×

zbMATH — the first resource for mathematics

A dissipation-based arc-length method for robust simulation of brittle and ductile failure. (English) Zbl 1156.74397
Summary: A robust method to trace the equilibrium path in non-linear solid mechanics problems is proposed. A general arc-length constraint based on the energy release rate is developed. Constraints have been derived for the cases of geometrically linear damage, geometrically linear plasticity and geometrically non-linear damage. All three constraints can efficiently be applied in a finite element context. Numerical simulations demonstrate that the proposed framework gives robust results for these cases. Applicability of the proposed framework to other types of constitutive and/or kinematic behaviour is predicted.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74R10 Brittle fracture
74R20 Anelastic fracture and damage
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Riks, An incremental approach to the solution of snapping and buckling problems, International Journal of Solids and Structures 15 pp 529– (1979) · Zbl 0408.73040
[2] Ramm, Nonlinear Finite Element Analysis in Structural Mechanics pp 63– (1981) · doi:10.1007/978-3-642-81589-8_5
[3] Crisfield, Accelerated solution techniques and concrete cracking, Computer Methods in Applied Mechanics and Engineering 33 (1-3) pp 585– (1982) · Zbl 0478.73088
[4] Geers, Enhanced solution control for physically and geometrically non-linear problems. Part I-the subplane control approach, International Journal for Numerical Methods in Engineering 46 pp 177– (1999) · Zbl 0957.74034
[5] Geers, Enhanced solution control for physically and geometrically non-linear problems. Part II-comparative performance analysis, International Journal for Numerical Methods in Engineering 46 pp 205– (1999) · Zbl 0957.74034
[6] de Borst, Computation of post-bifurcation and post-failure behaviour of strain-softening solids, Computers and Structures 25 pp 521– (1999)
[7] Alfano, Solution strategies for the delamination analysis based on a combination of local-control arc-length and line searches, International Journal for Numerical Methods in Engineering 58 (7) pp 999– (2003) · Zbl 1032.74660
[8] Gutiérrez, Energy release control for numerical simulations of failure in quasi-brittle solids, Communications in Numerical Methods in Engineering 20 pp 19– (2004) · Zbl 1047.74551
[9] Bathe, Finite Element Procedures (1996)
[10] Dugdale, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids 8 pp 100– (1960)
[11] Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture, Advances in Applied Mechanics 7 pp 55– (1962)
[12] Hillerborg, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement and Concrete Research 6 pp 773– (1976)
[13] Babuška, The partition of unity method, International Journal for Computational Methods in Engineering 40 (4) pp 727– (1997) · Zbl 0949.65117 · doi:10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N
[14] Belytschko, Elastic crack growth in finite elements with minimal remeshing, International Journal for Computational Methods in Engineering 45 (5) pp 601– (1999) · Zbl 0943.74061 · doi:10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S
[15] Wells, A new method for modelling cohesive cracks using finite elements, International Journal for Computational Methods in Engineering 50 (12) pp 2667– (2001) · Zbl 1013.74074 · doi:10.1002/nme.143
[16] Schellekens, On the numerical integration of interface elements, International Journal for Computational Methods in Engineering 36 (1) pp 43– (1993) · Zbl 0825.73840 · doi:10.1002/nme.1620360104
[17] Camacho, Computational modelling of impact damage in brittle materials, International Journal of Solids and Structures 33 pp 2899– (1996) · Zbl 0929.74101
[18] Remmers JJC. Discontinuities in solids and structures-a unifying computational approach. Dissertation, Delft University of Technology, 2006.
[19] Schlangen E. Experimental ad numerical analysis of fracture processes in concrete. Dissertation, Delft University of Technology, 1993.
[20] Rots, Smeared and discrete representations of localized fracture, International Journal of Fracture 51 pp 45– (1991)
[21] Peerlings, Gradient-enhanced modelling of concrete fracture, Mechanics of Cohesive-frictional Materials 3 pp 323– (1998)
[22] Chen, Constitutive Equations for Engineering Materials 1 (1994)
[23] Simo, A return mapping algorithm for plane stress elastoplasticity, International Journal for Computational Methods in Engineering 22 pp 649– (1986) · Zbl 0585.73059 · doi:10.1002/nme.1620220310
[24] Griffiths, Slope stability analysis by finite elements, Géotechnique 49 pp 387– (1999)
[25] de Borst R. Non-linear analysis of frictional materials. Dissertation, Delft University of Technology, 1986.
[26] Simo, An analysis of stress discontinuities induced by strain-softening in rate-independent inelastic solids, Computational Mechanics 12 pp 272– (1993) · Zbl 0783.73024
[27] von Mises, Mechanik der plastischen Formnderung von Kristallen, Zeitschrift fur Angewandte Mathematik und Mechanik 8 pp 161– (1928)
[28] Kumar, Properties of a three-dimensional Poisson-Voronoi tessellation: a Monte-Carlo study, Journal of Statistical Physics 67 pp 523– (1992)
[29] Allix, Geometrical and interfacial non-linearities in the analysis of delamination in composites, International Journal of Solids and Structures 36 pp 2189– (1999) · Zbl 0940.74016
[30] Wells, A consistent geometrically non-linear approach for delamination, International Journal for Numerical Methods in Engineering 54 pp 1333– (2002) · Zbl 1086.74043
[31] Xu, Void nucleation by inclusion debonding in an crystal matrix, Modelling and Simulation in Materials Science and Engineering 1 pp 111– (1993)
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.