×

zbMATH — the first resource for mathematics

On gradient-enhanced damage and plasticity models for failure in quasi-brittle and frictional materials. (English) Zbl 0840.73047
Summary: Gradient-enhanced damage and plasticity approaches are reviewed with regard to their ability to model localization phenomena in quasi-brittle and frictional materials. Emphasis is put on the algorithmic aspects. For the purpose of carrying out large-scale finite element simulations, efficient numerical treatments are outlined for gradient-enhanced damage and gradient-enhanced plasticity models. For the latter class of models a full dispersion analysis is presented. In this analysis, the fundamental role of dispersion in setting the width of localization bands is highlighted.

MSC:
74R99 Fracture and damage
74S05 Finite element methods applied to problems in solid mechanics
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
PDF BibTeX Cite
Full Text: DOI
References:
[1] Aifantis, E. C. 1984: On the microstructural origin of certain inelastic models. J. Eng. Mater. Technol. 106: 326-334
[2] Aifantis, E. C. 1987: The physics of plastic deformation. Int. J. Plasticity 3: 211-247 · Zbl 0616.73106
[3] Aifantis, E. C. 1992: On the role of gradients in the localization of deformation and fracture. Int. J. Eng. Sci. 30: 1279-1299 · Zbl 0769.73058
[4] Bazant, Z. P.; Pijaudier-Cabot, G. 1988: Nonlocal continuum damage, localization instability and convergence. J. Appl. Mech. 55: 287-293 · Zbl 0663.73075
[5] Borst, R.de 1991: Simulation of strain localisation: A reappraisal of the Cosserat continuum. Eng. Comp. 8: 317-332
[6] Borst, R.de; M?hlhaus, H.-B. 1992: Gradient-dependent plasticity: Formulation and algorithmic aspects. Int. J. Num. Meth. Eng. 35: 521-539 · Zbl 0768.73019
[7] Borst, R.de 1993: A generalisation for J 2-flow theory for polar continua. Comp. Meth. Appl. Mech. Eng. 103: 347-362 · Zbl 0777.73014
[8] Borst, R.de; Pamin, J.; Sluys, L. J. 1995 Gradient plasticity for localization problems in quasibrittle and frictional materials. In: Owen, D. R. J.; Onate, E.; Hinton, E. (eds). Proc. Fourth Int. Conf. on Computational Plasticity, Theory and Applications, pp. 509-533. Swansea: Pineridge Press · Zbl 0840.73047
[9] Coleman, B. D.; Hodgdon, M. L. 1985: On shear bands in ductile materials. Arch. Ration. Mech. Anal. 90: 219-247 · Zbl 0625.73041
[10] Huerta, A.; Pijaudier-Cabot, G. 1994: Discretization influence on the regularization by two localization limiters. ASCE J. Eng. Mech. 120: 1198-1218
[11] Lasry, D.; Belytschko, T. 1988: Localization limiters in transient problems. Int. J. Solids Structures 24: 581-597 · Zbl 0636.73021
[12] Lemaitre, J.; Chaboche, J. L. 1990: Mechanics of solid materials. Cambridge: Cambridge University Press · Zbl 0743.73002
[13] Loret, B.; Pr?vost, J. H. 1990: Dynamic strain localization in elasto-(visco-)Plastic solids, Part 1. Comp. Meth. Appl. Mech. Eng. 83: 247-273 · Zbl 0717.73030
[14] M?hlhaus, H.-B.; Vardoulakis, I. 1987: The thickness of shear bands in granular materials. Geotechnique 37: 271-283
[15] M?hlhaus, H.-B. 1989: Application of Cosserat theory in numerical solutions of limit load problems. Ing.-Arch. 59: 124-137
[16] M?hlhaus, H.-B.; Aifantis, E. C. 1991: A variational principle for gradient plasticity, Int. J. Solids Structures 28: 845-858 · Zbl 0749.73029
[17] Needleman, A. 1988: Material rate dependence and mesh sensitivity in localization problems. Comp. Meth. Appl. Mech. Eng. 67: 69-86 · Zbl 0618.73054
[18] Pamin, J. 1994: Gradient-dependent plasticity in numerical simulation of localization phenomena. Diss., Delft University of Technology, Delft
[19] Peerlings, R. H. J.; Borst, R.de; Brekelmans, W. A. M.; Vree, J. H. P.de 1995a. Computational modelling of gradient-enhanced damage for fracture and fatigue problems. In: Owen, D. R. J.;Onate, E.; Hinton, E. (eds). Proc. Fourth Int. Conf. on Computational Plasticity, Theory and Applications, pp. 975-986. Swansea: Pinerdge Press · Zbl 0882.73057
[20] Peerlings, R. H. J.; Borst, R. de; Brekelmans, W. A. M., Vree, J. H. P. de 1995b: Gradient-enhanced damage for quasi-brittle materials. Int. J. Num. Meth. Eng, submitted for publication · Zbl 0882.73057
[21] Pijaudier-Cabot, G.; Bazant, Z. P. 1987: Nonlocal damage theory. ASCE J. Eng. Mech. 113: 1512-1533
[22] Schreyer, H. L.; Chem., Z. 1986: One-dimensional softening with localization. ASME J. Appl. Mech. 53: 791-797
[23] Simo, J. C.; Taylor, R. L. 1985: Consistent tangent operators for rate-independent elasto-plasticity. Comp. Meth. Appl. Mech. Eng. 48: 101-118 · Zbl 0548.73018
[24] Simo, J. C.; Ju, J. W. 1987: Strain and stress-based continuum damage models: I. Formulation. Int. J. Solids Structures 23: 821-840 · Zbl 0634.73106
[25] Simo, J. C. 1988: Strain softening and dissipation: a unification of approaches. In Mazars, J.; I Bazant, Z. P. (eds). Cracking and Damage: Strain Localization and Size Effect, pp. 440-461. London-New York: Elsevier
[26] Sluys, L. J. 1992: Wave propagation, localisation and dispersion in softening solids. Dissertation, Delft University of Technology, Delft
[27] Sluys, L. J.; Borst, R.de 1992. Wave propagation and localisation in a rate-dependent cracked medium-Model formulation and one-dimensional examples. Int. J. Solids Structures29: 2945-2958
[28] Sluys, L. J.; Borst, R.de; M?hlhaus, H.-B. 1993: Wave propagation, localization and dispersion in a gradient-dependent medium. Int. J. Solids Structures 30: 1153-1171 · Zbl 0771.73017
[29] Sluys, L. J.; Borst, R.de 1994: Dispersive properties of gradient-dependent and rate-dependent media. Mech. Mater. 18: 131-149
[30] Sluys, L. J.; Cauvern, M.; Borst, R.de 1995: Discretization influence in strain-softening problems. Eng. Comput. 12: 209-228 · Zbl 0824.73080
[31] Vardoulakis, I.; Aifantis, E. C. 1991: A gradient flow theory of plasticity for granular materials. Acta Mechanica 87: 197-217 · Zbl 0735.73026
[32] Whitham, G. B. 1974: Linear and nonlinear waves.London and New York: Wiley · Zbl 0373.76001
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.