Shear heating

Methods

Heat caused by non-recoverable deformation can be specified in

GeoParams.MaterialParameters.Shearheating.ConstantShearheating Type

ConstantShearheating(Χ=0.0NoUnits)

Set the shear heating efficiency [0-1] parameter

$${\rm X}=cst$$

where $\text{Chi}$ is the shear heating efficiency [NoUnits]

Shear heating is computed as

$$H_s=\text{Chi}\cdot {\tau }_{ij}({\dot{\epsilon }}_{ij}-{\dot{\epsilon }}_{ij}^{el})$$source

Computational routines

To compute, use this:

GeoParams.MaterialParameters.Shearheating.compute_shearheating Function

H_s = compute_shearheating(s:<AbstractShearheating, τ, ε, ε_el)

Computes the shear heating source term

$$H_s=\text{Chi}\cdot {\tau }_{ij}({\dot{\epsilon }}_{ij}-{\dot{\epsilon }}_{ij}^{el})$$

Parameters

• $\text{Chi}$ : The efficiency of shear heating (between 0-1)

• ${\tau }_{ij}$ : The full deviatoric stress tensor [4 components in 2D; 9 in 3D]

• ${\dot{\epsilon }}_{ij}$ : The full deviatoric strainrate tensor

• ${\dot{\epsilon }}_{ij}^{el}$ : The full elastic deviatoric strainrate tensor

source

H_s = ComputeShearheating(s:<AbstractShearheating, τ, ε)

Computes the shear heating source term when there is no elasticity

$$H_s=\text{Chi}\cdot {\tau }_{ij}{\dot{\epsilon }}_{ij}$$

Parameters

• $\text{Chi}$ : The efficiency of shear heating (between 0-1)

• ${\tau }_{ij}$ : The full deviatoric stress tensor [4 components in 2D; 9 in 3D]

• ${\dot{\epsilon }}_{ij}$ : The full deviatoric strainrate tensor

source

GeoParams.MaterialParameters.Shearheating.compute_shearheating! Function

compute_shearheating!(H_s, s:<AbstractShearheating,  τ, ε, ε_el)

Computes the shear heating source term in-place

$$H_s=\text{Chi}\cdot {\tau }_{ij}({\dot{\epsilon }}_{ij}-{\dot{\epsilon }}_{ij}^{el})$$

Parameters

• $\text{Chi}$ : The efficiency of shear heating (between 0-1)

• ${\tau }_{ij}$ : The full deviatoric stress tensor [4 components in 2D; 9 in 3D]

• ${\dot{\epsilon }}_{ij}$ : The full deviatoric strainrate tensor

• ${\dot{\epsilon }}_{ij}^{el}$ : The full elastic deviatoric strainrate tensor

NOTE: The shear heating terms require the full deviatoric stress & strain rate tensors, i.e.:

$$2D:{\tau }_{ij}=\left(\begin{array}{cc}{\tau }_{xx}& {\tau }_{xz}\\ {\tau }_{zx}& {\tau }_{zz}\end{array}\right)$$

Since ${\tau }_{zx}={\tau }_{xz}$, most geodynamic codes only take one of the terms into account; shear heating requires all components to be used!

source

compute_shearheating!(H_s, s:<AbstractShearheating, τ, ε)

Computes the shear heating source term H_s in-place when there is no elasticity

$$H_s=\text{Chi}\cdot {\tau }_{ij}{\dot{\epsilon }}_{ij}$$

Parameters

• $\text{Chi}$ : The efficiency of shear heating (between 0-1)

• ${\tau }_{ij}$ : The full deviatoric stress tensor [4 components in 2D; 9 in 3D]

• ${\dot{\epsilon }}_{ij}$ : The full deviatoric strainrate tensor

source