Figure 9:

Deformations of the Cook’s membrane benchmark (Section 4.2), along with mean values of J within each element calculated via equation (69), using a neo-Hookean material model, equations (41) – (44), with $G=83.3333\frac{\text{dyn}}{{\text{cm}}^2}$. The background Eulerian grid is not shown. Shown here are solid meshes with Q1 elements and m = 289 DOF. The first row shows cases with ν_stab = .4, and the second row shows cases with ν_stab = −1 (here equivalent to κ_stab = 0 and no volumetric-based stabilization). The first column depicts cases with modified invariants, and the second column depicts cases with unmodified invariants. Notice that the case with modified invariants with nonzero numerical bulk modulus have the smoothest deformations and provides the best volume conservation, whereas those of the case with unmodified invariants and zero numerical bulk modulus behave unphysically.