Simulating Granular Flow Dynamics and Other Applications using the Material Point Method

Transcription

1 Simulating Granular Flow Dynamics and Other Applications using the Material Point Method Pedro Arduino 1 7 th MPM Workshop University of Utah Salt Lake City, Utah March 14-15, Department of Civil and Environmental Engineering University of Washington Seattle, WA

2 Participants Carter Mast Current Ph.D. student Wen-Chia Current Ph.D. student Woo Kuen Shin Ph.D. at UW (2009) John A. Moore MSE at UW (Spring 2007) Pedro Arduino Peter Mackenzie-Helnwein Greg Miller Acknowledgements NSF CMMI UW-RRF

3 Research Goals Motivation Looking at the big picture As civil engineers, we are interested in designing, building, and maintaining critical infrastructure Resiliency and sustainability Long term behavior Response to disaster Must rely heavily on models Physical based Numerical based Numerical simulations are a critical component for evaluating the resiliency and sustainability of critical infrastructure

4 Research Goals Motivation

5 Research Goals Motivation

6 Research Goals Motivation

7 Research Goals Motivation Looking at the big picture What are the short and long term effects of natural disasters on civil infrastructure? Earthquakes Tsunamis Landslides Debris flows The ability to answer this question is directly linked to our ability model these events as well as their interaction with the built environment

8 Research Goals Motivation Landslides and Debris Flows Highly dynamic Composed of several materials Can exhibit both solid-like and fluid-like behavior

9 Research Goals Goals Establish a computational framework Unified approach for modeling fluids and solids Capture behavior associated with multiple phases Mixing and separation Mechanical behavior Applications Landslide and debris flows Interaction with protective structures Other areas of engineering

10 Mechanical behavior Solid phase Large deformation History dependent Finite strains Material failure ψ ( ε, ξ) σ = ρ ε L σ = ρ c( ε, ξ) : L v f ( σ, ξ) 0 λ 0 f λ = v ε 0 Fluid phase Rate dependent but no history Large deformation Nearly incompressible σ = p1 + 2µ div v = 0 s v

11 Material Point Method (MPM) To reduce computational expense Use a regular, rectangular grid. Eliminates need for cell search algorithms Mapping between global and local coordinates is easily accomplished Allows for dynamic node/cell creation and deletion Problematic for representing general surface geometry We developed two distinct approaches for incorporating general boundary geometry Use linear shape functions. Cheapest option for rectangular cells/elements Widely used Leads to kinematic locking.

12 Anti-Locking Strategies in the MPM

13 Anti-Locking Strategies in the MPM Kinematic Locking Locking refers to the build up of fictitious stiffness) A result of a cell s/element s inability to reproduce the correct mode shapes We are concerned with two types of locking: Volumetric Locking Dominant in the incompressible limit for both solids and fluids Shear Locking Problematic for any material with moderate shear stiffness (or highly viscous fluids) 5 th and 6 th MPM workshops

14 Anti-Locking Strategies in the MPM Kinematic Locking Dam break using the Standard MPM algorithm

15 Anti-Locking Strategies in the MPM Kinematic Locking Dam break using the Standard MPM algorithm Particle pressure (kpa)

16 Anti-Locking Strategies in the MPM Mitigating Locking Approximation functions Acceleration field Strain field Stress field

17 Anti-Locking Strategies in the MPM Mitigating Locking Control Volumes Cell-based α c, β c α c, β c α c, β c α c, β c Node-based α 7, β 7 α 8, β 8 α 9, β 9 α i, β i α c, β c ε p ε p (α c ) σ p σ p (β c ) ε p σ p Hybrid-based vol Σ i N i ε i (α i ) + dev ε p (α c ) vol Σ i N i σ i (β i ) α 4, β 4 α 5, β 5 α 6, β α 1, β 1 α 2, β 2 α 3, β 3 ε p Σ i N i ε i (α i ) σ p Σ i N i σ i (β i ) + dev σ p (β c )

18 Modeling Fluid Behavior Dam break revisited Particle pressure (kpa)

19 Modeling Fluid Behavior Dam break revisited Particle pressure (kpa) at t = 2.0 s

20 Modeling Solid Behavior Material Models Elastic Linear, nonlinear, isotropic Ductile J2 Pressure Dependent Drucker Prager Matusoka Nakai

21 Modeling Elastic Solid Behavior Elastic response Vibrating cantilever beam

22 Modeling Elastic Solid Behavior Vibrating beam Normal stress

23 Modeling Elastic Solid Behavior Vibrating beam Shear stress

24 Modeling Granular Materials Material Models Pressure Dependent Drucker-Prager

25 Modeling Granular Material Experimental Results 35

26 Modeling Granular Materials Material Models Pressure Dependent Matsuoka-Nakai

27 Modeling Granular Materials Material Models

28 Modeling Granular Materials Material Models

29 Modeling Granular Materials Model Validation Simple Shear Tests

30 Modeling Granular Materials Model Validation Triaxial Compression

31 Applications 41

32 Applications Taylor Bar Impact

33 Applications Taylor Bar Impact

34 Applications Taylor Bar Impact

35 Applications Taylor Bar Impact

36 Applications Taylor Bar Impact

37 Applications Planar Sand Column Collapse

38 Applications Planar Sand Column Collapse

39 Applications Planar Sand Column Collapse

40 Applications Planar Sand Column Collapse

41 Applications Planar Sand Column Collapse

42 Applications Avalanche Control

43 Applications Avalanche Control

44 Applications Avalanche Control

45 Applications Avalanche Control

46 Applications Avalanche Control

47 Applications Avalanche Control

48 Applications Parametric Force Analysis

49 Applications Parametric Force Analysis

50 Applications Parametric Force Analysis

51 Applications Parametric Force Analysis

52 Applications Parametric Force Analysis

53 Applications Parametric Force Analysis w c [m] w c [m] H b [m] w c [m] w c [m] H b [m]

54 Applications Parametric Force Analysis

55 Applications Effects of Approach Angle

56 Applications Effects of Approach Angle

57 Applications Effects of Approach Angle

58 Applications Effects of Approach Angle

59 Applications Effects of Approach Angle

60 Questions? 70

61 Applications Effects of Approach Angle

62 Applications Effects of Approach Angle

63 Conclusions Pedro s First Conclusion Point 1 Subpoint 1

64 Questions?

65 Research Goals Goals Capture behavior associated with multiple phases

66 Material Point Method (MPM) Detailed formulation of the MPM Weak form Approximation functions Particle-based integration

67 Material Point Method (MPM) Detailed formulation of the MPM Solving for nodal values

68 Material Point Method (MPM) Detailed formulation of the MPM Particle update (assume linear elastic material)

69 Material Point Method (MPM) Detailed anti-locking formulation Volumetric Approach

70 Material Point Method (MPM) Detailed anti-locking formulation Volumetric-Deviatoric Approach

71 Material Point Method (MPM) Detailed anti-locking formulation Cell-Based Anti-Locking

72 Material Point Method (MPM) Detailed anti-locking formulation Node-Based Anti-Locking

73 Material Point Method (MPM) Detailed anti-locking formulation Node-Based Anti-Locking

74 Material Point Method (MPM) Detailed anti-locking formulation Large deformation flow chart

75 Anti-Locking Strategies in the MPM Mitigating Locking Draining water tank (Standard MPM)

76 Anti-Locking Strategies in the MPM Mitigating Locking Draining water tank (Cell-based anti-locking)