Multiscale Semi-Lagrangian Reproducing Kernel Particle Method for Modeling Damage Evolution in Geomaterials
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.
KeywordsReproducing kernel Semi-Lagrangian Micro-cracks informed damage model Geomaterials
- M.D. Adley, A.O. Frank, K.T. Danielson, S.A. Akers, J.L. O’Daniel, The Advanced Fundamental Concrete (AFC) model, Technical Report ERDC/GSL TR-11-xx (in publication), U.S. Army Engineer Research and Development Center, VicksburgGoogle Scholar
- J.S. Chen, Y. Wu, Stability in Lagrangian and semi-Lagrangian reproducing kernel discretizations using nodal integration in nonlinear solid mechanics, in Computational Methods in Applied Sciences, ed. by V.M.A. Leitao, C.J.S. Alves, C.A. Duarte (Springer, Berlin, 2007), pp. 55–77Google Scholar
- P.C. Guan, S.W. Chi, J.S. Chen, T.R. Slawson, M.J. Roth, Semi-Lagrangian reproducing kernel particle method for fragment-impact problems Int. J. Impact Eng. (2011) submittedGoogle Scholar
- X. Ren, J.S. Chen, J. Li, T.R. Slawson, M.J. Roth, Micro-cracks informed damage model for brittle solids Int. J. Solids Struct. 48(10), 1560–1571 (2011)Google Scholar