16. MATERIAL and PHASE Namelists

16.1. Overview

A database of materials, their properties and attributes are defined using the MATERIAL, PHASE, and PHASE_CHANGE namelists. Not all materials are necessarily included in the simulation, but only those specified by the PHYSICS namelist variable materials. This allows one to reuse material input blocks without needing to prune out unused materials which would otherwise negatively impact performance. In Truchas usage, one or more phases comprise a material. A single-phase material is defined by a MATERIAL namelist, and the namelist specifies all properties and attributes of the material. A multi-phase material is defined by a MATERIAL namelist and an optional PHASE namelist for each of the material phases. Properties and attributes that apply to all phases can be defined in the MATERIAL namelist. Properties and attributes specific to a given phase are defined in the PHASE namelist for the phase, and these superced eany that might be defined in the MATERIAL namelist for the phase. Additional information that defines the transformation between phases is specified using the PHASE_CHANGE namelist.

16.2. The MATERIAL Namelist

The MATERIAL namelist defines a material, either single-phase or multi-phase, that is available to be used in a simulation. In addition to the property and attribute variables described below, the namelist has the following variables.

name A unique name for the material used to reference it.

phases A multi-phase material is defined by assigning a value to phases. This is a list of two or more unique phase names that comprise the material. The phases must be listed in order from low to high temperature phases. The phase names will be referenced by PHASE_CHANGE namelists and by optional PHASE namelists. Consecutive pairs of phases must be accompanied by a corresponding PHASE_CHANGE namelist.

16.3. The PHASE Namelist

The PHASE namelist defines properties and attributes specific to one phase of a multi-phase material. It is optional. Any properties or attributes defined here supersede those defined in the parent MATERIAL namelist. In addition to the property and attribute variables described below, the PHASE namelist has the following variable.

name The name of the phase. This is one of the names assigned to the phases variable of the MATERIAL namelist for the parent material.

16.4. Property and Attribute Variables

The following variables specify the values of material properties and attributes. Unless otherwise noted, they may appear in both the MATERIAL and PHASE namelists. Many properties can be either constant-valued or a function. Variables ending with the suffix _func specify the name of a FUNCTION namelist that defines a function that computes the value of the property.

Thermodynamic Properties

The following property variables are used by the heat transport model:

  • density

  • specific_heat, specific_heat_func, ref_temp, and ref_enthalpy

  • specific_enthalpy_func

  • conductivity, conductivity_func

The material mass density (mass per volume) is specified by density. It is limited to constant values and all phases in a multi-phase material are currently constrained to have the same density (but see density_delta_func for flow and tm_linear_cte for solid mechanics.) Consequently this variable may only appear in the MATERIAL namelist.

There are two options for defining the temperature-dependent specific enthalpy function \(h(T)\) of a material or phase. The first specifies the specific heat \(C_p(T)\) (energy per unit mass per degree temperature) using specific_heat for a constant or specific_heat_func for a function of temperature. In the latter case it must either be a tabular function or a polynomial without a \(T^{−1}\) term. An analytic antiderivative of the specific heat will be generated by Truchas and used for \(h(T)\). For a single-phase material or the lowest-temperature phase of a multi-phase material, there is an arbitrary constant of integration. By default it is chosen such that \(h(0) = 0\). It can be chosen instead such that \(h(T_{ref}) =h_{ref}\) by specifying values for the optional variables ref_temp and ref_enthalpy, which default to 0. These latter two variables may only appear in the MATERIAL namelist.

The second option is to specify the specific enthalpy function \(h(T)\) (energy per unit mass) directly using specific_enthalpy_func. The function must be strictly increasing, and when used for a phase of a multi-phase material, it must incorporate the latent heat associated with the transformation from the adjacent lower-temperature phase (when there is one).

The thermal conductivity (power per unit length per degree temperature) of a material or phase is specified by conductivity for a constant or conductivity_func for a function. The function is assumed to be a function of temperature \(T\), or \((T,\phi_1,...,\phi_n)\) when coupled with solutal species transport.

