Configurational Forces and the Dynamics of Defects

The notion of a configurational force is entirely in keeping with our aim of developing effective theories for characterizing the behavior of materials. In 

The central observation associated with the definition of configurational forces is that the total energy of the body of interest and associated loading devices depends explicitly on the positions of the various defects within that body. A small excursion of a given defect from position Xj to Xj + S i will result in an attendant change of the total energy. The configurational force on that defect associated with that motion is defined via 

As noted above, the notion of a configurational force may be advanced as a basis for considering the dynamics of defects themselves since, once such forces are in hand, the temporal evolution of these defects can be built up in turn by the application of an appropriate kinetic law which postulates a relation of the form V = v(driving force). 

To further elaborate the underlying idea of a configurational force, we appeal to the examples indicated schematically in fig. 2.8. Fig. 2.8(a) shows an interface within a solid and illustrates that by virtue of interfacial motion the area of the interface can be reduced. If we adopt a model of the interfacial energy in which it is assumed that this energy is isotropic (i.e. y does not depend upon the local interface normal n), the driving force is related simply to the local curvature of that interface. Within the theory of dislocations, we will encounter the notion of image dislocations as a way of guaranteeing that the elastic fields for dislocations in finite 

In iight of the definition of the contigurationai force given above, we may expioit this expiicit dependence of the eiastic energy on the position of the defect to rewrite the force as 

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