Summary
The paper deals with the systematic development of variational methods and associated finite element schemes for the approximate analysis of elastoplastic continua. The major difference between these novel models and existing ones consists in treating the yield condition as an a posteriori (‘natural’) constraint and not as an a priori (‘essential’) constraint. The advantages of this approach over existing ones are pointed out and discussed from a theoretical and a computational standpoint as well.
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Karamanlidis, D.: Variationsprinzipien der geometrisch nichtlinearen Elasto-Plastostatik und ihre Anwendbarkeit im Rahmen der Finite-Element-Methode. Internal Report, 1st Inst. of Mechanics, Technical University of Berlin West, Berlin West 1977.
Spilker, R. L.: A study of elasto-plastic analysis by the assumed-stress hybrid finite-element model, with application of thick shells of revolution. Thesis presented to the Massachusetts Institute of Technology, Cambridge, Mass., 1974, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Pian, T. H. H.: Variational principles for incremental finite element methods. Journal of the Franklin Institute302, 473–488 (1976).
Washizu, K.: Variational methods in elasticity or plasticity, 3rd Edition. Pergamon Press 1982.
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Karamanlidis, D. On some new variational formulations and finite element models in classical elastoplasticity. Acta Mechanica 68, 57–69 (1987). https://doi.org/10.1007/BF01182016
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DOI: https://doi.org/10.1007/BF01182016