Path-dependent micromechanical effects

Two examples of path-dependent micromechanical effects are models of Swegle and Grady [13] for thermal trapping in shear bands and Follansbee and Kocks [14] for path-dependent evolution of the mechanical threshold stress in copper. 

Although the difference in final strength f, integrated through both the actual shock wave and the computational shock wave, will be mitigated by dynamic recovery (saturation) processes, this is still a substantial effect, and one that should not be left to chance. These are very important practical considerations in dealing with path-dependent, micromechanical constitutive models of all kinds. 

We also want to point out the difference between simple rate-dependent phenomena and path-dependent effects. Simple rate dependence means that the internal micromechanical state (as possibly represented by some meso-scale variables) depends only on the current deformation and current rate of deformation the material has no memory of the past. In terms of dislocation dynamics and (7.1), a simple rate-dependent constitutive description would be one in which... 

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