Equilibrium mechanics model of multiscaling by segmentation: Asymptotic solution for macro-meso-micro damage in anti-plane shear deformation

Keeping in mind that the present modeling process involves segmentation and connection, the latter requires a scale invariant criterion. To this end, the volume energy density function is used with a length parameter or an area parameter so that the product can cross scale. The details of this procedure would be beyond the scope of this discussion. Nevertheless, ample evidence will be shown in the work to follow that the volume energy density function is fundamental not only to the scale shifting process but also in the ways how microscopic constraints can influence macroscopic behavior.