 |
ASPECT
|
|
ASPECT
|
Private Attributes | |
| MaterialUtilities::CompositionalAveragingOperation | viscosity_averaging |
| EquationOfState::MulticomponentIncompressible< dim > | equation_of_state |
| std::vector< double > | viscosities |
| std::vector< double > | thermal_conductivities |
| Rheology::Elasticity< dim > | elastic_rheology |
Functions used in dealing with run-time parameters | |
| void | parse_parameters (ParameterHandler &prm) override |
| static void | declare_parameters (ParameterHandler &prm) |
Additional Inherited Members | |
 Public Types inherited from aspect::MaterialModel::Interface< dim > | |
| using | MaterialModelInputs = MaterialModel::MaterialModelInputs< dim > |
| using | MaterialModelOutputs = MaterialModel::MaterialModelOutputs< dim > |
| Static Public Member Functions inherited from aspect::MaterialModel::Interface< dim > | |
| static void | declare_parameters (ParameterHandler &prm) |
| Static Public Member Functions inherited from aspect::SimulatorAccess< dim > | |
| static void | get_composition_values_at_q_point (const std::vector< std::vector< double >> &composition_values, const unsigned int q, std::vector< double > &composition_values_at_q_point) |
| Protected Attributes inherited from aspect::MaterialModel::Interface< dim > | |
| NonlinearDependence::ModelDependence | model_dependence |
An implementation of a simple linear viscoelastic rheology that only includes the deviatoric components of elasticity. Specifically, the viscoelastic rheology only takes into account the elastic shear strength (e.g., shear modulus), while the tensile and volumetric strength (e.g., Young's and bulk modulus) are not considered. The model is incompressible and allows specifying an arbitrary number of compositional fields, where each field represents a different rock type or component of the viscoelastic stress tensor. The stress tensor in 2D and 3D, respectively, contains 3 or 6 components. The compositional fields representing these components must be named and listed in a very specific format, which is designed to minimize mislabeling stress tensor components as distinct 'compositional rock types' (or vice versa). For 2D models, the first three compositional fields must be labeled ve_stress_xx, ve_stress_yy and ve_stress_xy. In 3D, the first six compositional fields must be labeled ve_stress_xx, ve_stress_yy, ve_stress_zz, ve_stress_xy, ve_stress_xz, ve_stress_yz.
Expanding the model to include non-linear viscous flow (e.g., diffusion/dislocation creep) and plasticity would produce a constitutive relationship commonly referred to as partial elastoviscoplastic (e.g., pEVP) in the geodynamics community. While extensively discussed and applied within the geodynamics literature, notable references include: Moresi et al. (2003), J. Comp. Phys., v. 184, p. 476-497. Gerya and Yuen (2007), Phys. Earth. Planet. Inter., v. 163, p. 83-105. Gerya (2010), Introduction to Numerical Geodynamic Modeling. Kaus (2010), Tectonophysics, v. 484, p. 36-47. Choi et al. (2013), J. Geophys. Res., v. 118, p. 2429-2444. Keller et al. (2013), Geophys. J. Int., v. 195, p. 1406-1442.
The overview below directly follows Moresi et al. (2003) eqns. 23-32. However, an important distinction between this material model and the studies above is the use of compositional fields, rather than particles, to track individual components of the viscoelastic stress tensor. The material model will be updated when an option to track and calculate viscoelastic stresses with particles is implemented.
Moresi et al. (2003) begins (eqn. 23) by writing the deviatoric rate of deformation ( \(\hat{D}\)) as the sum of elastic ( \(\hat{D_{e}}\)) and viscous ( \(\hat{D_{v}}\)) components: \(\hat{D} = \hat{D_{e}} + \hat{D_{v}}\). These terms further decompose into \(\hat{D_{v}} = \frac{\tau}{2\eta}\) and \(\hat{D_{e}} = \frac{\overset{\nabla}{\tau}}{2\mu}\), where \(\tau\) is the viscous deviatoric stress, \(\eta\) is the shear viscosity, \(\mu\) is the shear modulus and \(\overset{\nabla}{\tau}\) is the Jaumann corotational stress rate. This later term (eqn. 24) contains the time derivative of the deviatoric stress ( \(\dot{\tau}\)) and terms that account for material spin (e.g., rotation) due to advection: \(\overset{\nabla}{\tau} = \dot{\tau} + {\tau}W -W\tau\). Above, \(W\) is the material spin tensor (eqn. 25): \(W_{ij} = \frac{1}{2} \left (\frac{\partial V_{i}}{\partial x_{j}} - \frac{\partial V_{j}}{\partial x_{i}} \right )\).
