Multiple-scale meshfree adaptivity for the simulation of adiabatic shear band formation

The Reproducing Kernel Particle Method (RKPM), one of the major meshfree methods, is applied to the analysis of shear localization problem. The total Lagrangian formulation of RKPM and explicit time integration are employed in order to simulate the adiabatic sheer band formation in a thermo-viscoplastic material. The multiresolution study based on multiple-scale RKPM is then accomplished and an efficient measure of the high-scale component is accordingly proposed for meshfree adaptive procedures. A time-marching strategy is also suggested and successfully implemented for the process of transient adaptive refinement. Numerical examples are finally presented to demonstrate the performance of meshfree adaptivity and to ensure the feasibility of the high-scale detector for multiple-scale refinements.