Simulation-based Disaster Prediction and Damage Assessment Using Meshfree Method

Transcription

1 Simulation-based Disaster Prediction and Damage Assessment Using Meshfree Method Jiun-Shyan (JS) Chen Department of Structural Engineering Center for Extreme Events Research (CEER) Jacobs School of Engineering, UCSD

2 Background Full scale experiments could be time consuming, expensive, and quite often impossible. Numerical prediction of disaster damages is effective, reproducible, but often challenging.

3 Meshfree Approximation and Discretization NP C Finite open cover II 1 NP NP I 1 I x 1, x I 1 I Partition of unity subordinated to the open covering C MLS/RK approximation (Liu et al., 1995, Chen et al, 1996) n I ( x) ( x - xi ) b ( x) a( x -xi) 0 x x x x 3, 3 i1 i Reproducing Conditions NP ( x) x x, 0 n I I I 1 T 1 I ( x) H (0) M ( x) H( x xi ) a ( x xi ) NP T M( x) H( x x ) H ( x x ) ( x x ) I 1 I I a I H( x xi ) 1,( x xi ),,( x xi ) Error bound (W. Han et al., 2001): h p 1 x x u u Ca u, n p1,

4 Comparison of Meshfree and Finite Element Method Finite Element Method Meshfree Method (MLS, RK, PU etc.) N I Unique Properties of Meshfree Methods Arbitrary order of smoothness (elasticity, plates/shells) and roughness (shearbands, cracks, shocks) in the approximation Straightforward adaptive model refinement Effective for large deformation and fragment impact modeling Easy embedment of enrichment functions Intrinsic length scale for regularization of materials instability Smooth contact algorithm for large sliding contact Effective in modeling microstructural evolution (change of topology), multis-scale materials modeling, image based modeling, etc.

5 Comparison of Lagrangian, Semi-Lagrangian, and Eulerian Discretizations Lagrangian Kernel supp f a I at t 0 I I t t 0 I 0 ai Semi - Lagrangian Kernel supp f a I supp f at t t at t 0 supp f at t t ai Eulerian Kernel n n t t I t t n n Lagrangian kernel : z X - XI / a a( z) : Semi-Lagrangian kernel : z x - x( XI, t) / a * Eulerian kernel : z x - xi / a supp f a I at any t I Grid Point Matrial Point J. S. Chen, C. Pan, C. T. Wu, and W. K. Liu, Computer Methods in Applied Mechanics and Engineering, 139: , 1996 J. S. Chen, C. Pan, C. M. O. L. Roque, H.P. Wang, Computational Mechanics, 22: , 1998

6 Bonded Rubber Under Compression and Shear

7 Elastomeric Applications Engine Mount Struck Mount Hydro Mount 7

8 Sheet Metal Drawing (a) t=0 Drawing depth d=0 (d) t=0.35 Drawing depth d=28 mm (b) t=0.15 Drawing depth d=12 mm (e) t=0.50 Drawing depth d=40 mm (c) t=0.25 Drawing depth d=20 mm

9 RKPM Adaptive Refinement Given a set S of n distinct points in R d, the Voronoi cell of point p is defined as p vo( p) { xr d dist( x, p) dist( x, q) q S p} Y. You, J. S. Chen, H. Lu, Computational Mechanics, 31: , 2003

10 Error Indicator Reproducing Kernel Reproducing kernel as a low pass filter * h h h u ( x) u ( x )* ( x) u ( x) ( x - x) dx u ( xi) ( x - xi) a Let ( x x ) = ( x) * h a u ( x) u ( xi) I ( x) Reproducing properties NP I1 x x, k 0,1, n a k k I I Low-pass filter properties 1 1 u ( x) u ( x) u '( x)( x x) u ( x)( x x) u ( )( x x) n! ( n1)! h h h h( n) n h( n1) n1 L NP I1 u ( x) uh ( x) * h L H u ( x) u ( x )* ( x ) [u ( x) u ( x )]* ( x) NP L H a L H [ u ( x ) u ( x )]* ( x ) u ( x) u ( x )* ( x ) I1 NP I1 I I I I h * u ( x) u ( x) error indicator I Y. You, J. S. Chen, H. Lu, Computational Mechanics, 31: , 2003 Spectral Response

