Shakedown with Non Associated Flow Rule
First, we present the concept of bifunctional which allows to extend the calculus of variation in case of a material admitting a bipotential. Next, the bound theorems of the shakedown analysis are generalized for this class of plastic materials. The key of the proof is that the normality rule is conserved but in an implicit form. The theory is illustrated by the problem of a thin walled tube under constant tension and alternating cyclic torsion. We recover the value of the shakedown factor given by Lemaitre and Chaboche and we prove that it is the exact one.
KeywordsBack Stress Residual Stress Field Thin Walled Tube Constant Tension Associate Flow Rule
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- de Saxcé, G. and Tritsch, J. B. (2000). Shakedown of elastic-plastic structures with non linear kinematical hardening by the bipotential approach. In Weichert, D., and Maier, G., eds., Inelastic Analysis of Structures under Variable Loads: Theory and Engineering Applications, Solid Mechanics and its Applications, 83. Dordrecht: Kluwer Academic Publishers, 167–182.Google Scholar
- Hjiaj, M. (1999). Algorithmes adaptés à l’analyse de structures constituées de matériaux non standards et à l’estimation a posteriori de l’erreur. Thèse de Doctorat de la Faculté Polytechnique de Mons, Belgique.Google Scholar
- Lemaitre, J. and Chaboche, J.L. (1990). Mechanics of Solid Materials, Cambridge University Press.Google Scholar
- Martin, J.B. (1975). Plasticity, fundamentals and general results. MA: MIT Press.Google Scholar
- Pontes, I.D.S., Borges, L.A., Zouain, N. and Andrade, I.J.P. (2000). A variational formulation and algorithm for collapse in softening materials. Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2000, Barcelona.Google Scholar