Fabric Presentation

1
Fabric Presentation

• David Powell
• UC Berkeley
• 2006

2
Multiscale Modeling

• Fabric has Multiscale Structure
• Capture Macroscale Behavior with Purely
  Microscale Information
• Avoid Phenomenological Modeling

3
Fibril Model

• Single Yarn Contains 350 Individual Fibrils
• Fibril Misalignment is Unavoidable
• Model Yarn Response Using Behavior of Fibrils

4
Fibril/Yarn Model

• Stretch of a Single Fibril
• Yarn Stress Response
• Effective Youngs Modulus

5
Fibril Model

• Numerical Simulation of Yarn
• Random Misalignment of Fibrils vs. Perfectly
  Aligned
• Response Used to Create Yarn Element

6
Macroscale Problem

• Lumped Mass Model
• Nodes at Suture Points
• Intersection of Yarns
• System of Equations
• 367,500 (3 x 350 x 350) DoF
• (3,675 DoF per Square Inch)
• Solve with Fixed-Point Iteration
• Coupled Fabric/Projectile problem

7
Macroscale Problem

• Dynamic Equilibrium
• Iterative Scheme
• Finite Difference Approximation

8
Projectile/Fabric Interaction

• Replace Energy Balance with Force Calculation
  Allow for 3-D Motion
• Determine Forces Needed to Keep Nodes from
  Penetrating Projectile
• Apply Reaction Forces to Projectile
• Calculate Total Force and Torque
• Solve for Motion of Projectile

9
Algorithm

• FOR A SHEET/PROJECTILE PAIR
• STEP 0 STARTING TIME STEP VALUE
• ( UPPER TIME STEP DISCRETIZATION SIZE
  LIMIT)
• STEP 1 SOLVE FOR DISPLACEMENTS VIA EQUILIBRIUM
• ENFORCE CONTACT NODES MAY NOT PENETRATE
  PROJECTILE
• STEP 2 SOLVE FOR CAUCHY STRESSES
• STEP 3 COMPUTE FIBRIL RUPTURE IN EACH YARN

• STEP 4 COMPUTE PROJECTILE POSITION
• (1) C ALCULATE FORCES AND MOMENTS FROM CONTACT
• (2) APPLY LINEAR AND ANGULAR MOMENTUM BALANCE
• STEP 5 ERROR CHECK
• IF TOLERANCE MET AND THEN
• INCREMENT TIME AND GO TO STEP 1
• WITH AND
• IF TOLERANCE NOT MET AND THEN
• CONSTRUCT NEW TIME STEP
• RESTART AT AND GO TO STEP 1 WITH

10
Simulated Displacement

• BC Fixed Along 2 Sides
• Failure at Projectile

11
2 Sides Test
12
Simulated Damage

• Begins at edge of projectile
• Initiates at weak spots in fabric
• Asymmetry due to variation in Youngs modulus

13
Simulated Displacement

• BC Pinned at Corners
• Failure at Boundaries

14
4 Corners
15
Simulated Damage

• Failure initiates at inside edge of washer
• Failure proceeds around sides from there

16
Comparison of Simulation to Experiments

• BC 2 Sides Clamped
• Incoming Angle - 0 to 20 degrees
• No initial Angular Velocity

17
(No Transcript)