Solve using a Maxwell linear viscoelastic material rheology conceptually, a spring (GM
) and dashpot (ηM
) in series.
Benchmark #1b: Solve using a Burgers body rheological description - conceptually, a Maxwell element in series with a Kelvin-Voigt element (a spring (GKV) and dashpot (ηKV) in parallel).
Benchmark #1c: Solve using a Maxwell power-law material description conceptually, a spring (GM) and dashpot (ηeff) in series. The dashpot has a nonlinear viscosity that depends on the second invariant of the stress tensor, σ. For these benchmarks, we assume a power law rheology with n=3, that is:
ηeff = ηref (σref /σ)2
- Test relevant constitutive relations
- Verify shear relaxation only no bulk relaxation
- Verify that mesh geometry introduces no errors
- Model size: 24 km by 24 km by 24 km (0 km ≤ x; y ≤ 24 km; -24 km ≤ z ≤ 0 km)
- Maxwell elastic material properties: Poisson solid, GM = 30 GPa
- Maxwell viscoelastic material properties: ηM = 1018 Pa-s
- Burgers body material properties: Maxwell element as above, Kelvin-Voigt element has GKV = 10 GPa, M = 1017 Pa-s
- Power-law material properties: ηref = 1018 Pa-s and ref = 105 Pa. (Note: This value is chosen because the maximum initial elastic stress is of order 106 Pa, only a fraction of that is deviatoric, and the deviatoric stress decreases with time.)
- Density and Gravity: None
- Boundary conditions:
- Bottom pinned
- Sides pinned in x and y; free in z
- Top pinned in x and y; +1 m of displacement imposed in z
- Coarse mesh node spacing: dx = dy = dz = 2 km
Requested Output and Results:
Mesh Variations: As memory, time, and patience allow, run models at 1/2, 1/4, and 1/8, etc. the original coarse mesh spacing, investigate variable mesh spacing, and/or employ a variety of element types. For All Benchmark Variations:
- Stresses along a path through (0,0,-24) and (24,24,0) at t = 0, 1, 5, and 10 years.
- Displacements along a path through (0,0,-24) and (24,24,0) at t = 0, 1, 5, and 10 years.
- CPU time, wallclock time, memory usage info, compiler info, and platform info
Analytical solutions for each material rheology will be posted at geoweb.mit.edu/fe
Benchmark #1 should be completed for each material rheology used in any of the benchmarking exercise.