Investigating localization phenomena using finite element and meshless methods

This thesis investigates the validity of meshless methods and finite element methods in the investigation of strain localization phenomena in which is an important factor in many nonlinear solid mechanics problems. The term strain localization refers to the appearance of patterns of deformation that are restricted to narrow regions in the solid domain. Most often the deformation observed is that of shear, such a form of localization is referred to as a shear band. The thickness of typical shear bands for metals are approximately 10–30 μm which is typically orders of magnitude less than the dimensions of the specimen. Even with significant mesh refinement, it becomes difficult to observe this extremely small length scale with traditional numerical method.

Several benchmark problems are solved using traditional finite element methods and reproducing kernel particle method (RKPM) which is a particle meshless methods. These problems include tensile instability of a bar, pressure instability in a cylindrical shell, and the Kalthoff Problem. In addition a variety of material laws were employed for each method and problem; some of which include J2 plasticity and thermo-viscoplasticity. (Abstract shortened by UMI.)