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Multiscale Semi-Lagrangian Reproducing Kernel Particle Method for Modeling Damage Evolution in Geomaterials

  • J. S. ChenEmail author
  • P. C. Guan
  • S. W. Chi
  • X. Ren
  • M. J. Roth
  • T. R. Slawson
  • M. Alsaleh
Conference paper
Part of the Springer Series in Geomechanics and Geoengineering book series (SSGG, volume 11)

Abstract

Damage processes in geomaterials typically involve moving strong and weak discontinuities, multiscale phenomena, excessive deformation, and multi-body contact that cannot be effectively modeled by a single-scale Lagrangian finite element formulation. In this work, we introduce a semi-Lagrangian Reproducing Kernel Particle Method (RKPM) which allows flexible adjustment of locality, continuity, polynomial reproducibility, and h- and p-adaptivity as the computational framework for modeling complex damage processes in geomaterials. Under this work, we consider damage in the continua as the homogenization of micro-cracks in the microstructures. Bridging between the cracked microstructure and the damaged continuum is facilitated by the equivalence of Helmholtz free energy between the two scales. As such, damage in the continua, represented by the degradation of continua, can be characterized from the Helmholtz free energy. Under this framework, a unified approach for numerical characterization of a class of damage evolution functions has been proposed. An implicit gradient operator is embedded in the reproduction kernel approximation as a regularization of ill-posedness in strain localization. Demonstration problems include numerical simulation of fragment-impact of concrete materials.

Keywords

Reproducing kernel Semi-Lagrangian Micro-cracks informed damage model Geomaterials 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • J. S. Chen
    • 1
    Email author
  • P. C. Guan
    • 1
  • S. W. Chi
    • 1
  • X. Ren
    • 1
  • M. J. Roth
    • 2
  • T. R. Slawson
    • 2
  • M. Alsaleh
    • 3
  1. 1.Civil & Environmental EngineeringUniversity of CaliforniaLos AngelesUSA
  2. 2.U. S. Army Engineer Research and Development CenterVicksburgUSA
  3. 3.Caterpillar Inc.MossvilleUSA

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