Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Local existence and uniqueness for quasistatic finite plasticity with grain boundary relaxation


Author: Patrizio Neff
Journal: Quart. Appl. Math. 63 (2005), 88-116
MSC (2000): Primary 74A35, 74C05, 74C10, 74C20, 74D10, 74E05, 74E10, 74E15, 74G30, 74G65, 74N15
DOI: https://doi.org/10.1090/S0033-569X-05-00953-9
Published electronically: January 20, 2005
MathSciNet review: 2126571
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with a phenomenological model of initially isotropic finite-strain multiplicative elasto-plasticity for polycrystals with grain boundary relaxation (Neff, Cont. Mech. Thermo., 2003). We prove a local in time existence and uniqueness result of the corresponding initial boundary value problem in the quasistatic rate-dependent case. Use is made of a generalized Korn first inequality (Neff, Proc. Roy. Soc. Edinb. A, 2002) taking into account the incompatibility of the plastic deformation $F_p$. This is a first result concerning classical solutions in geometrically exact nonlinear finite visco-plasticity for polycrystals. Global existence is not proved and cannot be expected due to the natural possibility of material degradation in time.


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Additional Information

Patrizio Neff
Affiliation: AG6, Fachbereich Mathematik, Darmstadt University of Technology, Schlossgartenstrasse 7, 64289 Darmstadt, Germany
Address at time of publication: Department of Mathematics, University of Technology, Darmstadt
Email: neff@mathematik.tu-darmstadt.de

DOI: https://doi.org/10.1090/S0033-569X-05-00953-9
Keywords: Plasticity, visco-plasticity, solid mechanics, elliptic systems, variational methods.
Received by editor(s): May 13, 2004
Published electronically: January 20, 2005
Article copyright: © Copyright 2005 Brown University

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