On the stability of quasi-static paths for finite dimensional elastic-plastic systems with hardening

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 87, Issue 4, 2007, Pages 303-313

  Martins, J A C ^a   Monteiro Marques, M D P ^b   Petrov, A ^c  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b UNIVERSITY OF LISBON   (Portugal)

^c WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

Differential inclusions; Existence; Hardening; Plasticity; Stability

Indexed keywords

EID: 34248188043     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.200510315     Document Type: Article

References (13)

1. H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Mathematics Studies, No. 5, Notas de Matemática (50) (North-Holland Publishing Co., Amsterdam, 1973).
2. G. Duvaut and J. L. Lions, Inequalities in mechanics and physics, Grundlehren der Mathematischen Wissenschaften, 219, translated from the French by C.W. John (Springer-Verlag, Berlin, 1976).
3. J. Krejčí, Hysteresis, Convexity and Dissipation in Hyperbolic Equations (Gakkotosho, Tokyo, 1996).
4. B. Loret, F. Simões, and J. A. C. Martins, Flutter instability and ill-posedness in solids and fluid-saturated porous media, in: Material Instabilities in Elastic and Plastic Solids (Udine, 1999), edited by H. Petryk, CISM Courses and Lectures, Vol. 414 (Springer, Vienna, 2000), pp. 109-207.
5. J.A.C. Martins, M.D.P. MonteiroMarques, and A. Petrov, A report on the stability of quasi-static paths for finite dimensional elastic-plastic systems with hardening, Relatório ICIST, Vol. DTC 1/2007 (Instituto Superior Técnico, Lisboa, Portugal, 2007).
6. J. A. C. Martins, F. M. F. Simões, A. Pinto da Costa, and I. Coelho, Three examples on "(in)stability of quasi-static paths" (submitted) (2004).
7. J. Martins, N. Rebrova, and V. Sobolev, Math. Methods Appl. Sci. 29, 741-750 (2006).
8. R. O'Malley, Jr., Singular Perturbation Methods for Ordinary Differential Equations, Applied Mathematical Sciences, Vol.89 (Springer-Verlag, New York, 1991).
9. R.E. Showalter and P. Shi, J. Math. Anal. Appl. 216(1), 218-245 (1997).
10. R. E. Showalter and P. Shi, Comput. Methods Appl. Engrg. 151(1), 501-511 (1998).
11. A. Vasilieva, V. Butuzov, and L. Kalachev, The Boundary Function Method for Singular Perturbation Problems, SIAM Studies in Applied Mathematics (SIAM, Philadelphia, 1995).
12. A. Visintin, Journal of Physics: Conference Series 22, 222-234 (2005).
13. E. Zeidler, Nonlinear functional analysis and its applications III, Variational methods and optimization, translated from the German by Leo F. Boron (Springer-Verlag, New York, 1985).