Benchmark C8

VMC8
Aluminum Bar Impacting a Rigid Boundary

Overview

Reference: M. L. Wilkins, M. W. Guinan, "Impact of Cylinders on a Rigid Boundary", Journal of Applied Physics, Vol. 44 No. 3, 1973, pp. 1200.
Analysis Type(s): Nonlinear Transient Dynamic Analysis (ANTYPE = 4)
Element Type(s):
2D 4-Node Structural Solid Elements (PLANE182)
2D 8-Node Structural Solid Elements (PLANE183)
Input Listing: vmc8.dat

Test Case

A cylindrical aluminum bar impacts a rigid wall at a velocity Vo. Determine the deformed length of the bar and perform axisymmetric analyses with the element types noted above.

Figure 601: Aluminum Bar Problem Sketch

Aluminum Bar Problem Sketch

Material PropertiesGeometric PropertiesLoading
E = 70 x 109 N/M2
ET = 100 x 106 N/M2
σyp = 420 x 106 N/M2
υ = 0.3
ρ = 2700 Kq/m3
= 2.347 cm
d = 0.762 cm
Vo = 478 m/sec

Representative Finite Element Models

2D Axisymmetric Model

Assumptions, Modeling Notes, and Solution Comments

  1. The test case is modelled as a 2D axisymmetric analysis with elements PLANE182 and PLANE183. Each analysis consists of two load steps. The first load step is static and serves to define the initial velocity. The second load step resolves the nonlinear transient effects.

  2. The material behavior is assumed to be elastic perfectly plastic and obey a bilinear isotropic hardening law. The elastic wave propagation speed is defined as . The time required for the elastic wave to travel across a typical element in the radial direction is used to define the minimum number of substeps. A time span of 4.5 x 10-5 seconds allows the bar to impact and realize its maximum deflection. Auto time stepping (AUTOTS) is used to control the time step increments. The large deflection effects are included using NLGEOM. Solution efficiency is improved by relaxing the convergence criteria (CNVTOL).

  3. In comparison, the plane and solid elements perform equally well as the viscoplastic elements for the strain levels encountered in this problem. Introducing a rate-dependent material property to the problem would illustrate advantage to viscoplastic elements.

  4. Using POST26, plots of the displacement vs. time (Figure 602: Deformed Shape) and equivalent plastic strain (Figure 603: Time History Graphs - for the center node on the impact face) vs. time are produced.

Results Comparison

Target Solution: Lf = .01319 m (Obtained experimentally)

ETYPLf,mRatio
2.0141.067
182.0141.078
183.0141.069

Figure 602: Deformed Shape

Deformed Shape

PLANE183 Elements


Figure 603: Time History Graphs

Time History Graphs

(a) Free End Displacement vs. Time and (b) Impact Face - Equivalent Plastic Strain vs. Time