A new reproducing kernel formulation with embedded kernel stability for modeling extreme events

Abstract

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 [3]. 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.

Recording of the presentation

Location: Technical University of Catalonia (UPC), Vertex Building.

Date: 28 - 30 September 2015, Barcelona, Spain.

General Information

• Location: Technical University of Catalonia (UPC), Barcelona, Spain.
• Date: 28 - 30 September 2015
• Secretariat: International Center for Numerical Methods in Engineering (CIMNE).

External Links

• Particles 2015 Official Website of the Conference.
• CIMNE Multimedia Channel

References

[1] 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).

[2] 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).

[3] 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).