Inputs

BC

This is the mechanism for impositing boundary conditions on Set::Field objects of scalar type. Typical convention is for [prefix] to be given by the field name. For instance,

bc.temp.type.xhi = dirichlet dirichlet dirichlet
bc.temp.val.xhi  = 0.0 1.0 0.0

corresponds to the boundary condition for temperature. See the specific integrator for details.

BC::Constant

src/BC/Constant.cpp src/BC/Constant.H

This is the most commonly used standard boundary condition implementation. The name “Constant” refers to the invariance of the BC value or character along each face of the simulation domain; however, you may cause a change in the value with time by using a Numeric::Interpolator::Linear string.

The BC on each face is specified with a type string that specifies the nature of the BC, and a val that specifies the value. By default, all types are Dirichlet and all values are 0.0. The complete list of BC types are below:

Dirichlet boundary condition types can be specified with Dirichlet, dirichlet, EXT_DIR. Neumann boundary condition types are specified with Neumann, neumann. Periodic boundary conditions can be specified with Periodic, periodic, INT_DIR. Important: Ensure that your geometry is specified to be periodic using geometry.is_periodic. For instance, if periodic in x, set to 1 0 0

The BC values can be specified either as a number (e.g. 1.0) or using a linear interpolator string (e.g. (0,1:2.3,-0.1)).

The number of values and types must be either 0 (for defaults), 1 (to set the same for all field components) or N (where N=number of field components).

Parameter	Type	Values
[prefix].type.xlo	BC type on the lower x edge (2d) face (3d)
[prefix].type.xhi	BC type on the upper x edge (2d) face (3d)
[prefix].type.ylo	BC type on the lower y edge (2d) face (3d)
[prefix].type.yhi	BC type on the upper y edge (2d) face (3d)
[prefix].type.zlo	BC type on the lower z face (processed but ignored in 2d to prevent unused input errors)
[prefix].type.zhi	BC type on the upper z face (processed but ignored in 2d to prevent unused input errors)
[prefix].val.xlo	BC value on the lower x edge (2d) face (3d)
[prefix].val.xhi	BC value on the upper x edge (2d) face (3d)
[prefix].val.ylo	BC value on the lower y edge (2d) face (3d)
[prefix].val.yhi	BC value on the upper y edge (2d) face (3d)
[prefix].val.zlo	BC value on the lower z face (processed but ignored in 2d to prevent unused input errors)
[prefix].val.zhi	BC value on the upper z face (processed but ignored in 2d to prevent unused input errors)

BC::Expression

src/BC/Expression.cpp src/BC/Expression.H

Parameter	Type	Values
[prefix].type.xlo	BC type on the lower x edge (2d) face (3d)
[prefix].type.xhi	BC type on the upper x edge (2d) face (3d)
[prefix].type.ylo	BC type on the lower y edge (2d) face (3d)
[prefix].type.yhi	BC type on the upper y edge (2d) face (3d)
[prefix].type.zlo	BC type on the lower z face (processed but ignored in 2d to prevent unused input errors)
[prefix].type.zhi	BC type on the upper z face (processed but ignored in 2d to prevent unused input errors)

BC::Operator

src/BC/Operator/Operator.H

The BC::Operator family of BC classes are designed to work with implicit operators. They are not the same thing as other BC types and cannot be used in that same way. (This is not an ideal taxonomy for BC structures - we may transition other BC types to be subspaces of BC::Integrator.)

BC::Operator::Elastic

src/BC/Operator/Elastic/Elastic.H

Class of BC operators that work with Operator::Elastic.

BC::Operator::Elastic::Constant

src/BC/Operator/Elastic/Constant.H

This BC defines boundary conditions that are constant with respect to space. However they may change in time using the Numeric::Interpolator::Linear method.

In 2D, BCs are prescribed for each edge (4) and corner (4) on the boundary, for a total of 8 possible regions. In 3D, BCs are prescribed for each face (6), each edge (12), and each corner (8), for a total of 26 possible regions. Care must be taken to define BCs for edges/corners consistently with the faces/edges, or you will get poor convergence and inaccurate behavior. (See BC::Operator::Elastic::TensionTest for a reduced BC with streamlined load options.)

To define a boundary condition, you must define both a “type” and a “value” in each direction. The type can be “displacement”, “disp”, “neumann”, “traction”, “trac”. The value is the corresponding value. All BCs are, by default, dirichlet (displacement) with a value of zero.

