Example 2: Lagrangian modeling for an impact problem 1 PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY EXAMPLE 2

2 PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY Direct impact problem A rigid body (5 kg) with 50 m/sec impacts on the aluminum plate.  Aluminum plate Dimensions: 1m× 1m× 0.002m Material type: Linearly elastic behavior with isotropic hardening Element : Shell elements (S4R) Mesh size: 0.01m-0.05m Boundary condition: Four edges are fully constrained.  Rigid body impactor Shape: cylinder with two hemispherical caps Dimensions: 0.32 in length × 0.16 m in a diameter Length/ diameter = 2 Initial bird mass: 5 kg Magnitude of initial velocity: VZ = -50 m/s Rigid elements (R3D4)

3 EXAMPLE 2 Target structure Model type: Shell model Shape: Square plate Dimensions: 1m× 1m PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY

4 EXAMPLE 2 PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY Reference geometry for an Impactor Model type: Discrete rigid model Shape: Cylinder with hemispherical cap and straight end Dimensions: 0.16 m in a diameter × 0.32 m in length

5 EXAMPLE 2 PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY

6 EXAMPLE 2

7 PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY EXAMPLE 2 Coordinate (0,0,0) Coordinate (0.5, 0.5, 0.01)

8 PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY EXAMPLE 2

9 PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY EXAMPLE 2

10 PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY EXAMPLE 2

11 PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY EXAMPLE 2

12 PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY EXAMPLE 2

13 PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY EXAMPLE 2

14 PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY EXAMPLE 2 Animation

15 PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY EXAMPLE 2 Target: 0 <X < 0.8 Animation

Lagrangian modeling is very traditional, available  ABAQUS 6.12 documentation: Abaqus Analysis User's Manual “Rigid elements,” Section 30.3  ABAQUS 6.12 documentation: Abaqus Example Problems Manual “Rigid projectile impacting eroding plate,” Section PREPARED BY NORI. NANAMI, TEXAS A & M UNIVERSITY EXAMPLE 2