Rheologic Models

Material strength models, relating deviatoric stress to strain, have been incorporated into Fluidity. The simplest model is that of an incompressible elastic solid. In the following example an initially flat tetrahedral mesh is instantaneously subjected to gravity, resulting in elastic oscillations.

Elastic sheet as it is subjected to gravity (1x1x0.02 m)	Elastic sheet after 0.4 seconds
Elastic sheet after 0.6 seconds	Elastic sheet after 0.8 seconds

Geologic materials, which accumulate permanent deformation through plastic straining, are modelled using perfect plasticity. Initial tests have used the Drucker-Prager yield criterion, which allows higher deviatoric stresses to be maintained in the material with increasing pressure. If the yield surface is breached a cutting-plane algorithm is used to return the yielding point to the elastic domain. This is done under the assumption of non-associated plastic flow with normality enforced relative to a Von Mises surface so that plastic flow is incompressible (occurs on an isosurface of pressure). Initial validation tests on the slope collapse problem and on weak craters demonstrate its ability to reproduce physical behaviour.

Slope collapse problems are a good example of a geologic problem requiring modelling as an elastic-plastic solid. Several tests were run over a range of plasticity parameters (cohesion and angle of friction) and collapse was found to occur at a point in close agreement with published literature.

Strong elastic-plastic slope initially subjected to gravity with a normalised (to the density, gravity and vertical slope height) cohesion of 0.05 and an angle of internal friction of 20 degrees.	Strong elastic-plastic slope after 2.2 normalised (to the free fall time over the vertical slope height) units of time.	Strong elastic-plastic slope after 5.4 normalised units of time when permanent deformation accumulation has ceased.
Weak elastic-plastic slope initially subjected to gravity with a normalised (to the density, gravity and vertical slope height) cohesion of 0.036 and an angle of internal friction of 14.5 degrees.	Weak elastic-plastic slope after 2.2 normalised (to the free fall time over the vertical slope height) units of time.	Weak elastic-plastic slope after 5.4 normalised units of time when runaway slope collapse is occuring.