Configurational force defined

Fig, 4.38. The solid curve shows the driving force Q for insertion of a crack in the thin film as a function of crack depth rj. The dashed curve shows the corresponding configurational force defined by (4.60) tending to extend the crack depicted in Figure 4.37 steadily in the x—direction. 

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... 

The type of forces depends on the MD model exploited. A simulation is realistic — that is, it mimics the behavior of the real system — only to the extent that interatomic forces are similar to those that real atoms (or, more exactly, nuclei) would experience when arranged in the same configuration. Forces are usually obtained as the gradient of a potential energy function d>(rj), depending on the positions of the particles. The realism of the simulation therefore depends on the ability of the potential chosen to reproduce the behavior of the material under the conditions at which the simulation is mn. The forces can be defined as follows ... 

The spatial Cauchy stress tensor s is defined at time by f = sn, where t(x, t, n) is a contact force vector acting on an element of area da = n da with unit normal i and magnitude da in the current configuration. The element of area... 

In a second approach of the reactivity, one fragment A is represented by its electronic density and the other, B, by some reactivity probe of A. In the usual approach, which permits to define chemical hardness, softness, Fukui functions, etc., the probe is simply a change in the total number of electrons of A. [5,6,8] More realistic probes are an electrostatic potential cf>, a pseudopotential (as in Equation 24.102), or an electric field E. For instance, let us consider a homogeneous electric field E applied to a fragment A. How does this field modify the intermolecular forces in A Again, the Hellman-Feynman theorem [22,23] tells us that for an instantaneous nuclear configuration, the force on each atom changes by... 

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