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Hardt, Robert; Kinderlehrer, David

Elastic plastic deformation. (English) Zbl 0522.73029

Appl. Math. Optimization 10, 203-246 (1983).
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Cited in 21 Documents

MSC:

74C99 Plastic materials, materials of stress-rate and internal-variable type
74S30 Other numerical methods in solid mechanics (MSC2010)
74P99 Optimization problems in solid mechanics

Keywords:

elastic plastic deformation; solid continuum; potential energy functional; first variations gives equilibrium equations; stress expressed in terms of strain; duality of first problem and regularity properties of solution; existence of elastic and plastic states; transition to fracture
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\textit{R. Hardt} and \textit{D. Kinderlehrer}, Appl. Math. Optim. 10, 203--246 (1983; Zbl 0522.73029)
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References:

[1] Agmon S, Douglis A, Nirenberg L (1964) Estimates near the boundary for solutions of elliptic differential equations satisfying general boundary conditions, II. Comm Pure Appl Math 22:35-92 · Zbl 0123.28706
[2] Anzellotti G (to appear) On the extremal stress and displacement in Hencky plasticity
[3] Anzellotti G, Giaquinta M (1980) Existence of the displacement field for an elasto-plastic body. Manus Math 32:101-136 · Zbl 0465.73022
[4] Anzellotti G, Giaquinta M (1982) On the existence of the fields of stress and displacement for an elasto-perfectly plastic body in static equilibrium. J. Math Pure Appl 61:219-244 · Zbl 0467.73044
[5] Brezis H (1972) Integrales convexes dans les espaces de Sobolev. Israel J Math 13:9-23
[6] Brezis H (1972/73) Multiplicateur de Lagrange en torsion elastoplastique. Arch Rat Mech Anal 49:32-40 · Zbl 0265.35021
[7] Brezis H, Stampacchia G (1968) Sur la regularité de la solution d’inequations elliptiques. Bull Soc Math France 96:153-180
[8] Caffarelli L, Riviere N (1979) The Lipschitz character of the stress tensor, when twisting an elastic plastic bar. Arch Rat Mech Anal 69:31-36 · Zbl 0399.73044
[9] Courant R, Hilbert D (1962) Methods of mathematical physics, vol I. Wiley (Interscience), New York · Zbl 0099.29504
[10] Duvaut G, Lions JL (1972) Les inequations en mechanique et en physique. Dunod, Paris · Zbl 0298.73001
[11] Ekeland I, Temam R (1976) Convex analysis and variational problems. North-Holland, Amsterdam · Zbl 0322.90046
[12] Friedman A (1982) Variational principles and free boundary problems. Wiley-Interscience, New York · Zbl 0564.49002
[13] Gehring F (1973) TheL P integrability of the partial derivatives of a quasiconformal map. Acta Math 130:265-277 · Zbl 0258.30021
[14] Giaquinta M, Modica G (1979) Some regularity results for some classes of higher order elliptic systems. J Reine Angw Math 311:145-169 · Zbl 0409.35015
[15] Goffman C, Serrin J (1964) Sublinear functions of measures and variational integrals. Duke J Math 31:159-178 · Zbl 0123.09804
[16] Kinderlehrer D, Stampacchia G (1980) An introduction to variational inequalities and their applications. Academic Press, New York · Zbl 0457.35001
[17] Kohn R (1982) New integral estimates for deformations in terms of their nonlinear strains. Arch Rat Mech Anal 18:131-172 · Zbl 0491.73023
[18] Kohn R, Temam R (to appear) Dual spaces of stresses and strains with application to Hencky Plasticity. Appl Math Optim 10 · Zbl 0532.73039
[19] Love AEH (1944) A treatise on the mathematical theory of elasticity. Dover, New York · Zbl 0063.03651
[20] Morrey CB (1966) Multiple integrals in the calculus of variations. Springer-Verlag, New York · Zbl 0142.38701
[21] Prager W, Hodge P (1951) Theory of perfectly plastic solids. John Wiley, New York · Zbl 0044.39803
[22] Strang G (1979) A minimax problem in plasticity theory. Springer lecture notes in mathematics 701:319-333 · Zbl 0433.73034
[23] Suquet P (1979) Un espace fonctionnel pour les equations de la plasticite. Ann Fac Sc Toulouse 1:77-87. Also, thesis (1982) Universite Paris VI · Zbl 0405.46027
[24] Temam R (1979) Mathematical problems in plasticity theory. In: Cottle R, Gianessi F, Lions JL (eds) Complimentarity problems and variational inequalities. John Wiley, New York
[25] Temam R (1981) Existence theorems for the variational problems of plasticity. In: Atteia M, Bancel D, Gumowski I (eds) Nonlinear problems of analysis in geometry and mechanics. Pitman, London · Zbl 0504.73020
[26] Teman R (1981a) On the continuity of the trace of vector functions with bounded deformation. Applicable Anal 11:291-302 · Zbl 0504.46027
[27] Temam R, Strang G (1980) Functions of bounded deformation. Arch Rat Mech Anal 75:7-21 · Zbl 0472.73031
[28] Temam R, Strang G (1980a) Duality and relaxation in the variational problems of plasticity. J de Mecanique 19:493-527 · Zbl 0465.73033
[29] Ting TW (1971) Elastic-plastic torsion of simply connected cylindrical bars. Ind Univ Math J 20:1047-1076 · Zbl 0214.24705
[30] Ting TW (1977) Elastic plastic torsion over multiply connected domains. Annali SNS Pisa 4:291-312 · Zbl 0368.73042
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