The contact between the top exterior surface of the foam specimen and the rigid punch is modeled with the *CONTACT PAIR option. The specimen's surface is defined by means of the *SURFACE option. The spherical rigid punch is modeled as an analytical rigid surface with the *SURFACE option in conjunction with the *RIGID BODY option. An ABAQUS/Explicit model using RAX2 elements instead of an analytical rigid surface is also available. However, an analytical rigid surface provides a more accurate representation of curved geometries. Results for the analytical rigid surface case are presented here.
The mechanical interaction between the contact surfaces is assumed to be rough frictional contact in ABAQUS/Standard. Therefore, the *FRICTION, ROUGH option--which enforces a no slip constraint between the two surfaces--is used as a suboption of the *SURFACE INTERACTION property option. In ABAQUS/Explicit the friction coefficient between the punch and the foam is 0.95. The maximum shear traction due to friction is assumed to be ¾0=
p
3, or 0.127 MPa.
Loading and controls
The loading is applied by first moving the rigid surface punch into the foam specimen. This step is followed by a second unloading step in which the punch is returned to the original position. Very large deformations will take place, so the NLGEOM parameter is needed on the *STEP option in the
ABAQUS/Standard analysis. 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. In the rate-independent case the punch is moved down at a constant velocity within 0.6 seconds, while in the fast indentation problem the punch indents half of the thickness of the specimen over a period of 15 ms to demonstrate the plastic strain rate effect. In the latter case the velocity of the punch is ramped from zero to 20 m/s.
Results and discussion
The overall load-deflection response of the foam specimen for all four ABAQUS/Standard models is shown in Figure 1.1.7-2. As expected, the rate-dependent cases predict higher punch forces. The deformed configuration of the mesh at the end of the first loading step (showing actual displacements) is shown in Figure 1.1.7-3. The magnitude of the plastic strain is given in the contour plot of Figure 1.1.7-4. The figure shows that the plastic strain magnitude in the vicinity of the punch approaches 100%. pt = 0.02 MPa ¾0 = 0.22 MPa ¸ = 1.7 K = 1 ½ = 500
In addition, we use the following material properties for the rate-dependent case: D = 80 per sec
p = 1
Contact interaction
The contact between the top exterior surface of the foam specimen and the rigid punch is modeled with the *CONTACT PAIR option. The specimen's surface is defined by means of the *SURFACE option. The spherical rigid punch is modeled as an analytical rigid surface with the *SURFACE option in conjunction with the *RIGID BODY option. An ABAQUS/Explicit model using RAX2 elements instead of an analytical rigid surface is also available. However, an analytical rigid surface provides a more accurate representation of curved geometries. Results for the analytical rigid surface case are presented here.
The mechanical interaction between the contact surfaces is assumed to be rough frictional contact in ABAQUS/Standard. Therefore, the *FRICTION, ROUGH option--which enforces a no slip constraint between the two surfaces--is used as a suboption of the *SURFACE INTERACTION property option. In ABAQUS/Explicit the friction coefficient between the punch and the foam is 0.95. The maximum shear traction due to friction is assumed to be ¾0=
p
3, or 0.127 MPa.
Loading and controls
The loading is applied by first moving the rigid surface punch into the foam specimen. This step is followed by a second unloading step in which the punch is returned to the original position. Very large deformations will take place, so the NLGEOM parameter is needed on the *STEP option in the
ABAQUS/Standard analysis. 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. In the rate-independent case the punch is moved down at a constant velocity within 0.6 seconds, while in the fast indentation problem the punch indents half of the thickness of the specimen over a period of 15 ms to demonstrate the plastic strain rate effect. In the latter case the velocity of the punch is ramped from zero to 20 m/s.
Results and discussion
The overall load-deflection response of the foam specimen for all four ABAQUS/Standard models is shown in Figure 1.1.7-2. As expected, the rate-dependent cases predict higher punch forces. The deformed configuration of the mesh at the end of the first loading step (showing actual displacements) is shown in Figure 1.1.7-3. The magnitude of the plastic strain is given in the contour plot of Figure 1.1.7-4. The figure shows that the plastic strain magnitude in the vicinity of the punch approaches 100%.
The results differ very little between the linear and porous elastic models. This might be expected since the problem involves loading well into the plastic range, so that elastic effects are not likely to be significant (as long as the elasticity is sufficiently stiff to be realistic). However, in a case like this, the linear elastic modeling is more efficient computationally. In addition, it is not possible to unload the specimen for the rate-dependent case with porous elasticity. The crushable foam model with linear elasticity is, therefore, recommended for most applications.
