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This paper refers to standard models in the theory of inelastic deformations. We assume that non-linear inelastic constitutive function is of monotone type, that the growth condition holds and that the model is quasistatic. Initial, generic problem is transformed into an evolution equation in a maximal monotone field. Then we find solutions with very low regularity requirements of the forces acting on a body.
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Tom
Strony
763--775
Opis fizyczny
Bibliogr. 11 poz.
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Bibliografia
- [1] H.-D. Alber, Materials with Memory, Springer, Berlin, Heidelberg, New York, 1998.
- [2] J.-P. Aubin, A. Cellina, Differential Inclusions, Springer, Berlin, 1984.
- [3] L. C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, vol. 19, AMS, 2010.
- [4] P. Kamiński, Regularity of solutions to coercive and self-controlling viscoplastic problems, J. Math. Anal. Appl. 386 (2012), 505–527.
- [5] K. Chełmiński, Coercive limits for a subclass of monotone constitutive equations in the theory of inelastic material behaviour of metals, Mat. Stosow. 40 (1997), 41–81.
- [6] K. Chełmiński, On monotone plastic constitutive equations with polynomial growth condition, Math. Methods Appl. Sci. 22 (1999), 547–562.
- [7] W. Pompe, Existence theorems in the viscoplasitcity theory, Thesis, Fachbereich Mathematik TU Darmstadt, 2003.
- [8] K. Chełmiński, Coercive approximation of viscoplasticity and plasticity, Asymptot. Anal. 26 (2001), 115–135.
- [9] K. Chełmiński, P. Gwiazda, Convergence of coercive approximations for sctrictly monotone quasistatic models in inelastic deformation theory, Math. Methods Appl. Sci. 30 (2007), 1357–1374.
- [10] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Leyden, 1975.
- [11] P. Kamiński, Boundary regularity for self-controlling and Cosserat models of viscoplasticity: Interior estimates for models of power type, Math. Mech. Solids 17(7) (2012), 669–692.
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Bibliografia
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bwmeta1.element.baztech-6de0eeb3-ca13-45ba-a6d9-d2afac3c9ec2