1 Challenge the future Steel ball dropped into very fine sand (YouTube)

2 Challenge the future Simulation of sphere being shot into clay-like material (Al-Kafaji)

3 Challenge the future Stability analysis of a simplified 2-phase formulation in Geomechanics Miriam Mieremet Thursday, 8 January 2015

4 Challenge the future Content 1.Problem: Numerical instability with 2-phase MPM 2.Approach: Simplifications and methods 3.Study: Stability analysis with simplified 2-phase FEM 4.Conclusion 5.Outlook

5 Challenge the future Problem: Numerical instability with 2-phase MPM Cone Penetration Test (myv-sg.nl)

6 Challenge the future Numerical instability with 2-phase MPM 2-phase continuum Solid phase Water phase

7 Challenge the future 2-phase formulation Numerical instability with 2-phase MPM

8 Challenge the future Numerical instability with 2-phase MPM Material Point Method & Euler Cromer Method Initial configuration Calculation stepResetting the mesh

9 Challenge the future Numerical instability with 2-phase MPM Simulation of CPT with MPM (Ceccato) Stability Criterion 1-phase Unexpected instability 2-phase High permeability: Stable Low permeability: Unstable What is the right stability criterion?

10 Challenge the future Approach: Simplifications and methods

11 Challenge the future Simplifications and methods Problem:Study: Large deformationsSmall deformations Three dimensionsOne dimension 2-phaseSimplified 2-phase

12 Challenge the future Problem:Study: MPMFEM Tetrahedral elementsLinear elements Simplifications and methods

13 Challenge the future Stability analysis Von Neumann Method Matrix Method Simplifications and methods

14 Challenge the future Study: Stability analysis with simplified 2-phase FEM Oedometer Test

15 Challenge the future Variables velocity of solid phase velocity of water phase effective stress pore pressure Stability analysis with simplified 2-phase FEM

16 Challenge the future 2-phase formulation Stability analysis with simplified 2-phase FEM

17 Challenge the future Simplified 2-phase formulation Stability analysis with simplified 2-phase FEM

18 Challenge the future Finite Element space discretization Stability analysis with simplified 2-phase FEM

19 Challenge the future Euler Cromer time discretization Stability analysis with simplified 2-phase FEM

20 Challenge the future Von Neumann Method Space discretization Time discretization Error equation Fourier decomposition Stability analysis with simplified 2-phase FEM

21 Challenge the future Stability analysis with simplified 2-phase FEM Stability criterion Amplitude equation

22 Challenge the future Matrix Method Space discretization Error equation Eigenvalue decomposition Time discretization Stability analysis with simplified 2-phase FEM

23 Challenge the future Stability analysis with simplified 2-phase FEM Stability criterion Error equation

24 Challenge the future Stability analysis with simplified 2-phase FEM Compare analytical and numerical solution with

25 Challenge the future Stability analysis with simplified 2-phase FEM Compare analytical and numerical solution with

26 Challenge the future Conclusion Familiarization with geomechanical problems Investigation of 1- and 2-phase formulation Implementation in Matlab Literature study on stability analysis

27 Challenge the future Conclusion Stability criterion for simplified 2-phase FEM:

28 Challenge the future Outlook Stability analysis with 2-phase FEM (1D) Stability analysis with 2-phase FEM (3D) Study impact of…  Local Damping  Mass Scaling  Strain smoothening Introduction of stability criterion into Deltares MPM code