GEM - International Journal on Geomathematics

, Volume 8, Issue 2, pp 191–217 | Cite as

Meshfree generalized finite difference methods in soil mechanics—part II: numerical results

  • I. MichelEmail author
  • S. M. I. Bathaeian
  • J. Kuhnert
  • D. Kolymbas
  • C.-H. Chen
  • I. Polymerou
  • C. Vrettos
  • A. Becker
Original Paper


In geotechnical engineering, simulations are of utmost importance. Due to large deformations, meshfree methods are more suitable than classical meshbased methods. Nevertheless, they have to be validated on the laboratory scale in order to guarantee reliable conclusions for real life applications. In this contribution, we complete the theoretical description of the two novel meshfree generalized finite difference methods Finite Pointset Method (FPM) and Soft PARticle Code (SPARC) by numerical results for the standard benchmark problems oedometric and triaxial test. We focus on the quality of the results as well as on the rate-independent character of the numerical implementation of the nonlinear barodesy model for sand.


Generalized finite difference methods Meshfree methods Finite Pointset Method (FPM) Soft PARticle Code (SPARC) Barodesy model 

Mathematics Subject Classification

35D35 35Q74 65D05 65M99 



This paper presents results of the joint research project “Ein netzfreier numerischer Zugang zu Böden in Ruhe und im Fließen (A meshfree numerical approach for soils at rest and in flow). (1) Kaiserslautern, Germany: The group consisting of Prof. Dr.-Ing. C. Vrettos, Dr.-Ing. A. Becker (Division of Soil Mechanics and Foundation Engineering, University of Kaiserslautern), Dr. J. Kuhnert, Dr. I. Michel (Fraunhofer Institute for Industrial Mathematics ITWM) is supported by the “Deutsche Forschungsgemeinschaft (DFG)”, Germany. (2) Innsbruck, Austria: The group consisting of Prof. Dr.-Ing. D. Kolymbas, S.M.I. Bathaeian, Dr.-Ing. C.-H. Chen (temporarily), Dr.-Ing. I. Polymerou (temporarily) (Division of Geotechnical and Tunnel Engineering, University of Innsbruck) is supported by the “Fonds zur Förderung der wissenschaftlichen Forschung (FWF)”, Austria.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Fraunhofer Institute for Industrial Mathematics ITWMKaiserslauternGermany
  2. 2.Division of Geotechnical and Tunnel EngineeringUniversity of InnsbruckInnsbruckAustria
  3. 3.Division of Soil Mechanics and Foundation EngineeringUniversity of KaiserslauternKaiserslauternGermany

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