Parameter	Type	Values
[prefix].type.xloylozlo	3D Corner
[prefix].type.xloylozhi	3D Corner
[prefix].type.xloyhizlo	3D Corner
[prefix].type.xloyhizhi	3D Corner
[prefix].type.xhiylozlo	3D Corner
[prefix].type.xhiylozhi	3D Corner
[prefix].type.xhiyhizlo	3D Corner
[prefix].type.xhiyhizhi	3D Corner
[prefix].type.ylozlo	3D Edge
[prefix].type.ylozhi	3D Edge
[prefix].type.yhizlo	3D Edge
[prefix].type.yhizhi	3D Edge
[prefix].type.zloxlo	3D Edge
[prefix].type.zloxhi	3D Edge
[prefix].type.zhixlo	3D Edge
[prefix].type.zhixhi	3D Edge
[prefix].type.xloylo	3D Edge / 2D Corner
[prefix].type.xloyhi	3D Edge / 2D Corner
[prefix].type.xhiylo	3D Edge / 2D Corner
[prefix].type.xhiyhi	3D Edge / 2D Corner
[prefix].type.xlo	3D Face / 2D Edge
[prefix].type.xhi	3D Face / 2D Edge
[prefix].type.ylo	3D Face / 2D Edge
[prefix].type.yhi	3D Face / 2D Edge
[prefix].type.zlo	3D Face
[prefix].type.zhi	3D Face
[prefix].val.xloylozlo	3D Corner
[prefix].val.xloylozhi	3D Corner
[prefix].val.xloyhizlo	3D Corner
[prefix].val.xloyhizhi	3D Corner
[prefix].val.xhiylozlo	3D Corner
[prefix].val.xhiylozhi	3D Corner
[prefix].val.xhiyhizlo	3D Corner
[prefix].val.xhiyhizhi	3D Corner
[prefix].val.ylozlo	3D Edge
[prefix].val.ylozhi	3D Edge
[prefix].val.yhizlo	3D Edge
[prefix].val.yhizhi	3D Edge
[prefix].val.zloxlo	3D Edge
[prefix].val.zloxhi	3D Edge
[prefix].val.zhixlo	3D Edge
[prefix].val.zhixhi	3D Edge
[prefix].val.xloylo	3D Edge / 2D Corner
[prefix].val.xloyhi	3D Edge / 2D Corner
[prefix].val.xhiylo	3D Edge / 2D Corner
[prefix].val.xhiyhi	3D Edge / 2D Corner
[prefix].val.xlo	3D Face / 2D Edge
[prefix].val.xhi	3D Face / 2D Edge
[prefix].val.ylo	3D Face / 2D Edge
[prefix].val.yhi	3D Face / 2D Edge
[prefix].val.zlo	3D Face
[prefix].val.zhi	3D Face

BC::Operator::Elastic::TensionTest

src/BC/Operator/Elastic/TensionTest.H

Parameter	Type	Values
[prefix].type	Tension test type. (Only option right now is `uniaxial_stress_clamp`)
[prefix].disp	Applied displacement (can be interpolator)
[prefix].trac	Applied traction (can be interpolator)

IC

src/IC/IC.H

Initial condition (IC) objects are used to set fields to specified values, through mathematical expressions, images, etc. They are often used as initial conditions, but may be used generally to incorporate static or time-dependent values. All IC methods inherit from the base IC class, and are implemented by overriding the “Add” method. (Initialize uses Add after setting the field to zero.)

IC::BMP

src/IC/BMP.H

Initialize a field using a bitmap image. (2D only)

Note that in GIMP, you must select “do not write color space information” and “24 bit R8 G8 B8” when exporting the BMP file.

Parameter	Type	Values
[prefix].filename	BMP filename.	file path
[prefix].fit	How to position image in space	stretch fitheight fitwidth coord
[prefix].coord.lo	Location of lower-left corner in the domain
[prefix].coord.hi	Location of upper-right corner in the domain
[prefix].channel	Color channel to use	r g b R G B
[prefix].min	Scaling value - minimum	0.0
[prefix].max	Scaling value - maximum	255.0

IC::Cuboid

src/IC/Cuboid.H

Parameter	Type	Values
[prefix].center	Coordinates (X Y Z) of the center of the square/cube.
[prefix].length	Side legnth of cuboid
[prefix].eps	Regularization value

IC::Constant

src/IC/Constant.H

Basic IC that just sets the entire field to a constant value. Works with a single or multiple-component field.

