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We prove existence and uniqueness of strong global in tme solution for a subclass of monotone constitutive equations in the theory of inelastic material behaviour of metals without the coercivity assumption for the free energy function. We approximate noncoercive models by a sequence of coercive problems and prove the convergence result.
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Tom
Strony
41--81
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autor
- Fachbereich Mathematik Technische Hochschule Darmstadt Schlossgartnerstr.. 7 64289 Darmstadt, Germany
Bibliografia
- [1] H.-D. Alber, Global existence and boundedness of large solutions to nonlinear equations of viscoelasticity with hardening, Commun. Math. Phys. 166 (1995), 565-601.
- [2] H.-D. Alber, Mathernatische Theorie des inelastischen Materialverhaltens von Metallen, Mitt. Ges. Angew. Math. Mech. 18 (1995), 9-38.
- [3] H.-D. Alber, Initial-Boundary Value Problems for the Inelastic Material Behavior of Metals, Lecture Notes in Math, in preparation.
- [4] J. P. Aubin, A. Cellina, Differential Inclusions, Berlin, Heidelberg: Springer 1984.
- [5] D. Blanchard, P. Le Tallec, M. Ravachol, Numerical analysis of evolution problems in nonlinear small strains elastoviscoplasticity, Numer. Math. 55 (1989), 177-195.
- [6] H. Brézis, Operateurs maximaux monotones, North Holland, Amsterdam, 1973.
- [7] K. Chełmiński, Energy estimates and global in time results for a problem from nonlinear viscoelasticity, Bull. Acad. Polonaise Sci., Série Math. 44 (1996), 465-477.
- [8] K. Chełmiński, H. D. Alber, Existence theory for the equations of inelastic material behavior of metals - Transformation of interior variables and energy estimates, Roczniki PTM: Appl. Math. 39 (1996), 1-15.
- [9] K. Chełmiński, Stress L ͚ - estimates and the uniqueness problem for the quasistatic equations to the model of Bodner-Partom, To appear in Math. Methods Appl. Sci. (1997).
- [10] K. Chełmiński, Stress L ͚ - estimates and the uniqueness problem for the equations to the model of Bodner-Partom in the two dimensional case, To appear in Math. Methods. Appl. Sci. (1997).
- [11] K. Chełmiński, On initial-boundary value problems for the inelastic material behaviour of metals, To appear in Z. Angew. Math. Mech.
- [12] G. Duvaut, J. L. Lions, Les inéquations en méchanique et en physique, Paris: Dunod 1972.
- [13] L. C. Evans, Weak Convergence Methods for Partial Differential Equations, American Math. Society, Providence, 1990.
- [14] B. Halphen, Nguyen Quoc Son, Sur les matériaux standards généralisés, J. Méc. 14 (1975), 39-63.
- [15] I. R. Ionescu, M. Sofonea, Functional and numerical methods in viscoplasticity, Oxford, New York, Tokio: Oxford University Press, 1993.
- [16] C. Johnson, Existence theorems for plasticity problems, J. Math. Pures Appl. 55 (1976), 431-444.
- [17] C. Johnson, On plasticity with hardening, J. Math. Anal. Appl. 62 (1978), 325-336.
- [18] P. Le Tallec, Numerical analysis of viscoelastic problems, Paris: Masson. Berlin, Heidelberg, New York: Springer 1990.
- [19] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Paris: Dunod Gauthier-Villars, 1969.
- [20] J. J. Moreau, Application of convex analysis to the treatment of elastoplastic systems, In: P. Germain, B. Nayroles (eds.) 56-89, 1976.
- [21] J. J. Moreau, La notion de sur-potentiel et les liaisons unilatérales en élastostatique, C. R. Acad. Sci. Paris Sér. A267 (1968), 954-957.
- [22] J. Nečas, I. Hlaváček, Mathematical theory of elastic and elastico-plastic-bodies: An introduction, Amsterdam, Oxford, New York: Elsevier 1981.
- [23] A. Nouri, M. Rascle, A global existence and uniqueness theorem for a model problem in dynamic elasto-plasticity with isotropic strain-hardening, SIAM J. Math. Anal. 26 (1995), 850-868.
- [24] M. Rascle, Global existence of L2 -solutions in dynamical elasto-plasticity, Mat. Contemp. 11 (1996), 121-134.
- [25] P.-M. Suquet, Evolution problems for a class of dissipative materials, Quart. Appl. Math. 38 (1980/81), 391-114.
- [26] R. Temam, Problèmes mathématiques en plasticité, Paris: Gauthier-Villars 1983.
- [27] R. Temam, A generalized Norton-Hoff model and the Prandtl-Reuss law of plasticity, Arch. Rational Mech. Anal. 95 (1986), 137-183.
- [28] A. Visintin, Differential models of hysteresis, Berlin: Springer 1994.
- [29] E. Zeidler, Nonlinear functional analysis and its applications, IV, (Applications to mathematical physics.) New York: Springer 1988.
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bwmeta1.element.baztech-4f266e9b-a2bc-4c1f-b853-3990b895add0