A partitioned-modeling approach with moving jump conditions for localization (Q675515)

Based on properties of localization phenomena, a partitioned-modeling approach is proposed via moving jump conditions for localization problems. By taking the initial point of localization as a point where the type of the governing differential equation changes, i.e. from hyperbolic to elliptic type for dynamic problems and from elliptic to another elliptic type for static problems, a moving boundary between localized and non-localized deformation zones is defined through jump forms of conservation laws across the boundary. As a result, localization problems can be considered as shocks in fluids and solidification in heat transfer. To illustrate the proposed procedure, one-dimensional analytical solutions are given with an emphasis on the definition of boundary conditions and the experimental means to determine model parameters associated with localization.