Mechanics Analytic Validation

Module: devtests.mechanics.analytic.run

Section author: Christoph Augustin <christoph.augustin@medunigraz.at>

This example runs simple deformation tests on small meshes for which an equivalent analytic solution is known.

Experiments

The experiments all apply simple deformations to a unit cube:

../../_images/unit_cube.png

Uniaxial Strain

--experiment uniaxial

The uniaxial strain example constrains the x=0, y=0 and z=0 surfaces to lie in those planes, and applies a deformation on the x=1 surface to x=\lambda.

../../_images/uniaxial.png

Biaxial Strain

--experiment biaxial

The biaxial strain example constrains the x=0, y=0 and z=0 surfaces to lie in those planes, and applies a deformation on the x=1 and y=1 surfaces to x=\lambda and y=\lambda respectively.

../../_images/biaxial.png

Pure Shear

--experiment pshear

The pure shear example constrains the x=0, x=1, y=0 and z=0 surfaces to lie in those planes, and applies a deformation on the x=1 surface to x=\lambda.

../../_images/pure_shear.png

Material Models

All of the above experiments are carried out with the following material models:

  • neo-Hookean --material neohookean
  • St. Venant–Kirchhoff --material stvk
  • Mooney-Rivlin --material mooneyrivlin
  • Demiray --material demiray
  • compressible neo-Hookean --material neohookecomp
  • Holzapfel et al. (2000) material --material holzapfel2000
  • reduced Holzapfel et al. (2000) material --material rH2000
  • Gasser et al. (2006) material with dispersion --material gasser2006d
  • Guccione et al (1995) myocardial material --material guccione1995
  • Usyk et al (2000), Costa et al. (2001) material --material usyk2000
  • Holzapfel-Ogden (2009) material --material holzapfelogden2009
  • reduced Holzapfel-Ogden material --material rHO2009
  • reduced Holzapfel-Ogden material with dispersion --material rHO2009d

Todo

Some othotropic materials (gasser, usyk) struggle for uniaxial tests

Tests

uniaxial_neohookean_P1P0

Compare the calculated stresses for a “uniaxial” deformation using the “neohookean” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_neohookean_P1P1Bubble

Compare the calculated stresses for a “uniaxial” deformation using the “neohookean” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_mooneyrivlin_P1P0

Compare the calculated stresses for a “uniaxial” deformation using the “mooneyrivlin” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_mooneyrivlin_P1P1Bubble

Compare the calculated stresses for a “uniaxial” deformation using the “mooneyrivlin” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_demiray_P1P0

Compare the calculated stresses for a “uniaxial” deformation using the “demiray” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_demiray_P1P1Bubble

Compare the calculated stresses for a “uniaxial” deformation using the “demiray” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_rH2000_P1P0

Compare the calculated stresses for a “uniaxial” deformation using the “rH2000” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_rH2000_P1P1Bubble

Compare the calculated stresses for a “uniaxial” deformation using the “rH2000” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_guccione1995_P1P0

Compare the calculated stresses for a “uniaxial” deformation using the “guccione1995” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_guccione1995_P1P1Bubble

Compare the calculated stresses for a “uniaxial” deformation using the “guccione1995” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_rHO2009_P1P0

Compare the calculated stresses for a “uniaxial” deformation using the “rHO2009” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_rHO2009_P1P1Bubble

Compare the calculated stresses for a “uniaxial” deformation using the “rHO2009” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_rHO2009d_P1P0

Compare the calculated stresses for a “uniaxial” deformation using the “rHO2009d” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_rHO2009d_P1P1Bubble

Compare the calculated stresses for a “uniaxial” deformation using the “rHO2009d” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_holzapfel2000_P1P0

Compare the calculated stresses for a “uniaxial” deformation using the “holzapfel2000” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_holzapfel2000_P1P1Bubble

Compare the calculated stresses for a “uniaxial” deformation using the “holzapfel2000” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_holzapfelogden2009_P1P0

Compare the calculated stresses for a “uniaxial” deformation using the “holzapfelogden2009” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_holzapfelogden2009_P1P1Bubble

Compare the calculated stresses for a “uniaxial” deformation using the “holzapfelogden2009” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_fullholzapfelogden_P1P0

Compare the calculated stresses for a “uniaxial” deformation using the “fullholzapfelogden” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

uniaxial_fullholzapfelogden_P1P1Bubble

Compare the calculated stresses for a “uniaxial” deformation using the “fullholzapfelogden” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_neohookean_P1P0

Compare the calculated stresses for a “biaxial” deformation using the “neohookean” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_neohookean_P1P1Bubble

Compare the calculated stresses for a “biaxial” deformation using the “neohookean” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_mooneyrivlin_P1P0

Compare the calculated stresses for a “biaxial” deformation using the “mooneyrivlin” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_mooneyrivlin_P1P1Bubble

Compare the calculated stresses for a “biaxial” deformation using the “mooneyrivlin” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_demiray_P1P0

