# Benchmark 3

Viscoelastic relaxation of stresses resulting from an imposed simple shear strain. No body forces are imposed.

Benchmark #3a: Solve using a Maxwell viscoelastic material rheology

Benchmark #3b: Solve using a Burger's body rheological description

Benchmark #3c: Solve using a power-law material description

### Goals

• Test relevant constitutive relations
• Verify timing of output in specific codes (i.e., is output written at the beginning or end of the step).

### Detailed Description

• Model size: 24 km by 24 km by 24 km (0 km ≤ x; y ≤ 24 km; -24 km ≤ z ≤ 0 km)
• Elastic material properties: Poisson solid, G = 30 GPa
• Maxwell viscoelastic material properties: η = 1018 Pa-s
• Burger's body material properties: Maxwell element as above, Kelvin-Voigt element has GKV = 10 GPa, η= 1017 Pa-s
• Power-law material properties: ηref = 1018 Pa-s and σref = 10Pa. (Note: This value is chosen because the maximum initial elastic stress is of order 10Pa; although all of that is deviatoric, the deviatoric stress decreases with time.)
• Density and Gravity: None
• Boundary conditions: Bottom pinned
Sides pinned in y and z; free in x
Top pinned in y and z; 1 m of displacement imposed in x
• 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

### Truth

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