Some theoretical results about second-order work, uniqueness, existence and controllability independent of the constitutive equation

Journal of Engineering Mathematics

Volumn 52, Issue 1, 2005, Pages 53-61

  Chambon, René ^a  

^a LABORATOIRE SOLS SOLIDES STRUCTURES   (France)

Author keywords

Existence; Geomaterials; Localization; Non normality; Second order work; Uniqueness

Indexed keywords

BOUNDARY VALUE PROBLEMS; CONTROLLABILITY; GRANULAR MATERIALS; HARDENING; MATHEMATICAL MODELS; ROCKS; SOILS;

CONTINUUM MEDIA; DEVIATORIC BEHAVIOURS; GEOMATERIALS; INELASTIC RATE-DEPENDENT CONSTITUTIVE EQUATIONS;

CONTINUUM MECHANICS;

MATHEMATICAL METHOD;

EID: 22844452363     PISSN: 00220833     EISSN: 15732703     Source Type: Journal    
DOI: 10.1007/s10665-005-0442-8     Document Type: Article

References (21)

1. W.T. Koiter 1960 General theorems for elstic plastic solids In: I.N. Sneddon and R. Hill (eds.) Progress in Solid Mechnics 1 North Holland Publishing Comp Amsterdam 165-221
2. Y. Dafalias and I. Popov 1976 Plastic internal variables formalism of cyclic plasticity J. Appl. Mech. 98 645-650
3. C. Tamagnini G. Viggiani and R. Chambon 1999 A review of two different approaches to hypoplasticity In: D. Kolymbas (ed.) Constitutive Modelling of Granular Materials including Developments and Perspectives of Hypoplasticity Springer Berlin 107-145
4. O.C. Zienkiewicz and G.N. Pande 1977 Time-dependent multi-laminate model of rocks. A numerical study of deformation and failure of rock masses Int. Num. Analyt. Methods Geomech. 1 219-247
5. M. Jirasek and Z.P. Bazant 2002 Inelastic Analysis of Structures John Wiley and sons Chichester 758pp
6. R. Hill 1978 Aspect of invariance in solids mechanics Adv. Appl. Mech. 18 1-75
7. B. Raniecki and OT. Bruhns 1981 Bounds to bifurcation stresses in solids with non associated plastic flow rule at finite strain J. Mech. Phys. Solids 29 153-172
8. R. Chambon and D. Caillerie 1999 Existence and uniqueness theorems for boundary-value problems involving incrementally non linear models Int. J. Solids Struct. 36 5089-5099
9. D. Bigoni 1999 Bifurcation and instability on non associative elastoplastic solids In: H. Petryk (ed.) CISM Material Instabilities in Elastic and Plastic Solids Springer Wien, New York 1-52
10. R. Nova 1994 Controllability of the incremental response of soil specimens subjected to arbitrary loading programmes J. Mech. Behav. Materials 5 221-243
11. S. Imposimato and R. Nova 1998 An investigation on the uniqueness of the incremental response of elstoplastic models for virgin sand Mech. Cohesive Frictl. Material 3 65-87
12. El Hassan N. (1997). Modélisation théorique et numérique de la localisation de la déformation dans les géomatériaux. PhD thesis. Université Joseph Fourier Grenoble France, 345 pp
13. Niemunis A. Extended Hypoplasticiy for Soils. Habilitation thesis, Bochum, Germany (2002) 191 pp.
14. H. Petryk 1999 Theory of material instability in incrementally nonlinear plasticity In: H. Petryk (ed.) CISM Material Instabilities in Elastic and Plastic Solids Springer Wien, New York 261-331
15. H. Petryk 2000 General conditions for uniqueness in materials with multiple mechanisms in inelastic deformation J. Mech. Phys. Solids 48 367-396
16. J. Rice 1976 The localization of plastic deformation In: W.D. Koiter (ed.) Proceedings of the International Congress of Theoretical and Applied Mechanics North Holland Publishing Comp Amsterdam 207-220
17. R. Chambon S. Crochepeyre and R. Charlier 2001 An algorthm and a method to search bifurcation points in non linear problems Int. J. Num. Methods Engng. 51 315-332
18. Nova R. (1989). Liquefaction, stability, bifurcation, of soil via strainhardening plasticity. In: Sikora Z. (ed). Proceedings of the International Workshop on Bifurcation and Localization in Soil and Rocks. Gdansk pp. 117-131
19. R. Chambon and S. Crochepeyre 1998 Daphnis a new model for the description of post-localization behavior: Application to sands Mech. Cohesive Frictl. Material. 3 127-153
20. R. Chambon and V. Roger 2003 Mohr-Culomb mini CLoE model: Uniqueness and localization studies, links with normality rule Int. J. Num. Analyt. Methods Geomech. 27 49-68
21. C. Dascalu I.R. Ionescu and M. Campillo 2000 Fault finitness and initiation of dynamic shear instability Earth Planet. Sci. Lett. 177 163-176 163-176