Appl Math Optim 56:19–35 (2007)
2007 Springer Science+Business Media, Inc.
Well-Posedness of Dynamic Cosserat Plasticity
and Krzysztof Chelmi´nski
Department of Mathematics, University of Technology Darmstadt,
64289 Darmstadt, Germany
Faculty of Mathematics and Information Science, Warsaw University of Technology,
00661 Warsaw, Poland
Abstract. We investigate the regularizing properties of generalized continua of
micropolar type for dynamic elasto-plasticity. To this end we propose an extension
of classical inﬁnitesimal elasto-plasticity to include consistently non-dissipative
micropolar effects and we show that the dynamic model allows for a unique,
global in-time solution of the corresponding rate-independent initial boundary value
problem of pure Dirichlet-type. The methods of choice are the Yosida approxi-
mation and a passage to the limit.
Key Words. Plasticity, Polar-materials, Non-simple materials.
AMS Classiﬁcation. 74A35, 74A30, 74C05, 74H20, 74H25.
This article is a sequel to work begun in . There we have established the regularizing
power and well-posedness of a geometrically linear Cosserat model  in conjunction
with quasistatic rate-independent elasto-plasticity. In this contribution we extend these
results to cover also the dynamic case for the pure Dirichlet problem.
Classical ideal plasticity is known to be an ill-posed problem. In the quasistatic case
the displacement solution is neither unique (even in the class of continuous functions)
nor smooth in space (slip lines), see the counterexample on p. 77 of  based on 
and  and the discussion of regularity in , , , , , ,  and .
The second author was supported by Polish government Grant KBN No. 1-P03A-031-27.