Compare the calculated stresses for a “biaxial” deformation using the “demiray” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_demiray_P1P1Bubble

Compare the calculated stresses for a “biaxial” deformation using the “demiray” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_rH2000_P1P0

Compare the calculated stresses for a “biaxial” deformation using the “rH2000” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_rH2000_P1P1Bubble

Compare the calculated stresses for a “biaxial” deformation using the “rH2000” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_gasser2006d_P1P0

Compare the calculated stresses for a “biaxial” deformation using the “gasser2006d” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_gasser2006d_P1P1Bubble

Compare the calculated stresses for a “biaxial” deformation using the “gasser2006d” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_guccione1995_P1P0

Compare the calculated stresses for a “biaxial” deformation using the “guccione1995” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_guccione1995_P1P1Bubble

Compare the calculated stresses for a “biaxial” deformation using the “guccione1995” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_usyk2000_P1P0

Compare the calculated stresses for a “biaxial” deformation using the “usyk2000” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_usyk2000_P1P1Bubble

Compare the calculated stresses for a “biaxial” deformation using the “usyk2000” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_rHO2009_P1P0

Compare the calculated stresses for a “biaxial” deformation using the “rHO2009” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_rHO2009_P1P1Bubble

Compare the calculated stresses for a “biaxial” deformation using the “rHO2009” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_rHO2009d_P1P0

Compare the calculated stresses for a “biaxial” deformation using the “rHO2009d” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_rHO2009d_P1P1Bubble

Compare the calculated stresses for a “biaxial” deformation using the “rHO2009d” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_holzapfel2000_P1P0

Compare the calculated stresses for a “biaxial” deformation using the “holzapfel2000” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_holzapfel2000_P1P1Bubble

Compare the calculated stresses for a “biaxial” deformation using the “holzapfel2000” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_holzapfelogden2009_P1P0

Compare the calculated stresses for a “biaxial” deformation using the “holzapfelogden2009” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_holzapfelogden2009_P1P1Bubble

Compare the calculated stresses for a “biaxial” deformation using the “holzapfelogden2009” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_fullholzapfelogden_P1P0

Compare the calculated stresses for a “biaxial” deformation using the “fullholzapfelogden” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

biaxial_fullholzapfelogden_P1P1Bubble

Compare the calculated stresses for a “biaxial” deformation using the “fullholzapfelogden” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_neohookean_P1P0

Compare the calculated stresses for a “pshear” deformation using the “neohookean” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_neohookean_P1P1Bubble

Compare the calculated stresses for a “pshear” deformation using the “neohookean” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_mooneyrivlin_P1P0

Compare the calculated stresses for a “pshear” deformation using the “mooneyrivlin” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_mooneyrivlin_P1P1Bubble

Compare the calculated stresses for a “pshear” deformation using the “mooneyrivlin” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_demiray_P1P0

Compare the calculated stresses for a “pshear” deformation using the “demiray” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_demiray_P1P1Bubble

Compare the calculated stresses for a “pshear” deformation using the “demiray” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_rH2000_P1P0

Compare the calculated stresses for a “pshear” deformation using the “rH2000” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_rH2000_P1P1Bubble

Compare the calculated stresses for a “pshear” deformation using the “rH2000” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_guccione1995_P1P0

Compare the calculated stresses for a “pshear” deformation using the “guccione1995” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_guccione1995_P1P1Bubble

Compare the calculated stresses for a “pshear” deformation using the “guccione1995” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_usyk2000_P1P0

Compare the calculated stresses for a “pshear” deformation using the “usyk2000” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_usyk2000_P1P1Bubble

Compare the calculated stresses for a “pshear” deformation using the “usyk2000” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_rHO2009_P1P0

Compare the calculated stresses for a “pshear” deformation using the “rHO2009” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_rHO2009_P1P1Bubble

Compare the calculated stresses for a “pshear” deformation using the “rHO2009” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_rHO2009d_P1P0

Compare the calculated stresses for a “pshear” deformation using the “rHO2009d” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_rHO2009d_P1P1Bubble

Compare the calculated stresses for a “pshear” deformation using the “rHO2009d” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_holzapfel2000_P1P0

Compare the calculated stresses for a “pshear” deformation using the “holzapfel2000” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_holzapfel2000_P1P1Bubble

Compare the calculated stresses for a “pshear” deformation using the “holzapfel2000” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_holzapfelogden2009_P1P0

Compare the calculated stresses for a “pshear” deformation using the “holzapfelogden2009” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_holzapfelogden2009_P1P1Bubble

Compare the calculated stresses for a “pshear” deformation using the “holzapfelogden2009” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_fullholzapfelogden_P1P0

Compare the calculated stresses for a “pshear” deformation using the “fullholzapfelogden” material model against the analytic solution.

Tags: SHORT MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)

pshear_fullholzapfelogden_P1P1Bubble

Compare the calculated stresses for a “pshear” deformation using the “fullholzapfelogden” material model against the analytic solution.

Tags: FAST MECHANICS

Checks:

  • Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)