Here [Mathematical Expression Omitted] is the viscoplastic strain rate; [Mathematical Expression Omitted] is the pre-exponential factor given by the product of the number density of shear transformation sites (D), the volume-averaged shear strain increment per transformation (2[[Gamma].
Another shortcoming of the model was that it did not account for the thermoreversible nature of the shear transformation and was, therefore, not capable of predicting nonmonotonic loading or strain recovery in the unloaded state.
We take the distribution in material state to be directly related to the distribution in, for example, local free volume, local energy barrier to deformation, or associated shear transformation sites where we consider high local free volume to correspond to low activation barrier and therefore greater probability of a local shear transformation event.
denotes the probability distribution of available shear transformation events and f([[Gamma].
This state may be characterized in a number of (mechanistically and operationally) equivalent ways, such as a distribution of local free volume, a distribution of internal stress due to nonuniform polymer chain packing, or a distribution of activation energies for the thermalized, local inelastic shear transformations that occur in the glassy state.
Setting [Psi] = 1 means that the full material volume is available for shear transformations, at all times.
During the initial stages of deformation (of previously undeformed material), S will increase rapidly as energy is stored locally by inelastic shear transformations of spatially well separated sites.
where [Omega] is the effective frequency of inelastic shear transformations and [[Omega].