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Plasticity

Plasticity is a non-linear rheology that is activated once stresses exceed a certain yield criteria.

Implemented laws

The following plastic law are implemented:

GeoParams.MaterialParameters.ConstitutiveRelationships.DruckerPrager Type
julia
DruckerPrager=30, Ψ=0, C=10e6Pa)

Sets parameters for Drucker-Prager plasticity, where the yield stress σy is computed by

σy=(PPf)tan(ϕ)+C

with ϕ being the friction angle (in degrees), C cohesion, P dynamic pressure and Pf the fluid pressure (both positive under compression).

Yielding occurs when the second invariant of the deviatoric stress tensor, τII=(0.5τijτij)0.5 touches the yield stress. This can be computed with the yield function F and the plastic flow potential Q, which are respectively given by

F=τIIcos(ϕ)Csin(ϕ)(PPf)Q=τIIsin(Ψ)(PPf)

Here, Ψ is the dilation angle, which must be zero for incompressible setups.

Plasticity is activated when F(τIItrial) (the yield function computed with a trial stress) is >0. In that case, plastic strainrate ε˙ijpl is computed by:

ε˙ijpl=λ˙Qσij

where λ˙ is a (scalar) that is nonzero and chosen such that the resulting stress gives F(τIIfinal)=0, and σij=P+τij denotes the total stress tensor.

source
GeoParams.MaterialParameters.ConstitutiveRelationships.DruckerPrager_regularised Type
julia
DruckerPrager_regularised=30, Ψ=0, C=10e6Pa, η_vp=1e20Pa*s)

Sets parameters for reularised Drucker-Prager plasticity, where the yield stress σy is computed by

σy=(PPf)tan(ϕ)+C+2ηvpε̇IIpl

with ϕ being the friction angle (in degrees), C cohesion, P dynamic pressure, Pf the fluid pressure (both positive under compression), ηvp the regularization viscosity and ε̇IIpl the invariant of the plastic strainrate

Yielding occurs when the second invariant of the deviatoric stress tensor, τII=(0.5τijτij)0.5 touches the yield stress. This can be computed with the yield function F and the plastic flow potential Q, which are respectively given by

F=τIIcos(ϕ)Csin(ϕ)(PPf)2ηvpε˙ε̇IIplQ=τIIsin(Ψ)(PPf)

Here, Ψ is the dilation angle, which must be zero for incompressible setups.

Plasticity is activated when F(τIItrial) (the yield function computed with a trial stress) is >0. In that case, plastic strainrate ε˙ijpl is computed by:

ε˙ijpl=λ˙Qσij

where λ˙ is a (scalar) that is nonzero and chosen such that the resulting stress gives F(τIIfinal)=0, and σij=P+τij denotes the total stress tensor.

source

Computational routines

Usually, plasticity should be defined as part of a CompositeRheology structure and calculations can be done as with all other rheology computations by using compute_τII.