A generalized variable formulation for gradient dependent softening plasticity

International Journal for Numerical Methods in Engineering

Volumn 39, Issue 21, 1996, Pages 3731-3755

  Comi, Claudia ^a   Perego, Umberto ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

Finite elements; Generalized variables; Gradient plasticity; Localization; Softening

Indexed keywords

BOUNDARY VALUE PROBLEMS; DIFFERENCE EQUATIONS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBLEM SOLVING;

GRADIENT DEPENDENT SOFTENING PLASTICITY; LINEAR COMPLEMENTARITY PROBLEM;

ELASTOPLASTICITY;

EID: 0030283656     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19961115)39:21<3731::AID-NME24>3.0.CO;2-Z     Document Type: Article

References (41)

1. A. Nadai, Plasticity, McGraw-Hill, New York, 1931.
2. A. Bascoul, E. H. Benaija, Y. Berthaud, J. M. Torrenti and Z. Zizi, 'Analysis of localization in concrete through stereophotogrammetry, speckle laser and replica', Cement Concr. Res., 26, 1340-1350 (1993).
3. R. de Borst, L. J. Sluys, H. B. Mühlhaus and J. Pamin, 'Fundamental issues in finite element analyses of localization of deformation', Eng. Comput., 10, 99-121 (1993).
4. E. C. Aifantis, 'The physics of plastic deformations', Int. J. Plasticity, 3, 211-247 (1987).
5. E. C. Aifantis, 'On the role of gradients in the localization of deformation and fracture', Int. J. Eng. Sci., 30, 1279-1299 (1987).
6. H. L. Schreyer and Z. Chen, 'One-dimensional softening with localization', ASME J. Appl. Mech., 53, 791-797 (1986).
7. D. Lasry and T. Belytschko, 'Localization limiters in transient problems', Int. J. Solids Struct., 24, 581-597 (1988).
8. R. de Borst and H. B. Mühlhaus, 'Gradient-dependent plasticity: formulation and algorithmic aspects', Int. j. numer. methods eng., 35, 521-539 (1992).
9. L. J. Sluys, R. de Borst and H. B. Mühlhaus, 'Wave propagation, localization and dispersion in a gradient dependent medium', Int. J. Solids Struct., 30, 1153-1171 (1993).
10. R. de Borst, J. Pamin and L. J. Sluys, 'Gradient plasticity for localization problems in quasi-brittle and frictional materials', in D. R. J. Owen, E. Onate and E. Hinton (eds.), Comptas IV, Vol. 1, Pineridge Press, Barcelona, 1995, pp. 509-533.
11. J. P. Pamin, Gradient dependent plasticity in numerical simulation of localization phenomena, Ph.D. Thesis, Delft University Press, Delft, 1994.
12. C. Comi and U. Perego, 'A regularization technique for elastoplastic softening analyses based on generalized variables', in D. R. J. Owen, E. Onate and E. Hinton (eds.), Comptas IV, Vol. 1, Pineridge Press, Barcelona, 1995, pp. 535-546.
13. F. Meftah, J. M. Reynouard and O. Merabet, 'A layered beam element for gradient plasticity', in D. R. J. Owen, E. Onate and E. Hinton (eds.), Complas IV, Vol. 2, Pineridge Press, Barcelona, 1995, pp. 2117-2127.
14. C. Comi and A. Corigliano, 'On uniqueness of the dynamic finite-step problem in gradient-dependent softening plasticity', Int. J. Solids Struct., to appear (1996).
15. B. Mühlhaus and E. C. Aifantis, 'A variational principle for gradient plasticity', Int. J. Solids Struct., 28, 845-857 (1991).
16. C. Simo, J. G. Kennedy and R. L. Taylor, 'Complementary mixed finite element formulations for elastoplasticity', Comp. Methods Appl. Mech. Eng., 74, 177-206 (1989).
17. C. Simo and T. Honein, 'Variational formulation, discrete conservation laws, and path-domain independent integrals for elasto-viscoplasticity', ASME J. Appl. Mech., 57, 488-497 (1990).
18. G. Romano, L. Rosati and F. Marotti de Sciarra, 'A variational theory for finite-step elastoplastic problem', Int. J. Solids Struct., 30, 2317-2334 (1993).
19. C. Comi and U. Perego, 'A unified approach for variationally consistent finite elements in elastoplasticity', Comp. Methods Appl. Mech. Eng., 121, 323-344 (1995).
