A meshfree numerical approach for soils at rest and in flow

• Applicants: Dr. Jörg Kuhnert; Professor Dr.-Ing. Christos Vrettos
• Subject Area: Applied Mechanics, Statics and Dynamics ; Geotechnics, Hydraulic Engineering
• Term: from 2010 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 178974611

• Final Report Year: 2019

Final Report Abstract

Major advantages of meshfree numerical simulation schemes – easy handling, absence of mesh generation and mesh management – mostly show for applications in continuum mechanics with moving or free surfaces as well as phase boundaries, fluid structure interaction or rather large deformations in context of Lagrangian methods, or for applications with significant mesh topology changes (e.g. crack growth and damage propagation). The majority of applications of meshfree methods refers to fluids. In contrast to fluids, sand is a solid, as it can sustain shear stresses. Being a particulate material, however, sand can undergo very large and even non-topological deformations. Hence, the mathematical description of its mechanical behavior is not simple. An additional difficulty arises from its hysteretic behavior (think of its memory capacity and of the plastic deformation). Further difficulties arise from barotropy, pyknotropy, and from its tendency to asymptotically approach the so-called critical density. In the project "Soft Particles –Flow", we have used the constitutive relations offered by hypoplasticity and barodesy to develop a meshfree numerical approach based on the Finite Pointset Method (FPM) to simulate quasi-static processes. Since these material models are rate-independent, they can not be directly used for dynamic processes and require further development regarding rate-sensitivity. As the design is still in the early stages of research, we have focused on a Drucker-Prager yield criterion to model dynamic processes with FPM. It only defines the internal friction angle. Due to its simplicity, there are several drawbacks in the accuracy and the calibration of the model, but it leads to a stable and fast numerical scheme. During the numerical experiments, not only the influence of the material model but also of the boundary conditions between the granular material and the bounding geometry has been investigated to some extend. There is still a lot potential research in this area.

Publications

• (2019) Different ways of Fluid Structure Interaction (FSI) in the MESHFREE Finite-Pointset-Method (FPM). In: Griebel, M. and Schweitzer, M.A. (eds) Meshfree Methods for Partial Differential Equations IX, IWMMPDE2017. LNCSE, Vol. 129, Springer, Cham, pp. 73–92
  J. Kuhnert, I. Michel, R. Mack
  (See online at https://doi.org/10.1007/978-3-030-15119-5_5)
• (2012) Barodesy: a New Constitutive Frame for Soils. Geotech Lett, 2:17–23
  D. Kolymbas
  (See online at https://doi.org/10.1680/geolett.12.00004)
• (2013) Meshfree generalized finite difference methods in soil mechanics – part I: theory. Int J Geomath, 4:167–184
  I. Ostermann, J. Kuhnert, D. Kolymbas, C.-H. Chen, I. Polymerou, V. Šmilauer, C. Vrettos, D. Chen
  (See online at https://doi.org/10.1007/s13137-013-0048-7)
• (2014) The Finite Pointset Method (FPM) and an Application in Soil Mechanics. In: E. Pardo-Igúzquiza et al. (eds) Mathematics of Planet Earth. Lecture Notes in Earth System Sciences. Springer, Berlin, Heidelberg, pp. 815-818
  J. Kuhnert, I. Ostermann
  (See online at https://doi.org/10.1007/978-3-642-32408-6_176)
• (2015) Meshfree numerical simulation in soil mechanics with the Finite Pointset Method (FPM). Proceedings of IAMG 2015 – 17th Annual Conference of the International Association for Mathematical Geosciences, pp. 652–658
  I. Michel, J. Kuhnert
  
• (2016) Finite Pointset Method (FPM) in selected industrial applications. US-ACM Conference on Isogeometric Analysis and Meshfree Methods, La Jolla, USA
  J. Kuhnert
  
• (2017) Further Development of Soft PARticle Code (SPARC). GeoDACH, Stuttgart, Germany
  I. Bathaeian
  
• (2017) Meshfree generalized finite difference methods in soil mechanics – part II: numerical results. Int J Geomath, 8(2):191–217
  I. Michel, S.M.I. Bathaeian, J. Kuhnert, D. Kolymbas, C.-H. Chen, I. Polymerou, C. Vrettos, A. Becker
  (See online at https://doi.org/10.1007/s13137-017-0096-5)
• (2017) MESHFREE simulation in continuum and fluid mechanics: From geomechanical to medical applications. Geomathematics Meets Medical Imaging, Speyer, Germany
  I. Michel, J. Kuhnert, F. Nick, B. Metsch
  
• (2017) Meshfree simulation of avalanches with the Finite Pointset Method (FPM). Geophysical Research Abstracts, Vol. 19, EGU2017-13203 (EGU General Assembly 2017, Vienna, Austria)
  I. Michel, J. Kuhnert, D. Kolymbas
  
• (2017) Simulation of shear bands with Soft PARticle Code (SPARC) and FE. Int J Geomath, 8(1):135–151
  B. Schneider-Muntau, C.-H. Chen, S.M.I. Bathaeian
  (See online at https://doi.org/10.1007/s13137-016-0091-2)
• (2018) Simulation of settlement and bearing capacity of shallow foundations with soft particle code (SPARC) and FE. Int J Geomath, 9(2):359–375
  B. Schneider-Muntau, S.M.I. Bathaeian
  (See online at https://doi.org/10.1007/s13137-018-0109-z)
• (2019) Numerically obtained vortices in granular media. Int J Numer Anal Methods Geomech
  D. Kolymbas, I. Bathaeian
  (See online at https://doi.org/10.1002/nag.2984)
• (2019) Parallel Detection of Subsystems in Linear Systems Arising in the MESHFREE Finite Pointset Method. In: Griebel, M. and Schweitzer, M.A. (eds) Meshfree Methods for Partial Differential Equations IX, IWMMPDE2017. LNCSE, Vol. 129, Springer, Cham, pp. 93–115
  F. Nick, H.-J. Plum, J. Kuhnert
  (See online at https://doi.org/10.1007/978-3-030-15119-5_6)
• (2019) Parameter identification for soil simulation based on the Discrete Element Method and application to small-scale shallow penetration tests. VI International Conference on Particle-based Methods – Fundamentals and Applications, PARTICLES 2019, Barcelona
  J. Jahnke, S. Steidel, M. Burger, S. Papamichael, A. Becker, C. Vrettos