### Benchmark 1

Viscoelastic relaxation of stresses resulting from an imposed uniaxial strain. No body forces are imposed. Material should have infinite bulk viscosity (i.e., should not relax in volume, only in shear).

*Benchmark 1a:* 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: η_{eff} = η_{ref} (σ_{ref} /σ)^{2}

#### GOALS:

- Test relevant constitutive relations
- Verify shear relaxation only no bulk relaxation
- Verify that mesh geometry introduces no errors

#### DETAILED DESCRIPTION:

- 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, G
_{M}= 30 GPa - Maxwell viscoelastic material properties: η
_{M}= 10^{18}Pa-s - Burgers body material properties: Maxwell element as above, Kelvin-Voigt element has GKV = 10 GPa, M = 10
^{17}Pa-s - Power-law material properties: η
_{ref}= 10^{18}Pa-s and ref = 10^{5}Pa. (Note: This value is chosen because the maximum initial elastic stress is of order 10^{6}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

#### 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

#### TRUTH:

Analytical solutions for each material rheology will be posted at geoweb.mit.edu/fe.

#### ADDITIONAL NOTES:

Benchmark 1 should be completed for each material rheology used in any of the benchmarking exercise.