Two techniques are employed to eliminate volumetric locking in this problem. The first involves refining the mesh in both corners at the bottom of the rubber model to reduce mesh distortion in these areas. The second introduces a small amount of compressibility into the rubber material model. Provided the amount of compressibility is small, the results obtained with a nearly incompressible material will be very similar to those obtained with an incompressible material; the presence of compressibility alleviates the volumetric locking.

Compressibility is introduced by setting the material constant to a nonzero value. The value is chosen so that the initial Poisson's ratio, , is close to 0.5. The equations given in “Hyperelastic behavior of rubberlike materials,” Section 17.5.1 of the ABAQUS Analysis User's Manual, can be used to relate and in terms of and (the initial shear and bulk moduli, respectively) for the polynomial form of the strain energy potential. For example, the hyperelastic material coefficients obtained earlier from the test data (see “The hyperelastic material parameters” in “Preprocessing—creating the model with ABAQUS/CAE,” Section 10.7.2) 176051 and 4332.63; thus, setting 5.E–7 yields 0.46.

A model that incorporates the above features is shown in Figure 10–68 (this mesh can be generated easily by changing the edge seeds in ABAQUS/CAE).

The displaced shape associated with this model is shown in Figure 10–69. It is clear from this figure that the mesh distortion has been reduced significantly in the critical regions of the rubber model and that the volumetric locking has been eliminated.