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A note on approximation of Prandtl-Reuss plasticity through Cosserat plasticity
Author(s):
Krzysztof
Chelminski;
Patrizio
Neff
Journal:
Quart. Appl. Math.
66
(2008),
351-357.
MSC (2000):
Primary 35Q72, 74A35;
Secondary 74A30, 74C05, 74C10
Posted:
February 8, 2008
MathSciNet review:
2416777
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Abstract:
In this note we investigate the regularizing properties of Cosserat elasto-plastic models in a geometrically linear setting. For vanishing Cosserat effects we show that the model with microrotations approximates the classical Prandtl-Reuss solution in an appropriate measure-valued sense.
References:
-
- [1]
- K. Chełmiński, Global existence of weak-type solutions for models of monotone type in the theory of inelastic deformations, Math. Meth. Appl. Sci. 25 (2002), 1195-1230. MR 1925440 (2003g:74036)
- [2]
- P. Neff and K. Chełmiński, Infinitesimal elastic-plastic Cosserat micropolar theory. Modelling and global existence in the rate-independent case, Proc. Roy. Soc. Edinburgh Sect. A 135 (2005), 1017-1039. MR 2187223 (2006h:74012)
- [3]
- P. Neff and K. Chełmiński, Approximation of Prandtl-Reuss Plasticity through Cosserat-Plasticity, Preprint FB Mathematik TU Darmstadt 2468 (2006).
- [4]
- P. Neff and K. Chełmiński, Well-posedness of dynamic Cosserat plasticity, Appl. Math. Optimisation 56 (2007), 19-35. MR 2334604
- [5]
- P. Neff, K. Chełmiński, W. Müller and C. Wieners, Numerical solution method for an infinitesimal elastic-plastic Cosserat model, Math. Mod. Meth. Appl. Sci. 17 (2007), 1211-1239. MR 2342988
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- P. Neff, The Cosserat couple modulus for continuous solids is zero viz the linearized Cauchy-stress tensor is symmetric, Z. Angew. Math. Mech. 86 (2006), 892-912. MR 2268295
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- R. Temam, A generalized Norton-Hoff model and the Prandtl-Reuss law of plasticity, Arch. Rat. Mech. Anal. 95 (1986), 137-183. MR 850094 (88a:73028)
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Additional Information:
Krzysztof
Chelminski
Affiliation:
Faculty of Mathematics and Information Science, Warsaw University of Technology
Email:
kchelmin@mini.pw.edu.pl
Patrizio
Neff
Affiliation:
Fachbereich Mathematik, Technische Universität Darmstadt
Email:
neff@mathematik.tu-darmstadt.de
PII:
S0033-569X-08-01095-9
Keywords:
Plasticity,
polar-materials,
monotone flow rules,
Cosserat continua
Received by editor(s):
September 14, 2006
Posted:
February 8, 2008
Additional Notes:
The first author was partially supported by the Polish government grant: KBN no. 1-P03A-031-27
Copyright of article:
Copyright
2008,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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