Parameter	Type	Values
[prefix].value	Array of constant values. The number of values should equal either 1 or N where N is the number of fab components	required

IC::Ellipse

src/IC/Ellipse.H

If number_of_inclusions is specified, then multiple ellipses are specified. In this case, each parameter must have number_of_inclusion*M values, where M is the number of values specified for the single ellipse case.

Parameter	Type	Values
[prefix].x0	Coorinates of ellipse center
[prefix].eps	Diffuse boundary thickness	0.0
[prefix].A	DxD square matrix defining an ellipse.
[prefix].a	If `A` is not defined, then assume a sphere with radius `a`
[prefix].number_of_inclusions	Number of ellipses
[prefix].center	center of the ellipse
[prefix].x0	center of the ellipse
[prefix].A	either a vector containing ellipse radii, or a matrix defining the ellipse
[prefix].A	Same
[prefix].radius	Array of radii [depricated]
[prefix].eps	Regularization for smooth boundary
[prefix].invert	Flip the inside and the outside

IC::Expression

src/IC/Expression.H

Initialize a field using a mathematical expression. Expressions are imported as strings and are compiled real-time using the AMReX Parser.

Works for single or multiple-component fields. Use the regionN (N=0,1,2, etc. up to number of components) to pass expression. For example:

ic.region0 = "sin(x*y*z)"
ic.region1 = "3.0*(x > 0.5 and y > 0.5)"

for a two-component field. It is up to you to make sure your expressions are parsed correctly; otherwise you will get undefined behavior.

Constants You can add constants to your expressions using the constant directive. For instance, in the following code

psi.ic.type=expression
psi.ic.expression.constant.eps = 0.05
psi.ic.expression.constant.R   = 0.25
psi.ic.expression.region0 = "0.5 + 0.5*tanh((x^2 + y^2 - R)/eps)"

the constants eps and R are defined by the user and then used in the subsequent expression. The variables can have any name made up of characters that is not reserved. However, if multiple ICs are used, they must be defined each time for each IC.

Parameter	Type	Values
[prefix].coord	coordinate system to use: “cartesian” (for x,y,z,t) and “polar” (for r, theta, z, t)

IC::Laminate

src/IC/Laminate.H

Create a single laminate with specified orientation, thickness, and offset.

Parameter	Type	Values
[prefix].number_of_inclusions	How many laminates (MUST be greater than or equal to 1).	1
[prefix].orientation	Vector normal to the interface of the laminate
[prefix].eps	Diffuse thickness
[prefix].mollifier	Type of mollifer to use (options: dirac, [gaussian])
[prefix].singlefab	Switch to mode where only one component is used.
[prefix].invert	Take the complement of the laminate

IC::PS

src/IC/PS.H

Fill a domain with randomly packed and sized spheres.

Warning

This is not used for anything useful as far as we can see. It will likely be removed shortly.

Parameter	Type	Values
[prefix].nspheres	Total number of spheres
[prefix].matrix	Value for the matrix [0.0]
[prefix].inclusion	Value for the inclusion [1.0]

IC::PSRead

src/IC/PSRead.H

Fill a domain (region where field=0) with packed spheres (regions where field=1). Sphere locations and radii are determined from an xyzr file.

Parameter	Type	Values
[prefix].eps	Diffuseness of the sphere boundary
[prefix].filename	Location of .xyzr file	file path
[prefix].verbose	Verbosity (used in parser only)
[prefix].mult	Coordinate multiplier
[prefix].invert	Coordinate multiplier
[prefix].x0	Coordinate offset

IC::PerturbedInterface

src/IC/PerturbedInterface.H

Initialize a perturbed interface using Fourier Modes

Notes: 1. todo Extend this class to allow for 3D perturbations, currently only 2D are allowed 2. todo Allow for cosine (or complex exponential) expansions rather than just sin. 3. note This is a two grain only initial condition. 4. note This replaces the depricated “perturbed_bar” initial condition from previous versions

The interface is defined as the \(x=0\) plane (2D), or the \(x=0,z=0\) plane (3D). The equation for the interface is given by \(y(x,z) = \sum_{n\in \{n_1,\ldots,n_N\}} A_n \sin(n\pi x/L_x)\) where \(A_n\) are the amplitudes (stored in #wave_amplitudes), \(n_1,\ldots,n_N\subset\mathbb{Z}_+\) are wave numbers (stored in #wave_numbers), and \(L_x\) is the length in the x direction (obtained using the #geom object).

