Emergence of coherent localized structures in shear deformations of temperature dependent fluids
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2016-12-24Preprint Posting Date
2014-11-22Online Publication Date
2016-12-24Print Publication Date
2017-04Permanent link to this record
http://hdl.handle.net/10754/583109
Metadata
Show full item recordAbstract
Shear localization occurs in various instances of material instability in solid mechanics and is typically associated with Hadamard-instability for an underlying model. While Hadamard instability indicates the catastrophic growth of oscillations around a mean state, it does not by itself explain the formation of coherent structures typically observed in localization. The latter is a nonlinear effect and its analysis is the main objective of this article. We consider a model that captures the main mechanisms observed in high strain-rate deformation of metals, and describes shear motions of temperature dependent non-Newtonian fluids. For a special dependence of the viscosity on the temperature, we carry out a linearized stability analysis around a base state of uniform shearing solutions, and quantitatively assess the effects of the various mechanisms affecting the problem: thermal softening, momentum diffusion and thermal diffusion. Then, we turn to the nonlinear model, and construct localized states - in the form of similarity solutions - that emerge as coherent structures in the localization process. This justifies a scenario for localization that is proposed on the basis of asymptotic analysis in \cite{KT}.Citation
Katsaounis, T., Olivier, J., & Tzavaras, A. E. (2016). Emergence of Coherent Localized Structures in Shear Deformations of Temperature Dependent Fluids. Archive for Rational Mechanics and Analysis, 224(1), 173–208. doi:10.1007/s00205-016-1071-2Sponsors
Research partially supported by the EU FP7-REGPOT project "Archimedes Center for Modeling, Analysis and Computation" and the "DIKICOMA" project of the Hellenic Secretariat of Research and Technology. Part of this work was completed at the Department of Applied Mathematics, University of Crete, Greece.Publisher
Springer NaturearXiv
1411.6131Additional Links
http://arxiv.org/abs/1411.6131ae974a485f413a2113503eed53cd6c53
10.1007/s00205-016-1071-2