A PARTITIONED-MODELING APPROACH WITH MOVING JUMP CONDITIONS FOR LOCALIZATION

Although many investigations have been performed on localization probl ems, there still exist some pressing issues. Specifically, it is diffi cult to show in general well-posed governing equations. Based on the e ssential features of localization phenomena, a partitioned-modeling ap proach is proposed here via moving jump conditions for localization pr oblems. By taking the initial point of localization as that point wher e the type of the governing differential equation changes, i.e. a hype rbolic to an elliptic type for dynamic problems and an elliptic to ano ther elliptic type for static problems, a moving boundary between loca lized and non-localized deformation zones is defined through jump form s of conservation laws across the boundary. As a result, localization problems might be considered in the same category as shocks in fluids and solidification in heat transfer. To illustrate the proposed proced ure, one-dimensional analytical solutions are given with an emphasis o n the definition of boundary conditions and the experimental means to determine model parameters associated with localization. Future resear ch is then discussed on an extension to general cases.