Quasistatic evolution problems for pressure-sensitive plastic materials

Milan Journal of Mathematics

Volumn 75, Issue 1, 2007, Pages 117-134

  Del Maso, Gianni ^a   Demyanov, Alexey ^a   DeSimone, Antonio ^a  

^a SISSA   (Italy)

Author keywords

Prandtl Reuss plasticity; Pressure sensitive yield criteria; Quasistatic evolution; Rate independent processes

Indexed keywords

EID: 38749137369     PISSN: 14249286     EISSN: 14249294     Source Type: Journal    
DOI: 10.1007/s00032-007-0071-y     Document Type: Article

References (19)

1. G. Anzellotti, Pairings between measures and bounded functions and compensated compactness. Ann. Math. Pura Appl. (4) 135 (1983), 293-318.
2. G. Anzellotti, On the extremal stress and displacement in Hencky plasticity. Duke Math. J. 51 (1984), 133-147.
3. D. Bigoni, A. Piccolroaz, Yield criteria for quasibrittle and frictional materials. Int. J. Solids Struct. 41 (2004), 2855-2878.
4. H. Brezis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hubert. North-Holland, Amsterdam-London; American Elsevier, New York, 1973.
5. G. Dal Maso, A. DeSimone, M.G. Mora, Quasistatic evolution problems for linearly elastic-perfectly plastic materials. Arch. Ration. Mech. Anal. 180 (2006), 237-291.
6. A. DeSimone, C. Tamagnini, Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains. Int. J. Numer. Anal. Meth. Geomech. 29 (2005), 73-101.
7. V.S. Desphande, N. Fleck, Isotropic constitutive models for elastic foams. J. Mech. Phys. Solids 28 (2000), 1253-1283.
8. A.L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: part I, yield criteria and flow rules for porous ductile media. Int. J. Engng. Mat. Tech. 99 (1977), 2-15.
9. E. Gagliardo, Caratterizzazione delle tracce sulla frontiera relative ad alcune classi di funzioni in n variabili. Rend. Sem. Mat. Univ. Padova 27 (1957), 284-305.
10. C. Goffman, J. Serrin, Sublinear functions of measures and variational integrals. Duke Math. J. 31 (1964), 159-178.
11. R. V. Kohn , R. Temam, Dual spaces of stresses and strains, with applications to Hencky plasticity. Appl. Math. Optim. 10 (1983), 1-35.
12. H. Matthies, G. Strang, E. Christiansen, The saddle point of a differential program. Energy Methods in Finite Element Analysis, Glowinski R., Rodin E., Zienkiewicz O.C. ed., Wiley, New York, 1979, 309-318.
13. A. Mielke, Evolution of rate-independent systems. In: Evolutionary equations. Vol. II. Edited by C M. Dafermos and E. Feireisl, Handbook of Differential Equations. Elsevier/North-Holland, Amsterdam, 2005, 461-559.
14. N.S. Ottosen, A failure criterion for concrete. J. Eng. Mech. Div.-ASCE 103 (1977), 527-535.
15. W. Rudin, Real and Complex Analysis. McGraw-Hill, New York, 1966.
16. P. Suquet, Sur les équations de la plasticité: existence et régularité des solutions. J. Mécanique, 20 (1981), 3-39.
17. R. Temam, Mathematical problems in plasticity. Gauthier-Villars, Paris, 1985.
18. Translation of Problèmes mathématiques en plasticité. Gauthier-Villars, Paris, 1983.
19. R. Temam, G. Strang, Duality and relaxation in the variational problem of plasticity. J. Mécanique, 19 (1980), 493-527.