The Jaumann stress-rate can also be approximated using terms from the time at the previous time step ( \(t\)) and current time step ( \(t + \Delta t^{e}\)): \(\smash[t]{\overset{\nabla}{\tau}}^{t + \Delta t^{e}} \approx \frac{\tau^{t + \Delta t^{e} - \tau^{t}}}{\Delta t^{e}} - W^{t}\tau^{t} + \tau^{t}W^{t}\). In this material model, the size of the time step above ( \(\Delta t^{e}\)) can be specified as the numerical time step size or an independent fixed time step. If the latter case is a selected, the user has an option to apply a stress averaging scheme to account for the differences between the numerical and fixed elastic time step (eqn. 32). If one selects to use a fixed elastic time step throughout the model run, this can still be achieved by using CFL and maximum time step values that restrict the numerical time step to a specific time.
The formulation above allows rewriting the total rate of deformation (eqn. 29) as \(\tau^{t + \Delta t^{e}} = \eta_{eff} \left ( 2\hat{D}^{t + \triangle t^{e}} + \frac{\tau^{t}}{\mu \Delta t^{e}} + \frac{W^{t}\tau^{t} - \tau^{t}W^{t}}{\mu} \right )\).
The effective viscosity (eqn. 28) is a function of the viscosity ( \(\eta\)), elastic time step size ( \(\Delta t^{e}\)) and shear relaxation time ( \( \alpha = \frac{\eta}{\mu} \)): \(\eta_{eff} = \eta \frac{\Delta t^{e}}{\Delta t^{e} + \alpha}\) The magnitude of the shear modulus thus controls how much the effective viscosity is reduced relative to the initial viscosity.
Elastic effects are introduced into the governing stokes equations through an elastic force term (eqn. 30) using stresses from the previous time step: \(F^{e,t} = -\frac{\eta_{eff}}{\mu \Delta t^{e}} \tau^{t}\). This force term is added onto the right-hand side force vector in the system of equations.
The value of each compositional field representing distinct rock types at a point is interpreted to be a volume fraction of that rock type. If the sum of the compositional field volume fractions is less than one, then the remainder of the volume is assumed to be 'background material'.
Several model parameters (densities, elastic shear moduli, thermal expansivities, thermal conductivies, specific heats) can be defined per-compositional field. For each material parameter the user supplies a comma delimited list of length N+1, where N is the number of compositional fields. The additional field corresponds to the value for background material. They should be ordered ``background, composition1, composition2...''. However, the first 3 (2D) or 6 (3D) composition fields correspond to components of the elastic stress tensor and their material values will not contribute to the volume fractions. If a single value is given, then all the compositional fields are given that value. Other lengths of lists are not allowed. For a given compositional field the material parameters are treated as constant, except density, which varies linearly with temperature according to the thermal expansivity.
When more than one compositional field is present at a point, they are averaged arithmetically. An exception is viscosity, which may be averaged arithmetically, harmonically, geometrically, or by selecting the viscosity of the composition with the greatest volume fraction.
Definition at line 148 of file viscoelastic.h.
|
overridevirtual |
Function to compute the material properties in out given the inputs in in.
Implements aspect::MaterialModel::Interface< dim >.
|
overridevirtual |
This model is not compressible, so this returns false.
Implements aspect::MaterialModel::Interface< dim >.
|
static |
Declare the parameters this class takes through input files.
|
overridevirtual |
Read the parameters this class declares from the parameter file.
Reimplemented from aspect::MaterialModel::Interface< dim >.
|
overridevirtual |
If this material model can produce additional named outputs that are derived from NamedAdditionalOutputs, create them in here. By default, this does nothing.
Reimplemented from aspect::MaterialModel::Interface< dim >.
|
private |
Enumeration for selecting which viscosity averaging scheme to use.
Definition at line 200 of file viscoelastic.h.
|
private |
Definition at line 202 of file viscoelastic.h.
|
private |
Vector for field viscosities, read from parameter file.
Definition at line 207 of file viscoelastic.h.
|
private |
Vector for field thermal conductivities, read from parameter file.
Definition at line 212 of file viscoelastic.h.
|
private |
Definition at line 214 of file viscoelastic.h.