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| From Dislocation Motion to an Additive Velocity Gradient Decomposition, and Some Simple Models of Dislocation Dynamics |
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Citation： |
Amit ACHARYA,Xiaohan ZHANG.From Dislocation Motion to an Additive Velocity Gradient Decomposition, and Some Simple Models of Dislocation Dynamics[J].Chinese Annals of Mathematics B,2015,36(5):645~658 |
| Page view： 1005
Net amount： 874 |
Authors： |
Amit ACHARYA; Xiaohan ZHANG |
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| Abstract： |
A mathematical theory of time-dependent dislocation mechanics of
unrestricted geometric and material nonlinearity is reviewed. Within
a ``small deformation" setting, a suite of simplified and
interesting models consisting of a nonlocal Ginzburg Landau
equation, a nonlocal level set equation, and a nonlocal generalized
Burgers equation is derived. In the finite deformation setting, it
is shown that an additive decomposition of the total velocity
gradient into elastic and plastic parts emerges naturally from a
micromechanical starting point that involves no notion of plastic
deformation but only the elastic distortion, material velocity,
dislocation density and the dislocation velocity. Moreover, a
plastic spin tensor emerges naturally as well. |
Keywords： |
Dislocations, Plasticity, Continuum mechanics, Finite deformation |
Classification： |
74C99 |
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