3.2.10 Indentation of a crushable foam plate

Products: ABAQUS/Standard  ABAQUS/Explicit  

Two indentation problems are considered: a square plate of polyurethane foam indented by a rigid, cylindrical punch and a cylindrical plate of the same kind of foam indented by a rigid, hemispherical punch. The examples illustrate a typical application of crushable foam materials used as energy absorption devices. The effect of rate dependence of the foam is shown. Results are presented for ABAQUS/Standard and for both the isotropic and volumetric hardening foam models in ABAQUS/Explicit.

Problem description

Material

Uniaxial and hydrostatic compression tests have been conducted on a block of sample polyurethane foam material by Schluppkotten (1999). The yield stress in uniaxial compression is plotted against the axial plastic strain in Figure 3.2.10–2. Insignificant lateral deformation is observed during uniaxial compression. The hydrostatic compression test results show that the initial yield stress in hydrostatic compression, , is almost the same as that in uniaxial compression, . The elastic response is approximated by the following constants:


7.5 MPa (Young's modulus),
0.0 (elastic Poisson's ratio).

The material parameters for the isotropic hardening foam model in ABAQUS/Explicit are

1.0 (yield strength ratio),
0.0 (plastic Poisson's ratio),

and the material parameters for the crushable foam model in ABAQUS/Standard and the volumetric hardening foam model in ABAQUS/Explicit are

1.0 (compression yield strength ratio),
0.1 (tension yield strength ratio).

The density for the polyurethane foam analyzed in this example is

60 kg/m3.

In addition, the experimental results provide the following material properties for the rate-dependent case:

4638.0 per sec,
2.285.

Contact interaction

The contact between the top exterior surface of the foam plate and the rigid punch is modeled with the *CONTACT PAIR option. Both the cylindrical and hemispherical rigid punches are modeled as analytical rigid surfaces using the *SURFACE option in conjunction with the *RIGID BODY option. Coulomb friction is modeled between the punch and the plate with a friction coefficient of 0.2. The maximum shear traction due to friction is assumed to be , or 0.115 MPa.

Loading and controls

The punch is fully constrained except in the vertical direction, in which motion is prescribed such that the maximum indentation depth is about 90% of the thickness of the plate.

ABAQUS/Standard

The impactor is displaced statically to indent the foam. To model the large deformations of the foam, the NLGEOM parameter is used on the *STEP option. For nonassociated flow cases UNSYMM=YES is used on the *STEP option. This is important to obtain an acceptable rate of convergence during the equilibrium iterations, since the nonassociated flow plasticity model used for the foam has a nonsymmetric stiffness matrix.

The accuracy of the equilibrium solution within a time increment is controlled by iterating until the out-of-balance forces reduce to a small fraction of an average force magnitude calculated internally by ABAQUS. The rough punch causes an inhomogeneous stress state: stresses are higher in the region of the mesh near the punch. This tends to cause an underestimation of the average force magnitude since the reference force magnitude is averaged over the entire mesh. To avoid an excessive number of iterations, the *CONTROLS, PARAMETERS=FIELD option is used to relax the convergence tolerance.

ABAQUS/Explicit

The plate is indented quasi-statically when the foam is modeled without rate dependence. The SMOOTH parameter on the *AMPLITUDE option is used to specify the displacement of the punch and to promote a quasi-static solution. The plate is indented dynamically when the foam is modeled with rate effects. For this case a ramped velocity profile is prescribed such that the maximum velocity is 5.4 m/sec.

Results and discussion

Input files

Reference

Figures

Figure 3.2.10–1 Model for foam indentation by cylindrical or hemispherical punch.

Figure 3.2.10–2 Uniaxial compression test of a sample material.

Figure 3.2.10–3 Cylindrical punch force versus penetration response.

Figure 3.2.10–4 Hemispherical punch force versus penetration response.

Figure 3.2.10–5 Deformed configuration and contours of the equivalent plastic strain for indentation with cylindrical impactor and the isotropic hardening foam model in ABAQUS/Explicit.

Figure 3.2.10–6 Deformed configuration and contours of the volumetric compacting plastic strain for indentation with cylindrical impactor and the volumetric hardening foam model in ABAQUS/Explicit.

Figure 3.2.10–7 Deformed configuration and contours of the equivalent plastic strain for indentation with hemispherical impactor and the isotropic hardening foam model in ABAQUS/Explicit.

Figure 3.2.10–8 Deformed configuration and contours of the volumetric compacting plastic strain for indentation with hemispherical impactor and the volumetric hardening foam model in ABAQUS/Explicit.

Figure 3.2.10–9 Deformed configuration and contours of the volumetric compacting plastic strain for indentation with cylindrical impactor in ABAQUS/Standard.

Figure 3.2.10–10 Deformed configuration and contours of the volumetric compacting plastic strain for indentation with hemispherical impactor in ABAQUS/Standard.