Mathematical analysis of thermoplasticity with linear kinematic hardening

• Autorzy: Chełmiński K. , Racke R.
• Języki publikacji: EN

Abstrakty

EN

We study thermoplasticity with the Prandtl-Reuss flow rule and with a linear evolution equation for the kinematic hardening. The yield function associated with the system under consideration depends explicitly on the temperature. To have a control on the temperature, we slightly modify the heat equation and prove that an approximation process, based on the Yosida approximation, converges to a global in time solution of the (modified) system of thermoplasticity.

Słowa kluczowe

EN

theory of inelastic deformations; thermoplasticity; kinematic hardening; maximal monotone operators

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2006
• Tom: Vol. 12, nr 1
• Strony: 37--57
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Chełmiński K.

autor

Racke R.

• Faculty of Mathematics and Information Science. Warsaw Univeristy of Technology, Pl. Politechniki 1 00-661 Warsaw, Poland i Cardinal Stefan Wyszyński University Dewajtis 5 01-815 Warsaw, Poland,

Bibliografia

• [l] Alber, H.-D., Chełmiński, K., Quasistatic problems in Viscoplasticity theory. I: Models with linear hardening, in "Operator Theoretical Methods and Applications to Mathematical Physics" (The Erhard Meister memorial volume, I. Gohberg et al.), Oper. Theory Adv. Appl. 147 (2004), Birkhauser, Basel, 105-129.
• [2] Alber, H.-D., Chełmiński, K., Quasistatic problems in Viscoplasticity theory. II: Models with nonlinear hardening., Preprint 2190, Fachbereich Mathematik, TU Darmstadt (2002).
• [3] Anzellotti, G., Luckhaus, S., Dynamical evolution of elasto-perfectly plastic bodies, Appl. Math. Optim. 15 (1987), 121-140.
• [4] Alber, H.-D., Materials with Memory, Lecture Notesin Math. 1682, Springer, Berlin-Heidelberg-New York, 1998.
• [5] Aubin, J. P., Cellina, A., Differential Inclusions, Springer, Berlin-Heidelberg-New York, 1984.
• [6] Chełmiński, K., Gwiazda, P., Nonhomogeneous initial-boundary value problems for coercive and Belf-controlling models of monotone type, Contin. Mech. Thermodyn. 12 (2000),217-234.
• [7] Chełmiński, K., Neff, P., lnfinitesimal elastic-plastic Cosserat micropolar theory. Modeling and global existence in the rate-independent case, Proc. Roy. Soc. Edinburgh Sect. A 135 (2005), 1017-1039.
• [8] Chełmiński, K., On quasistatic inelastic models of the gradient type with convex composite constitutive equations, Cent. Eur. J. Math. 1 (2003),670-689.
• [9] Chełmiński, K., Coercive limits for a subclass of monotone constitutive equations in the theory of inelastic material behaviour of metals, Mat. Stos. 40 (1997), 41-81.
• [10] Chełmiński, K., Coercive approximation of Viscoplasticity and plasticity, Asymptot. Anal. 26 (2001), 105-133.
• [11] Haupt, P., Continuum Mechanics and Theory of Materials, Springer, Berlin, 2002.
• [12] Jiang, S., Racke, R., Evolution Equations in Thermoelasticity, Pitman Monogr. Surveys Pure Appl. Math. 112, Chapman & Hall/CRC, Boca Raton, 2000.
• [13] Suquet, P.-M., Evolution problems for a class of dissipative materials, Quart. Appl. Math. 38 (1980), 391-414.
• [14] Suquet, P.-M., Discontinuities and plasticity, in "Nonsmooth Mechanics and Applications" (J.J. Moreau .and P.D. Panagiotopoulos, eds.), CISM Courses and Lectures 302, Springer, Vienna-New York, 1988, 279-340.
• [15] Temam, R., Problemes Mathematiques en Plasticite, Gauthier- Villars, Paris, 1983.
• [16] Temam, R., A generalized Norton-Hoff model and the Prandtl-Reuss law of plasticity, Arch. Ration. Mech. Anal. 95 (1986), 137-183.