# 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.

### 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…

### 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…

## References

SHOWING 1-10 OF 23 REFERENCES

### Nonlinear analysis techniques for shear band formation at high-strain-rates

- Materials Science
- 1992

One of the most striking manifestations of instability in solid mechanics is the localization of shear strain into narrow bands during high speed, plastic deformations of metals. According to one…

### Analysis of shear layers in a fluid with temperature-dependent viscosity

- Physics
- 2001

The presence of viscosity normally has a stabilizing effect on the flow of a fluid. Howerver, experiments show that the flow of a fluid in which viscosity decreases as temperature increases tends to…

### Effective Equations for Localization and Shear Band Formation

- MathematicsSIAM J. Appl. Math.
- 2009

An asymptotic procedure motivated by the theory of relaxation and the Chapman–Enskog expansion is introduced and an effective equation for the evolution of the strain rate is derived, consisting of a second order nonlinear diffusion regularized by fourth order effects and with parameters determined by the degree of thermal softening, strain hardening, and strain-rate sensitivity.

### LOCALIZATION AND SHEAR BANDS IN HIGH STRAIN-RATE PLASTICITY

- Mathematics
- 2011

This article is devoted to the explanation of the onset of localization and the formation of shear bands in high strain-rate plasticity of metals. We employ the Arrhenius constitutive model and show…

### ADAPTIVE FINITE ELEMENT COMPUTATIONS OF SHEAR BAND FORMATION

- Geology
- 2010

We study numerically an instability mechanism for the formation of shear bands at high strain-rate deformations of metals. We use a reformulation of the problem that exploits scaling properties of…

### Analytical Characterization of Shear Localization in Thermoviscoplastic Materials

- Physics, Engineering
- 1987

Abstract : Critical conditions for shear localization in thermoviscoplastic materials are obtained in closed form for idealized models of simple shearing deformations. The idealizations, which…

### Instability and localization of plastic flow in shear at high strain rates

- Physics, Engineering
- 1987

### Effect of Strain Rate Upon Plastic Flow of Steel

- Materials Science
- 1944

An experiment has been designed to check a previously proposed equivalence of the effects of changes in strain rate and in temperature upon the stress‐strain relation in metals. It is found that this…