A note on approximation of Prandtl-Reuss plasticity through Cosserat plasticity
Authors:
Krzysztof Chełmiński and Patrizio Neff
Journal:
Quart. Appl. Math. 66 (2008), 351-357
MSC (2000):
Primary 35Q72, 74A35; Secondary 74A30, 74C05, 74C10
DOI:
https://doi.org/10.1090/S0033-569X-08-01095-9
Published electronically:
February 8, 2008
MathSciNet review:
2416777
Full-text PDF Free Access
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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
- Krzysztof Chełmiński, Global existence of weak-type solutions for models of monotone type in the theory of inelastic deformations, Math. Methods Appl. Sci. 25 (2002), no. 14, 1195–1230. MR 1925440, DOI https://doi.org/10.1002/mma.336
- Patrizio Neff and Krzysztof Chełmiński, Infinitesimal elastic-plastic Cosserat micropolar theory. Modelling and global existence in the rate-independent case, Proc. Roy. Soc. Edinburgh Sect. A 135 (2005), no. 5, 1017–1039. MR 2187223, DOI https://doi.org/10.1017/S030821050000425X
- P. Neff and K. Chełmiński, Approximation of Prandtl-Reuss Plasticity through Cosserat-Plasticity, Preprint FB Mathematik TU Darmstadt 2468 (2006).
- Patrizio Neff and Krzysztof Chelmiński, Well-posedness of dynamic Cosserat plasticity, Appl. Math. Optim. 56 (2007), no. 1, 19–35. MR 2334604, DOI https://doi.org/10.1007/s00245-007-0878-5
- Patrizio Neff, Krzysztof Chełmiński, Wolfgang Müller, and Christian Wieners, Numerical solution method for an infinitesimal elasto-plastic Cosserat model, Math. Models Methods Appl. Sci. 17 (2007), no. 8, 1211–1239. MR 2342988, DOI https://doi.org/10.1142/S021820250700225X
- Patrizio Neff, The Cosserat couple modulus for continuous solids is zero viz the linearized Cauchy-stress tensor is symmetric, ZAMM Z. Angew. Math. Mech. 86 (2006), no. 11, 892–912. MR 2268295, DOI https://doi.org/10.1002/zamm.200510281
- Roger Temam, A generalized Norton-Hoff model and the Prandtl-Reuss law of plasticity, Arch. Rational Mech. Anal. 95 (1986), no. 2, 137–183. MR 850094, DOI https://doi.org/10.1007/BF00281085
References
- 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)
- 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)
- P. Neff and K. Chełmiński, Approximation of Prandtl-Reuss Plasticity through Cosserat-Plasticity, Preprint FB Mathematik TU Darmstadt 2468 (2006).
- P. Neff and K. Chełmiński, Well-posedness of dynamic Cosserat plasticity, Appl. Math. Optimisation 56 (2007), 19–35. MR 2334604
- 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
- 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
- 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 Chełmiński
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
Keywords:
Plasticity,
polar-materials,
monotone flow rules,
Cosserat continua
Received by editor(s):
September 14, 2006
Published electronically:
February 8, 2008
Additional Notes:
The first author was partially supported by the Polish government grant: KBN no. 1-P03A-031-27
Article copyright:
© Copyright 2008
Brown University
The copyright for this article reverts to public domain 28 years after publication.
