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