Figure 1.1.7-5 shows a contour plot of the position of the yield surface at the end of the indentation in the rate-independent ABAQUS/Explicit case. Figure 1.1.7-6 shows the overall load-deflection
response of the foam specimen for both the rate-independent and the rate-dependent cases. Again, the rate-dependent case predicts higher punch forces.
Input files
ABAQUS/Standard input files
foamindent_ratedep_porous.inp
Rate-dependent case with porous elasticity, exponential hardening, and power law rate dependence.
foamindent_piecerate_linear.inp
Rate-dependent case with linear elasticity, tabular hardening, and power law rate dependence entered as a piecewise linear function.
foamindent_rateindep_porous.inp
Rate-independent case with porous elasticity and exponential hardening.
foamindent_rateindep_linear.inp
Rate-independent case with linear elasticity and tabular hardening.
foamindent_postoutput.inp
*POST OUTPUT analysis of foamindent_ratedep_porous.inp. ABAQUS/Explicit input files
crushfoam_anl.inp
Rate-independent case.
crushfoam.inp
Rate-independent case using a faceted surface representation.
crushfoam_rate_anl.inp
Rate-dependent case with power law rate dependence.
crushfoam_rate.inp
Rate-dependent case with power law rate dependence using a faceted surface representation. The results differ very little between the linear and porous elastic models. This might be expected since the problem involves loading well into the plastic range, so that elastic effects are not likely to be significant (as long as the elasticity is sufficiently stiff to be realistic). However, in a case like this, the linear elastic modeling is more efficient computationally. In addition, it is not possible to unload the specimen for the rate-dependent case with porous elasticity. The crushable foam model with linear elasticity is, therefore, recommended for most applications.
Figure 1.1.7-5 shows a contour plot of the position of the yield surface at the end of the indentation in the rate-independent ABAQUS/Explicit case. Figure 1.1.7-6 shows the overall load-deflection
response of the foam specimen for both the rate-independent and the rate-dependent cases. Again, the rate-dependent case predicts higher punch forces.
Input files
ABAQUS/Standard input files
foamindent_ratedep_porous.inp
Rate-dependent case with porous elasticity, exponential hardening, and power law rate dependence.
foamindent_piecerate_linear.inp
Rate-dependent case with linear elasticity, tabular hardening, and power law rate dependence entered as a piecewise linear function.
foamindent_rateindep_porous.inp
Rate-independent case with porous elasticity and exponential hardening.
foamindent_rateindep_linear.inp
Rate-independent case with linear elasticity and tabular hardening.
foamindent_postoutput.inp
*POST OUTPUT analysis of foamindent_ratedep_porous.inp. ABAQUS/Explicit input files
crushfoam_anl.inp
Rate-independent case.
crushfoam.inp
Rate-independent case using a faceted surface representation.
crushfoam_rate_anl.inp
Rate-dependent case with power law rate dependence.
crushfoam_rate.inp
crushfoam_tabular_anl.inp
Rate-dependent case with power law rate dependence entered as a piecewise linear function.
crushfoam_tabular.inp
Rate-dependent case with power law rate dependence entered as a piecewise linear function for a model using a faceted surface representation.
Figures
Figure 1.1.7-1 Model for foam indentation by spherical punch.
Figure 1.1.7-2 Punch force versus penetration response, ABAQUS/Standard.
crushfoam_tabular_anl.inp
Rate-dependent case with power law rate dependence entered as a piecewise linear function.
crushfoam_tabular.inp
Rate-dependent case with power law rate dependence entered as a piecewise linear function for a model using a faceted surface representation.
Figures
Figure 1.1.7-1 Model for foam indentation by spherical punch.
Figure 1.1.7-3 Deformed configuration showing actual displacements, ABAQUS/Standard.
Figure 1.1.7-4 Contours of magnitude of plastic strain, ABAQUS/Standard.
Figure 1.1.7-5 Yield surface position contours, ABAQUS/Explicit.
Figure 1.1.7-3 Deformed configuration showing actual displacements, ABAQUS/Standard.
Figure 1.1.7-4 Contours of magnitude of plastic strain, ABAQUS/Standard.
Figure 1.1.7-6 Punch force versus penetration response, ABAQUS/Explicit.
Sample listings
Figure 1.1.7-6 Punch force versus penetration response, ABAQUS/Explicit.