Reproducing Kernel Particle Method (RKPM) has been applied to many large deformation problems [1,2]. RKPM relies on polynomial reproducing conditions to yield desired accuracy and convergence properties, but requires appropriate kernel support coverage of neighboring particles to ensure kernel stability . This kernel stability condition is difficult to achieve for problems with large particle motion such as the fragment-impact processes commonly exist in many extreme events. A new reproducing kernel formulation with “quasi-linear” reproducing conditions is introduced. In this approach, the first order polynomial reproducing conditions are approximately enforced to yield a nonsingular moment matrix. With proper error control of the first completeness, nearly 2 nd order convergence rate in L2 norm can be achieved while maintaining kernel stability. The effectiveness of this new quasi-linear RKPM formulation is demonstrated by modelling fragment-impact and penetration extreme events.
|Location: Technical University of Catalonia (UPC), Vertex Building.|
|Date: 28 - 30 September 2015, Barcelona, Spain.|
 S. W. Chi, C. H. Lee, J. S. Chen, and P. C. Guan, “A Level Set Enhanced Natural Kernel Contact Algorithm for Impact and Penetration Modeling,” International Journal for Numerical Methods in Engineering, 102, 839–866 (2015).
 C. Guan, S. W. Chi, J. S. Chen, T. R. Slawson, M. J. Roth, “Semi-Lagrangian Reproducing Kernel Particle Method for Fragment-Impact Problems,” International Journal of Impact Engineering, 38, 1033-1047 (2011).
 J. S. Chen, C. Pan, C. T. Wu, and W. K. Liu, "Reproducing Kernel Particle Methods for Large Deformation Analysis of Nonlinear Structures," Computer Methods in Applied Mechanics and Engineering, 139, 195-227 (1996).