20. A. Capsoni and L. Corradi, 'Variational formulations for the plane-strain elastic-plastic problem for materials governed by von Mises criterion', Int. J. Plasticity (1996) to appear.
21. W. Prager, 'The general theory of limit design', Proc. 8th Int. Conf. on Appl. Mech., Instanbul, 2, 65-72 (1952).
22. L. Corradi, 'A displacement formulation for the finite element elastic-plastic problem', Meccanica, 18, 77-91 (1983).
23. C. Comi, G. Maier and U. Perego, 'Generalized variable finite element modelling and extremum theorems in stepwise holonomic elastoplasticity with internal variables', Comp. Methods Appl. Mech. Eng., 96, 213-237 (1992).
24. A. Capsoni and L. Corradi, 'A mixed finite element model for plane-strain elastic-plastic analysis: part I - formulation and assessment of the overall behaviour', Comp. Meth. Appl. Mech. Eng. (1996) to appear.
25. J. C. Simo, J. G. Kennedy and S. Govindjee, 'Non-smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms, Int. j. numer. methods eng., 26, 2161-2185 (1988).
26. U. Perego, 'Explicit backward-difference operators and consistent predictors for linear hardening elastic-plastic constitutive laws', Solid Mech. Archives, 13, 65-102 (1988).
27. O. L. Mangasarian, 'Solution of symmetric linear complementarity problems by iterative methods', J. Opt. Theor. Appl., 22, 465 (1977).
28. J. C. Simo and R. L. Taylor, 'Consistent tangent operators for rate-independent elastoplasticity', Comp. Methods Appl. Mech. Eng., 48, 101-118 (1985).
29. G. Bolzon, G. Maier and G. Novati, 'Some aspects of quasi-brittle fracture analysis as a linear complementarity problem', in Z. P. Bazant, Z. Bittnar, M. Jirásek and J. Mazars (eds.), Fracture and damage in quasi brittle structures, E & FN SPON press, 1994, pp. 159-174.
30. Z. P. Bazant and G. Pijaudier-Cabot, 'Nonlocal continuum damage, localization instability and convergence', ASME J. Appl. Mech., 55, 287-293 (1988).
31. A. Benallal and V. Tvergaard, 'Nonlocal continuum effects on bifurcation in the plane strain tension-compression test', J. Mech. Phys. Solids, 43, 741-770 (1995).
32. O. De Donato and G. Maier, 'Mathematical programming methods for the inelastic analysis of reinforced concrete frames allowing for limited rotation capacity', Int. j. numer. methods eng., 4, 307-329 (1972).
33. J. B. Martin, B. D. Reddy, T. B. Griffin and W. W. Bird, 'Application of mathematical programming concepts to incremental elastic-plastic analysis', Eng. Struct., 9, 171-176 (1987).
34. C. Comi, A. Corigliano and G. Maier, 'Extremum properties of finite-step solutions in elastoplasticity with nonlinear mixed hardening', Int. J. Solids Struct., 27, 965-981 (1991).
35. L. Corradi, 'On stress computation in displacement finite element models', Comp. Methods Appl. Mech. Eng., 54, 325-339 (1986).
36. B. H. Ahn, 'Iterative methods for linear complementarity problems with upper bounds on primary variables', Math. Programming, 26, 295-315 (1983).
37. R. Hill, 'A general theory of uniqueness and stability in elastic-plastic solids', J. Mech. Phys. Solids, 6, 236-249 (1958).
38. D. G. Murty, 'On the number of solutions to the complementary problem and spanning properties of complementary cones', Linear Algebra Appl., 5, 65-108 (1972).
39. R. W. Cottle and G. B. Dantzig, 'Complementary pivot theory of mathematical programming', in: Mathematics of Decision Science, Part I, G. B. Dantzig and A. F. Beinott Jr. (eds.), American Mathematical Society, Providence, RI, 1968, pp. 115-136.
40. J. C. Nagtegaal, D. M. Parks and J. R. Rice, On numerically accurate finite element solutions in the fully plastic range, Comp. Methods. Appl. Mech. Eng., 4, 153-177 (1974).
41. J. W. Rudnicki and J.R.Rice, 'Conditions for the localization of deformation in pressure sensitive dilatant materials', J. Mech. Phys. Solids, 23, 371-394 (1975).