Computer simulation of plastic flow

As with all other forms of plastic deformation in amorphous solids, we expect that in glassy polymers too the plastic deformation will consist of a series of discrete thermally assisted unit relaxation events on the atomic scale. Features of such discrete behavior have, e.g., been observed in deformation calorimetry by Oleinik (1991), who detected discrete unit inelastic events already in the pre-yield region in some glassy polymers. 

Deformation in pure shear is imposed in increments of border displacements followed by static potential-energy minimization. 

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 

Corresponding system plastic-strain increments are also obtained at the atomic level from the displacement gradients between the four relevant neighboring corner atoms of Delaunay tetrahedra for each external distortion increment and are allocated subsequently as an atomic site average to each Voronoi polyhedral atom environment by a special procedure of double space tessellation developed by Mott et al. (1992) for this purpose, leading eventually to volume averages of strain-increment tensors of all Voronoi atom environments to attain the system-wide strain-inerement tensor. 

Of the tensorial representations of system-stress and system-strain increment, only the two invariants of deviatoric equivalent stress and strain increments and the mean normal stress were retained by this well-established procedure (Mott et al. 1993). 

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