Macro-, Meso- and Micro-Damage Model Based on Singularity Representation for Anti-Plane Deformation

Abstract

Recent development of sub-micron devices in microelectronics and cell structure evolution in microbiology has indicated the need to understand how defects or imperfections initiate or migrate at the microscopic and atomic scale, where the chemical compositions are very unstable. Slight changes can built up and lead to significant alterations of the macroscopic behavior. Such effects have not received sufficient attention in the past at such lower scale. They are potential sources that can effect the initial stresses and strains at the microscopic and atomic scale, the magnitude of which depend on the evolution of the system. These initial disturbances will interact with energy transmitted through the system by external means. Macroscopically speaking, a system may be regarded to be in equilibrium but this does not necessarily apply to the lower scales. Hence, modeling of the macro/meso/micro behavior of physical systems requires the capability to cover scale range several orders of magnitude in lineal dimension.