Figure 11.

Percent change in structure volume for the soft elastic disc benchmark of sec. 5.2 as a function of time using eq. (65) with A.p₀ = 0 and B.p₀ = μ^e. Results are shown for Cartesian grids of size N = 64, 128, and 256 with relative Lagrangian mesh spacings M_fac = 4, 2, and 1. The amount of spurious volume change converges to zero at first order. At coarser relative mesh spacings, the partitioned (split) formulation yields substantially better volume (area in two spatial dimensions) conservation than the unified (unsplit) formulation. Volume conservation is substantially improved for the unified formulation by setting p₀ = μ^e. The volume change is less than 0.4% for all cases considered except for the unified formulation with p₀ = 0 and M_fac = 4.