, W. Bangerth, D. Davydov, T. Heister, L. Heltai, M. Kronbichler, M. Maier, J.-P. Pelteret, B. Turcksin, D. Wells:The deal.II finite element library: Design, features, and insights, Comp. Math. Appl. 81 (2021) 407-422. · Zbl 07288721
[3] S. Brach, E. Tanné, B. Bourdin, K. Bhattacharya:Phase-field study of crack nucleation and propagation in elastic-perfectly plastic bodies, Comp. Meth. Appl. Mech. Engineering 353 (2019) 44-65. · Zbl 1441.74201
[4] P. G. Ciarlet:The Finite Element Method for Elliptic Problems, Classics in Applied Mathematics 40, SIAM, Philadelphia (2002). · Zbl 0999.65129
[5] G. Dal Maso, R. Toader:Quasistatic crack growth in elasto-plastic materials: The two-dimensional case, Arch. Rational Mech. Analysis 196/3 (2010) 867-906. · Zbl 1304.74005
[6] G. Dal Maso, R. Toader:On the jerky crack growth in elastoplastic materials, Calc. Var. Partial Diff. Equations 59 (2020), art. no. 107. · Zbl 1443.74255
[7] L. De Lorenzis, A. McBride, B. D. Reddy:Phase-field modelling of fracture in single crystal plasticity, GAMM-Mitteilungen 39/1 (2016) 7-34. · Zbl 1397.74031
[8] Y. Descatha, P. Ledermann, J. C. Devaux, F. Mudry, A. Pineau, J. C. Lautridou:Experimental and numerical study of the different stages in ductile rupture - Application
[9] A. Ern, J.-L. Guermond:Theory and Practice of Finite Elements, Applied Mathematical Sciences 159, Springer, Berlin (2004). · Zbl 1059.65103
[10] D. Hull:Fractography Observing, Measuring and Interpreting Fracture Surface Topography, Cambridge Univerty Press, Cambridge (1999).
[11] J. W. Hutchinson:A Course on Nonlinear Fracture Mechanics, Department of Solid Mechanics, Technical University of Denmark (1979).
[12] A. Mielke, T. Roubiček:Rate-Independent Systems. Theory and Application, Springer, New York (2015). · Zbl 1339.35006
[13] M. Ortiz, A. Pandolfi:Finite-deformation irreversible cohesive elements for threedimensional crack-propagation analysis, Int. J. Numer. Meth. Engineering 44/9 (1999) 1267-1282. · Zbl 0932.74067
[14] J. R. Rice:Mathematical analysis in the mechanics of fracture, Math. Fundamentals 2/B2 (1968) 191-311.
[15] J. R. Rice, E. P. Sorensen:Continuing crack-tip deformation and fracture for planestrain crack growth in elastic-plastic solids, J. Mech. Physics Solids 26/3 (1978) 163-186. · Zbl 0384.73066
[16] A. Sartori, N. Giuliani, M. Bardelloni, L. Heltai:deal2lkit: A toolkit library for high performance programming in deal.II, SoftwareX 7 (2018) 318-327.
[17] L. R. Scott, S. Zhang:Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Computation 54/190 (1990) 483. · Zbl 0696.65007
[18] D. Wick, T. Wick, R. J. Hellmig, H.-J. Christ:Numerical simulations of crack propagation in screws with phase-field modeling, Comp. Materials Sci. 109 (2015) 367
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.