Fluid Flow Properties

The following attribute and property variables are used by the fluid flow model:

  • is_fluid

  • density

  • density_delta_func

  • viscosity, viscosity_func

The boolean attribute is_fluid is used to indicate whether or not the material or phase is a fluid. Its default value is \(F\) (or \(.false.\)) Materials and phases marked as fluid are included in the fluid flow model. The constant reference density \(\rho_o\) of a fluid material or phase is specified by density. This is the same density value used for heat transport. A temperature-dependent fluid density \(\rho(T)\) can be defined by giving its deviation from the reference density, \(\delta\rho(T) = \rho(T)−\rho_0\) using the variable density_delta_func. This is used only to compute the buoyancy body force of the Boussinesq approximation in the flow model. If not specified, no deviation from the reference density is assumed.

The dynamic viscosity (mass per length per time) of a material or phase is specified by viscosity for a constant or viscosity_func for a function of temperature. This is required for viscous flow problems (FLOW namelist variable inviscid = F).

Electromagentic Properties

The following property variables are used by the induction heating model:

  • electrical_conductivity, electrical_conductivity_func

  • electric_susceptibility, electric_susceptibility_func

  • magnetic_susceptibility, magnetic_susceptibility_func

The electrical conductivity of a material or phase is specified using either electrical_conductivity for aconstant, or electrical_conductivity_func for a function of temperature. The default value is \(0\). The electromagnetics solver assumes SI units by default and the units of electrical conductivity are \(Siemens\:per\:meter\). To use different units, the values for the PHYSICAL_CONSTANTS namelist variables vacuum_permeability and vacuum_permittivity must be redefined appropriately.

The electric susceptibility \(\chi_e\) of a material or phase is specified using either electric_susceptibility fora constant, or electric_susceptibility_func for a function of temperature. The relative permittivity is \(1 +\chi_e\). This property has a default value of zero, which is appropriate in most cases.

Thermomechanical Properties

The following properties are used by the solid mechanics model, and are only relevant to non-fluid materials and phases. Additional viscoplasticity parameters may be defined using the VISCOPLASTIC_MODEL namelist.

  • tm_ref_density

  • tm_ref_temp

  • tm_linear_cte, tm_linear_cte_func

  • tm_lame1, tm_lame1_func

  • tm_lame2, tm_lame2_func

The temperature at which a material or phase is stress-free is specified by tm_ref_temp and its density (mass per volume) at that temperature specified by tm_ref_density. Its linear coefficient of thermal expansion (inverse time) is specified by tm_linear_cte for a constant or tm_linear_cte_func for a function of temperature. The first and second Lamé constants \(\lambda\) and \(G\) (force per area) for a material or phase is specified by tm_lame1 and tm_lame2 for constants or tm_lame1_func and tm_lame2_func for functions of temperature.

Species Transport Properties

The following property variables are relevant to the solutal species transport model. The model allows for an arbitrary number of species with concentrations \(\{ \phi_i \}^n_{i=1}\), and the variables are arrays of length \(n\) with each element being the property for the corresponding species.

  • diffusivity, diffusivity_func

  • soret, soret_func

The diffusivity (area per time) of a species component in a material or phase is specified by the corresponding element of diffusivity for a constant or diffusivity_func for a function. A function is expected to be a function of all the species concentrations \((\phi_1,...,\phi_n)\), or when coupled with heat transfer, a function of temperature and concentrations \((T,\phi_1,...,\phi_n)\).

When coupled with heat transfer, the Soret coefficient (inverse temperature) of the thermodiffusion term for a species component in a material or phase is specified by the corresponding element of soret for a constant or soret_func for a function. A function is expected to be a function of temperature and concentrations \((T,\phi_1,...,\phi_n)\). This is optional. If not specified, thermodiffusion of the species component is not included in the model, but if defined for one phase of a multi-phase material, it must be defined for all its phases.