Defining an FEBioChem model

For the most part an FEBioChem model is a standard FEBio model with a few modifications. These are discussed in the following sections. Note that this user’s manual assumes version 4.0 of the FEBio file format.

Module¶

The type attribute of the Module tag needs the value reaction-diffusion.

<Module type="reaction-diffusion"/>

This will inform FEBio to load the reaction-diffusion solver that is part of the FEBioChem plugin.

This module does not include convection. If you want to include the convection term, you need to use the reaction-diffusion-convection module.

<Module type="reaction-diffusion-convection"/>

Now, a velocity field variable is added to the model, which can be defined in the Initial section of the input file. See section initial velocity for more information on how to initialize the velocity field.

Globals¶

The chemical species that are used in the model are defined in the Globals section of the FEBio input file. The species are defined identically to the way they are defined for a multiphasic problem and we refer to the FEBio user’s manual for more details. The following caveat applies:

A solute defines a chemical species that is not bound to the solid phase of a mixture. If a model doesn’t represent a mixture, each solute defines a chemical species. No child properties need to be defined for a solute.
A solid_bound defines a chemical species that is bound to the solid-phase of a mixture. Again, no child properties need to be defined for a solid bound species.

Solver¶

Make sure to set the solver type to the same name as the module. For instance, for a reaction-diffusion model, set

<solver type="reaction-diffusion">
...
</solver>

Material¶

The material type needed by this plugin is reaction-diffusion. It needs the following material properties. Note that not all are required.

Property	Description
`solid_volume_fraction`	The volume fraction of the solid phase
`species`	Specifies the properties of a chemical species
`solid_bound_species`	Specifies a species that remains bound to the solid phase of the mixture.
`reaction`	Specifies the chemical reaction.

The solid_volume_fraction is only required when modeling a mixture. It has an initial value of zero.

species property¶

Each chemical species that is used by the material must be defined in the material’s definition. (Note that this can be less than the total number of species in the model, as defined by the Globals section.). A particular species is referenced by name. For each species, the diffusivity parameter must be defined.

<species name="A">
    <diffusivity>0.05</diffusivity>
</species>

solid_bound_species property¶

Each solid-bound chemical species that is used by the material must be included in the material’s definition. (Note that this can be less than the total number of species in the model, as defined by the Globals section). For each solid-bound species, define the following material parameters.

Parameter	Description	Default
`rho0`	Initial apparent density (w.r.t. the mixture volume)	0
`density`	The true density of the solid-bound species	0
`rhomin`	The minimum value of the apparent density allowed	0
`rhomax`	The maximum value of the apparent density allowed	(ignored)
`molar_mass`	The molar mass of the solid-bound species.	0

reaction property¶

The reaction property allows you to define a chemical reaction. FEBioChem supports several different type of reactions. Note that currently FEBioChem only models forward reactions. To model a reversible reaction you must specify two reactions, where the first reaction defines the forward reaction and the second defines the reverse reaction. See the list of reactions for more details on defining specific reactions.

Initial values¶

For each species (but not solid-bound species), an initial value can be set in the Initial section of the FEBio input file via the init tag.

<ic type="initial concentration" node_set="set1">
    <dof>c1</dof>
    <value>1.0</value>
</init>

The dof parameter references the particular species (or solute). In this case, c1 references the solute with ID equal to 1. The node_set references a node set that needs to be defined in the Mesh section of the input file.

Boundary conditions¶

The syntax for defining fixed or prescribed is identical for any FEBio model. Use c[n] to reference a particular species (or solute, again no solid-bound species). Thus, for example, c1 references solute with ID one, c2 is the solute with ID 2, and so forth. An example of a fixed boundary condition looks like this.

<bc type="zero concentration" node_set="FixedSet1">
    <dof>c1</dof>
</bc>

An example of a prescribed boundary condition looks like this.

<bc type="prescribed concentration" node_set="PrescribedSet1">
    <dof>c1</dof>
    <value lc="1">1.0</value>
</prescribe>

The node_set attribute references nodesets that need to be defined in the Mesh section of the input file.

Prescribing a concentration flux¶

A concentration flux can be prescribed via a surface load of type concentration flux and is defined as follows.

<surface_load type="concentration flux" surface="SurfaceLoad1">
    <solute_id>1</solute_id>
    <flux lc="1">-1.0</flux>
</surface_load>

The surface attribute references a surface that is defined in the Mesh section. The solute_id references the ID of the corresponding solute as defined in the Globals section of the input file.

Plot Variables¶

The FEBioChem plugin defines several new plot variables. They are list in the table below.

Plot variable	Description
`concentration` / `actual concentration`	Get the true concentration of a species
`effective concentration`	Get the effective concentration of a species
`sbs concentration`	The true concentration of a solid-bound species
`sbs apparent density`	The apparent density of a solid-bound species
`solid volume fraction`	The solid volume fraction of the mixture

Note that the variables that references a species or a solid-bound species need to specify the name of the corresponding species as part of the plot variable definition. For instance,

<var type="concentration['c1']"/>

As with any other plot variable definition in FEBio, you can define an alias.

<var type="concentration['c1']=c1/>

The alias is the name of the data field that will be stored in the plot file, and thus will be show in FEBioStudio.

Initial velocity¶

For reaction-diffusion-convection problems, the fluid velocity needs to be initialized. This is done in the Initial section of the FEBio input file.

The following example sets the x-component of the velocity vector to 1.0.

<ic type="initial velocity" node_set="SomeNodeSet">
    <dof>vx</dof>
    <value>1.0</value>
</init>

You can also define a heterogeneous field. For instance,

<ic type="initial velocity" node_set="SomeNodeSet">
    <dof>vx</dof>
    <value type="map">init_vel<value/>
</init>

Here, init_vel is a node data field that is defined in the MeshData section.

You can also use a mathematical expression to set the initial velocity field.

<ic type="initial velocity" node_set="SomeNodeSet">
    <dof>vx</dof>
    <value type="math">4*(0.5 - Y)*(Y + 0.5)<value/>
</init>