Explicit dynamics: Taylor impact of a copper cylinder, final length against the Hawkyard and Taylor theories
Explicit dynamics (impact)PASS · 0.5%A perfectly plastic copper cylinder hits a rigid wall at 91.5 m/s (rho U^2 / sigma = 0.25). The explicit solver in the finite-strain formulation is run until the cylinder comes to rest; the final length is compared with the energy-balance theory of Hawkyard and the momentum theory of Taylor, both one-dimensional models evaluated numerically here. The cylinder cross-section is a square of the same area as the circle of the classical problem, since both theories depend on the area only. The kinetic energy of the impact must go into plastic work and the energy balance must close within 1 %. The result is a comparison with theory, not with a test.A perfectly plastic copper cylinder hits a rigid wall at 91.5 m/s (rho U^2 / sigma = 0.25). The explicit solver in the finite-strain formulation is run until the cylinder comes to rest; the final length is compared with the energy-balance theory of Hawkyard an… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- Cylinder of length 25.4 mm, square cross-section of area pi * 3.81^2 mm2, 48 x 10 x 10 HEX8 elements (structured, the whole body, no symmetry planes).
- Material
- Copper: E = 124 GPa, nu = 0.34, rho = 8960 kg/m3; J2, perfect plasticity, yield 300 MPa.
- Boundary conditions
- Initial velocity 91.5 m/s along -x for the whole body; rigid wall at x = 0 (penalty contact, no friction); finite strains; no bulk viscosity; time-step factor 0.8; the end time covers the stop and the elastic ringing.
- Measured quantity
- L1/L0 from the displacements of the rear and front faces against the Hawkyard and the Taylor value; energy balance |E_total - W_wall - KE0| / KE0; residual kinetic energy.
WebCAE Terminal
Paste these commands into the Terminal panel inside WebCAE. They use the same text DSL as the application; run one command per line:
units mm
material E=124e9 nu=0.34 density=8960 plasticity=j2 yield=300e6
box dx=25.4 dy=6.75305 dz=6.75305
mesh hex nx=48 ny=10 nz=10
explicit endTime=0.00016973018 dtScale=0.8 saveStride=1000000 bulkQ1=0 bulkQ2=0 largeStrain=on
bc explicit_velocity body vx=-91.490632
bc rigid_wall plane x 0 friction=0
solve explicit
probe explicit_displacement_x x=25.4 id="uRear"
probe explicit_displacement_x x=0 id="uFront"
probe explicit_energy kind=kinetic time=0 id="ke0"
probe explicit_energy kind=kinetic id="keEnd"
probe explicit_energy kind=total id="etEnd"
probe explicit_external_work id="ewEnd"
probe explicit_steps id="steps"Results comparison
| Reference value | L1/L0 = 0.89574 (Hawkyard energy model), 0.89682 (Taylor momentum model) |
| Our result | L1/L0 = 0.9002energy balance 0.983 % |
| Deviation | 0.5% |
| Tolerance | 5% |
| Status | PASS · 0.5% |
| Element family | Solid element |
| Mesh details | hex8 48×10×10 (4800 elements (structured, native), 5710 explicit steps, finite strain;: webcae_solve (native) |
Updated: 2026-10-22 · WebCAE solver