Geodesic
Metodo della differenza ali'indietro e determinazione dei moduli tangenti per analisi evolutive elastoplastiche a passi finiti
Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 82 (1988) no. 1, pp. 75-89 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

Voir la notice de l'article

In this paper a backward difference technique is applied to the numerical time integration of elasto-plastic constitutive laws. Reference is made to isotropic constitutive models for which the yield functions depend on the first invariant of the stress tensor, on the second invariant of the stress deviator and on some suitable internal variables. For these models the implicit non-linear relations arising from the adopted integration scheme are established; these relations represent the material constitution in the finite-step. An expression for the "tangent matrix" consistent with such integration scheme is achieved in a unified form which is particularly convenient for computer implementations. 
@article{RLINA_1988_8_82_1_a10,
     author = {Perego, Umberto},
     title = {Metodo della differenza ali'indietro e determinazione dei moduli tangenti per analisi evolutive elastoplastiche a passi finiti},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali},
     pages = {75--89},
     year = {1988},
     volume = {Ser. 8, 82},
     number = {1},
     zbl = {0705.73050},
     mrnumber = {0999840},
     language = {it},
     url = {http://geodesic.mathdoc.fr/item/RLINA_1988_8_82_1_a10/}
}
TY  - JOUR
AU  - Perego, Umberto
TI  - Metodo della differenza ali'indietro e determinazione dei moduli tangenti per analisi evolutive elastoplastiche a passi finiti
JO  - Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali
PY  - 1988
SP  - 75
EP  - 89
VL  - 82
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/RLINA_1988_8_82_1_a10/
LA  - it
ID  - RLINA_1988_8_82_1_a10
ER  - 
%0 Journal Article
%A Perego, Umberto
%T Metodo della differenza ali'indietro e determinazione dei moduli tangenti per analisi evolutive elastoplastiche a passi finiti
%J Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali
%D 1988
%P 75-89
%V 82
%N 1
%U http://geodesic.mathdoc.fr/item/RLINA_1988_8_82_1_a10/
%G it
%F RLINA_1988_8_82_1_a10
Perego, Umberto. Metodo della differenza ali'indietro e determinazione dei moduli tangenti per analisi evolutive elastoplastiche a passi finiti. Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 82 (1988) no. 1, pp. 75-89. http://geodesic.mathdoc.fr/item/RLINA_1988_8_82_1_a10/

[1] Wilkins M.L. (1964) - Calculation of elastic plastic flow, in: Methods of Computational Physics, a cura di Alder B. et alii, Vol. 3, Academic Press, New York.

[2] Owen D.R.J. e Hinton E. (1980) - Finite elements in plasticity - theory and practice, Pineridge Press, Swansea. | MR | Zbl

[3] Ortiz M. e Simo J.C. (1986) - An analysis of a new class of integration algorithms for elastoplastic constitutive relations, «Int. J. Num. Meth. Eng.», 23, 353-366. | DOI | MR | Zbl

[4] De Borst R. (1984) - Implicit integration of stress-strain laws in thermoplasticity, Report N. BI-84-43/68.8.2002, Software Engineering Department/Section Diana, Rijswijk.

[5] Franchi A. e Genna F. (1987) - A numerical scheme for integrating the rate plasticity equations with an "a priori" error control, «Comp. Meth. Appl. Mech. Eng.», 60, 317-342. | DOI | MR | Zbl

[6] Simo J.C. e Hughes T.J.R. (1987) - General return mapping algorithms for rate independent plasticity, in: Atti del 2° Congresso su Constitutive Laws for Engineering Materials, a cura di Desai C.S., Krempl E., Kiousis P.D., Kundu T., Università dell'Arizona, 221-231.

[7] Hughes T.J.R. (1984) - Numerical implementation of constitutive models: rate independent deviatone plasticity, in: Theoretical Foundation for large Scale Computations of Nonlinear Material Behaviour, a cura di Nemat Nasser S., Asaro R.J., Hegemier G.A., Martinus Nijhoff Publishers, Dordrecht.

[8] Krieg R.D. e Krieg D.B. (1977) - Accuracies of numerical solution methods for the elastic perfectly plastic model, «J. Pressure Vessel Technology, ASME», 99, 510-515.

[9] Yoder P.J. e Whirley B.G. (1984) - On the numerical implementation of elastoplastic models, «J. Appl. Mech.», 51, 238-288. | Zbl

[10] Loret B. e Prévost J.M. (1986) - Accurate numerical solutions for Drucker-Prager elastic plastic models, «Comp. Meth. Appl. Mech. Eng.», 54, 259-277. | DOI | MR | Zbl

[11] Ortiz M. e Popov E.P. (1985) - Accuracy and stability analysis of integration algorithms for elastoplastic constitutive equations, «Int. J. Num. Meth. Eng.», 21, 1561-1576. | DOI | MR | Zbl

[12] Hibbitt H.D. (1985) - Some issues in numerical simulation of nonlinear structural response, in: Workshop on Computational Methods for Structural Mechanics and Dynamics, NASA Langley Research Center.

[13] Crisfield M.A. (1987) - Consistent schemes for plasticity computation with the Newton-Raphson method, in: Computational Plasticity, a cura di Owen D.R.J., Hinton E., Onate E., Pineridge Press, Swansea, 133-159. | MR

[14] Perego U. (1987) - Backward difference operators and consistent predictors for linear hardening elastic-plastic constitutive laws, di prossima pubblicazione su Solid Mechanics Archives. | Zbl

[15] Martin J.B., Reddy B.D., Griffin T.B. e Bird W.W. (1987) - Application of mathematical programming concepts to incremental elastic plastic analysis, di prossima pubblicazione su Engineering Structures. | MR

[16] Martin J.B. (1987), A complementary work hounding principle for forward integration along the path of loading for elastoplastic bodies, «J. Appl. Mech.», 109, 341-345. | Zbl

[17] Maier G. (1970) - A matrix structural theory of piecewise-linear plasticity with interacting yield planes, «Meccanica», 5, 55-66. | Zbl

[18] De Donato O. e Maier G. (1979) - Mathematical programming methods for the inelastic analysis of reinforced concrete frames allowing for limited rotation capacity, «Int. J. for Num. Meth. in Eng.», 4, 307-329. | Zbl

[19] Nagtegaal J.C. (1982) - On the implementation of inelastic constitutive equations with special reference to large deformation problems, «Comp. Meth. Appl. Mech. Eng.», 33, 469-484. | Zbl

[20] Simo J.C. e Taylor R.L. (1985) - Consistent tangent operators for rate independent elastoplasticity, «Comp. Meth. Appl. Mech. Eng.», 48, 101-118. | Zbl