Grain 1 is defined as being above \(y(x,z)\), Grain 2 is defined as being below.

Parameter	Type	Values
[prefix].wave_numbers	Wave numbers
[prefix].wave_amplitudes	Wave amplitudes
[prefix].normal	Which axis is normal to the interface (x,y,z)
[prefix].offset	Interface offset from origin
[prefix].reverse	If true, flip the interface (default:false)
[prefix].mollifier	Mollifier (options: dirac, [gaussian])
[prefix].eps	Magnitude of mollifier

IC::PNG

src/IC/PNG.H

Initialize a field using a PNG image. (2D only)

Parameter	Type	Values
[prefix].filename	BMP filename.	file path
[prefix].fit	How to fit. {options: stretch, fitheight, fitwidth}
[prefix].coord.lo	Lower-left coordinates of image in domain
[prefix].coord.hi	Upper-right coordinates of image in domain
[prefix].channel	Color channel to use (options: r, R, g, G, b, B, a, A)	r g b a R G B A
[prefix].min	Scaling value - minimum	0.0
[prefix].max	Scaling value - maximum	255.0

IC::Random

src/IC/Random.H

Parameter	Type	Values
[prefix].mult	Multiplier	1.0

IC::Sphere

src/IC/Sphere.H

Parameter	Type	Values
[prefix].radius	Radius of the sphere
[prefix].center	Vector location of the sphere center
[prefix].inside	Value of the field inside the sphere
[prefix].outside	Value of the field outside teh sphere
[prefix].type	Type - can be cylinder oriented along the x, y, z directions or full sphere.

IC::Trig

src/IC/Trig.H

This is an old-fashioned IC. You use IC::Expression instead.

Parameter	Type	Values
[prefix].nr	Number of real (cosin) waves
[prefix].ni	Number of imaginary (sin) waves
[prefix].dim	Spatial dimension
[prefix].alpha	Multiplier

IC::TabulatedInterface

src/IC/TabulatedInterface.H

Parameter	Type	Values
[prefix].xs	x location of points
[prefix].ys	y location of points

IC::Voronoi

src/IC/Voronoi.H

Parameter	Type	Values
[prefix].number_of_grains	Number of grains
[prefix].alpha	Value to take in the region [1.0]
[prefix].seed	Random seed to use

IO

IO::FileNameParse

src/IO/FileNameParse.cpp src/IO/FileNameParse.H

Parameter	Type	Values

IO::ParmParse

src/IO/ParmParse.cpp src/IO/ParmParse.H

This is a thin wrapper to the amrex::ParmParse class This class exists to add some additional parsing capability, e.g. parsing Set::Matrix and Set::Vector data types.

IO::ParmParse uses static Parse() functions to perform cascading class-based input parsing. See the Autodoc and Autotest section for instructions on adding documentation.

This is standard infrastructure code; make sure you know what you ard doing before you change it.

Query directives

Alamo uses different query directives to standardize reading inputs and automatic documentation. The type of query that is used (query vs query_required, etc) triggers different handlers and different automatic documentation procedures. For instance, the use of a query_default causes a default value to be set and added to the metadata file, and it also serves as a flag for the autodoc system to document that a default value is available. The following table is a reference for the different kinds of query directives.

BC Type	Description
query	Standard IO for bool, string, Set::Scalarthat does not enforce defaults or required values. Not recommended for general use.
query_required	Similar to query, but will abort if no value is specified. Required values are indicated by required.
query_default	Similar to query, but will fill with default value if no value is provided. Will also add default value to metadata. Default values are indicated by green badge values, e.g. 0.0.
query_validate	For strings, read in a value and enforce that the value is one of a supplied number of values. Optionally make required, or set the default value to the first supplied value. Acceptable options are indicated by blue badge values, e.g. 1.0, 2.0. If a default value is available, it is indicated by a green badge, e.g. 1.0.
query_file	Read in a string that defines a file name. Check to make sure that the file exists and is a regular file, and print an informative error message if not (this can be disabled). Also, copy the file to the output directory, with the full path preserved by replacing / with _. (This can also be disabled, but doing so is discouraged.) Default values are not allowed. File paths are indicated by file path.
queryarr	Read in an array of numbers into either a standard vector or into a `Set::Vector` or `Set::Scalar`. No defaults or existence checking is performed.
queryclass	Read a class object with a specified prefix. How that class is read in is determined by its `Parse` function.

