# Emergence of Coherent Localized Structures in Shear Deformations of Temperature Dependent Fluids

@article{Katsaounis2014EmergenceOC, title={Emergence of Coherent Localized Structures in Shear Deformations of Temperature Dependent Fluids}, author={Theodoros Katsaounis and Julien Olivier and Athanasios E. Tzavaras}, journal={Archive for Rational Mechanics and Analysis}, year={2014}, volume={224}, pages={173-208} }

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…

## 5 Citations

### Localization in Adiabatic Shear Flow Via Geometric Theory of Singular Perturbations

- MathematicsJ. Nonlinear Sci.
- 2019

This work considers a hyperbolic–parabolic system that expresses the above mechanism and construct self-similar solutions of localizing type that arise as the outcome of the above competition.

### Existence of Localizing Solutions in Plasticity via Geometric Singular Perturbation Theory

- MathematicsSIAM J. Appl. Dyn. Syst.
- 2017

This work aims to reveal the onset of localization into shear bands using a simple model developed from viscoplasticity, and exploits the properties of scale invariance of the model to construct a family of self-similar focusing solutions that capture the nonlinear mechanism of shear band formation.

### Localization of Adiabatic Deformations in Thermoviscoplastic Materials

- Physics
- 2016

We study an instability occurring at high strain-rate deformations, induced by thermal softening properties of metals, and leading to the formation of shear bands. We consider adiabatic shear…

### Localization in Adiabatic Shear Flow Via Geometric Theory of Singular Perturbations

- MathematicsJournal of Nonlinear Science
- 2019

We study localization occurring during high-speed shear deformations of metals leading to the formation of shear bands. The localization instability results from the competition between Hadamard…

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