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:
Uniaxial Strain
--experiment uniaxial
The uniaxial strain example constrains the 
, 
and
surfaces to lie in those planes, and applies a deformation on the
surface to 
.
Biaxial Strain
--experiment biaxial
The biaxial strain example constrains the , and
surfaces to lie in those planes, and applies a deformation on the
and 
surfaces to and 
respectively.
Pure Shear
--experiment pshear
The pure shear example constrains the , , and
surfaces to lie in those planes, and applies a deformation on the
surface to .
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
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 ANALYTIC
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.
Checks:
- Compare against analytic solution defined by analytic_solution(): max_error(stressTensor.igb.gz)