Atomic site stress tensor

An important feature of these models, which is particularly relevant for the understanding of their mechanical response, is the very high levels of their atomic site stress tensors associated with the disordered glassy state measured by a technique pioneered by Egami and Vitek (1983) in amorphous metals and discussed in Section 1.4.1. For example, Theodorou and Suter (1986) have calculated these atomic site stresses in polypropylene for the three different atomic environments of C, H, and CH3 by the method of Egami and Vitek. Their results for the average pressure field (p) and deviatoric shear field (r) (= d/VJ) for the three environments are given in Table 2.1 for the structure model of Theodorou and Suter (1985). 

Table 2.1 Characteristic quantities of the invariants p) and (r) [= ff/ /3) of the atomic site stress tensors for atomic environments of carbon (C), hydrogen (H), and methyi groups (CH3 = R) in atactic giassy poiypropyiene...

The system stress over the simulation cube after each distortion increment is obtained as a volume average of all atomic site stress tensors that, in turn, is based on the generalized formulation of Theodorou and Suter (1986) of the classical Born and Huang (1954) operations, which now include both torque and force interactions between atoms, giving the atomic site stress-tensor element for the th atom as... 

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