Projects per year
Abstract
We consider an exact reduction of a model of Field Dislocatin Mechanics to a scalar problem in one spatial dimension and investigate the existence of static and slow, rigidly moving single or collections of planar screw dislocation walls in this setting. Two classes of drag coefficient functions are considered, namely those with linear growth near the origin and those with constant or more generally sublinear growth there. A mathematical characterisation of all possible equilibria of these screw wall microstructures is give. We also prove the existence of travelling wave solutions for linear drag coefficient functinos at low wave speeds and rule out the existence of nonconstant bounded travelling wave solutions for sublinear drag coefficients functions. It turns out that the appropriate concept of a solution in this scalar case is that of a viscosity solution. The governing equation in the static case is not proper and it is shown that no comparison principle holds. The findings indicate a shortrange nature of the stress field of the individual dislocation walls, which indicates that the nonlinearity present in the model may have a stabilishing effect. We predict idealised dislocationfree cells of almost arbitrary size interspersed with dipolar dislocation wall microstructures as admissible equilibria of our model, a feature in sharp contrast with predictions of the possible nonmonotone equilibria of the corresponding GinzburgLandau phase field type gradient flow model.
Original language  English 

Pages (fromto)  20432053 
Number of pages  11 
Journal  Journal of the Mechanics and Physics of Solids 
Volume  58 
Issue number  12 
DOIs  
Publication status  Published  Dec 2010 
Fingerprint Dive into the research topics of 'Travelling wave solutions for a quasilinear model of field dislocation mechanics'. Together they form a unique fingerprint.
Projects
 2 Finished

Analysis of MulticScale Problems in Mathematical Chemistry
Zimmer, J.
Engineering and Physical Sciences Research Council
1/07/10 → 30/06/13
Project: Research council

Mathematical Challenges of Molecular Dynamics: A ChemoMathematical Forum
Zimmer, J.
Engineering and Physical Sciences Research Council
1/04/08 → 30/09/11
Project: Research council