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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. 

Additional Notes

None.
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