Bounding theorem in finite plasticity with hardening effect

Gao, Yang; Wierzbicki, Tomasz

doi:10.1090/qam/1012265

Authors: Yang Gao and Tomasz Wierzbicki
Journal: Quart. Appl. Math. 47 (1989), 395-403
MSC: Primary 73E99; Secondary 73G99
DOI: https://doi.org/10.1090/qam/1012265
MathSciNet review: MR1012265
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The complementary variational problems for finite plasticity with strain-hardening effect are developed in this paper based on the theory of convex analysis. A new lower bound theorem for the load intensity factor, in which the plastic yield condition is relaxed by a complementary plastic superpotential, is proved. A simple illustrative example is worked out.

Arnold Magowan Arthurs, Complementary variational principles, 2nd ed., The Clarendon Press, Oxford University Press, New York, 1980. Oxford Mathematical Monographs. MR 594935
J. T. Oden and J. N. Reddy, On dual-complementary variational principles in mathematical physics, Internat. J. Engrg. Sci. 12 (1974), 1–29 (English, with French, German, Italian and Russian summaries). MR 0451158, DOI https://doi.org/10.1016/0020-7225%2874%2990073-1

Yang Gao, On the Complementary Principles in Elastoplastic Systems and Panpenalty Finite Element Methods, Ph.D. Thesis, Tsinghua University, Beijing, 1985

Yang Gao and Gilbert Strang, Geometric nonlinearity: potential energy, complementary energy, and the gap function, Quart. Appl. Math. 47 (1989), no. 3, 487–504. MR 1012271, DOI https://doi.org/10.1090/qam/1012271
E. T. Onat, The influence of geometry changes on the load-deformation behavior of plastic solids, Plasticity: Proceedings of the Second Symposium on Naval Structural Mechanics, Pergamon, Oxford, 1960, pp. 225–238. MR 0119605
Jerzy Ploch and Tomasz Wierzbicki, Bounds for large plastic deformations of dynamically loaded continua and structures, Internat. J. Solids Structures 17 (1981), no. 2, 183–195. MR 610904, DOI https://doi.org/10.1016/0020-7683%2881%2990074-3
Ivar Ekeland and Roger Temam, Analyse convexe et problèmes variationnels, Dunod; Gauthier-Villars, Paris-Brussels-Montreal, Que., 1974 (French). Collection Études Mathématiques. MR 0463993

T. Wierzbicki, Berechnung Dynamisch Beanspruchter Konstruktionen, Werner-Verlag, 1983

Yang Gao, Panpenalty finite element programming for limit analysis, to be published in Computer and Structure, 1988

Yang Gao, On the complementary bounding theorems for limit analysis, Internat. J. Solids Structures 24 (1988), no. 6, 545–556. MR 947427, DOI https://doi.org/10.1016/0020-7683%2888%2990056-X

P. S. Symonds and N. Jones, Impulsive loading of fully clamped beams with finite deflections and strain-rate sensitivity, Internat. J. Mech. Sci. 14, 49–69 (1972)

N. Jones, Finite deflections of a rigid-viscoplastic strain-hardening annular plate loaded impulsively, J. Appl. Mech. 35, 349–356 (1968)

Jean-Jacques Moreau, On unilateral constraints, friction and plasticity, New variational techniques in mathematical physics (Centro Internaz. Mat. Estivo (C.I.M.E.), II Ciclo, Bressanone, 1973) Edizioni Cremonese, Rome, 1974, pp. 171–322. MR 0513445