11 Adaptivity in L-shaped Structure Adaptive refinement models Uniformly refined model 50 P= L-shaped domain in plane stress condition Error indicator for adaptive procedure 65 nodes 157 nodes 235 nodes -2 Stress in uniformly refined model Stress in adaptive refinement model Log(Error energy norm) nodes Uniformly Refined models Adaptive refinement models Log(Number of nodes)

12 Adaptive Refinement 80 mm 60mm 30 mm 50 mm Effective plastic strain Fixed fine model Progressive adaptivity model

13 Modeling of Microstructural Evolution gb Interface Enrichment Function Grain interior point Grain boundary point ( r ) ( s ) I I I Cubic B-spline ˆ ( r ) ( s ) ˆ I r (J. S. Chen, V. Kotta, H. Lu, D. Wang, D. Moldovan, D. Wolf, CMAME, 2004)

14 Level Set Simulation of Grain Growth (X. Zhang, J. S. Chen, S. Osher, IMMIJ, 2008)

15 Micro-crack informed Damage Model σ, e σe, y p homogenization 1 1 = d + ds V Y 2 up c y Ren, X., Chen, J. S., Li, J., M. J. Roth, T. Slawson, International Journal of Solids and Structures, 2011.

16 Stochastic Micro-Cracks Informed Damage Model Shear Stress 2.00E E E E E E E E E E E+00 Stress-strain curves Porosity=2.39% Porosity=3.22% Porosity=3.72% Porosity=4.35% Porosity=4.90% Porosity=5.82% Porosity=6.63% Porosity=7.19% Porosity=6.70% Porosity=8.56% Porosity=9.01% Shear strain Damage evolution Damage E E E E E E-03 Shear strain Porosity=2.39% Porosity=3.22% Porosity=3.72% Porosity=4.35% Porosity=4.90% Porosity=5.82% Porosity=6.63% Porosity=7.19% Porosity=6.70% Porosity=8.56% Porosity=9.01% Direct tensile RVE analyses Tensile Stress 6.00E E E E E E+06 Stress-strain curves Porosity=2.39% Porosity=3.22% Porosity=3.72% Porosity=4.35% Porosity=4.90% Porosity=5.82% Porosity=6.63% Porosity=7.19% Porosity=6.70% Porosity=8.56% Porosity=9.01% Damage evolution Porosity=2.39% Porosity=3.22% Porosity=3.72% Porosity=4.35% Porosity=4.90% Porosity=5.82% Porosity=6.63% Porosity=7.19% Porosity=6.70% Porosity=8.56% Porosity=9.01% 0.00E Tensile strain E E E E-04 Tensile strain

17 Validation Problem Reinforced concrete beams (Kulkarni and Shah 1999) Damage contours Load-displacement curves Cracking domain Crushing domain Tensile damage contour Compressive damage contour

18 Earth Excavation

19 Coupled RKPM-FEM Earth Moving Simulation

20 NASA-JPL Planetary Exploration Mission: Mars Mission Landing Rover Control Workstation Rover Task Planning Simulation of Soil-Wheel Interaction

21 Image Based Meshfree Model Generation

22 Process of Meshfree Solution Displacement field Stress fields Basava RR, Chen JS, Zhang Y, Sinha, S., Sinha, U, Hodgson, J, Csapo, R, Malis, V, CompIMAGE 2014, 2014.

23 Fragment Impact of Concrete Block Front Face of Target 5 Back Face of Target 5 Ref: M. Unosson (2000), Defense Research Establishment FOA Report M. Unosson and L. Nilsson (2006), Int. J Impact Engrg. vol 32 pp

24 Concrete Plate Penetration mm Simulation 127 mm Experiment 216 mm Simulation 216 mm Experiment 254 mm Simulation 254 mm Experiment Velocity (m/s) Time (s) Courtesy of Jesse Sherburn, Army ERDC 24

25 Bullet Penetration Through Concrete Plate Courtesy of Jason Roth, Tom Slawson,, Army ERDC

26 Slope Instability

27 Meshfree RKPM Modeling of Landslide 2015/2/8 Department of Systems Engineering and Naval Architecture Courtesy of Professor National Pai-Chen Taiwan Ocean Guan, University National Taiwan Ocean University 27

28 Meshfree RKPM Modeling of Landslide Saturated Slope Without Water One Meter Submerged Courtesy of Professor Pai-Chen Guan, National Taiwan Ocean University