Query macros

A set of preprocessor macros are defined so that you can call a query function using pp_ instead of pp.. For instance, the following two can be used interchangeably:

pp.query_required("myvar",myvar); /* function version */
pp_query_required("myvar",myvar); /* preprocessor macro version - preferred*/

Using the preprocessor macros enables code location information to be passed to the parser, so that more informative error messages will be printed out. Note that the ParmParse object must always be called pp for this to work.

IO::WriteMetaData

src/IO/WriteMetaData.cpp src/IO/WriteMetaData.H

This provide an IO routine for generating run-specific output. Every Alamo run produces a metadata file and (if applicable) a diff.patch file that reflects the exact state when the simulation was run. Note that the file WriteMetaData.cpp file is _always_ recompiled upon make, in order to pull the latest information about the local state at build.

This is standard infrastructure code; make sure you know what you ard doing before you change it.

Parameter	Type	Values

Integrator

src/Integrator/Integrator.cpp src/Integrator/Integrator.H

Pure abstract class for managing data structures, time integration (with substepping), mesh refinement, and I/O.

Native input file parameters:

max_step  = [maximum number of timesteps]
stop_time = [maximum simulation time]
timestep  = [time step for coarsest level]

amr.regrid_int = [number of timesteps between regridding]
amr.plot_int   = [number of timesteps between dumping output]
amr.plot_file  = [base name of output directory]

amr.nsubsteps  = [number of temporal substeps at each level. This can be
                  either a single int (which is then applied to every refinement
                  level) or an array of ints (equal to amr.max_level)
                  corresponding to the refinement for each level.]

Inherited input file parameters (from amrex AmrMesh class):

amr.v                  = [verbosity level]
amr.max_level          = [maximum level of refinement]
amr.n_proper           =
amr.grid_eff           =
amr.n_error_buff       =
amr.ref_ratio_vect     = [refinement ratios in each direction]
amr.ref_ratio          = [refinement ratio in all directions (cannot be used with ref_ratio_vect)]
amr.max_grid_x         =
amr.blocking_factor    =
amr.n_cell             = [number of cells on coarsest level]
amr.refine_grid_layout =
amr.check_input        =

Parameter	Type	Values
These are basic parameters that are, in general, common to all Alamo simulations.
max_step	Number of iterations before ending (default is maximum possible int)	2147483647
stop_time	Simulation time before ending	required
timestep	Nominal timestep on amrlev = 0	required
restart	Name of restart file to READ from
restart_cell	Name of cell-fab restart file to read from
restart_node	Name of node-fab restart file to read from
This allows the user to ignore certain arguments that would otherwise cause problems. Most generally this is used in the event of a “above inputs specified but not used” error. The primary purpose of this was to fix those errors that arise in regression tests.
ignore	Space-separated list of entries to ignore
These are parameters that are specific to the AMR/regridding part of the code.
amr.regrid_int	Regridding interval in step numbers	2
amr.base_regrid_int	Regridding interval based on coarse level only	0
amr.plot_int	Interval (in timesteps) between plotfiles (Default negative value will cause the plot interval to be ignored.)	-1
amr.plot_dt	Interval (in simulation time) between plotfiles (Default negative value will cause the plot dt to be ignored.)	-1.0
amr.plot_file	Output file	output
amr.cell.all	Turn on to write all output in cell fabs (default: off)	false
amr.cell.any	Turn off to prevent any cell based output (default: on)	true
amr.node.all	Turn on to write all output in node fabs (default: off)	false
amr.node.any	Turn off to prevent any node based output (default: on)	true
amr.abort_on_nan	Abort if a plotfile contains nan or inf.	true
amr.max_plot_level	Specify a maximum level of refinement for output files (NO REFINEMENT)	-1
amr.nsubsteps	Number of substeps to take on each level (default: 2)
amr.nsubsteps	Number of substeps to take on each level (set all levels to this value)	required

dynamictimestep.on	activate dynamic CFL-based timestep
dynamictimestep.verbose	how much information to print	0 1
dynamictimestep.nprevious	number of previous timesteps for rolling average	5
dynamictimestep.cfl	dynamic teimstep CFL condition	1.0
dynamictimestep.min	minimum timestep size allowed shen stepping dynamically	timestep
dynamictimestep.max	maximum timestep size allowed shen stepping dynamically	timestep
Information on how to generate thermodynamic data (to show up in thermo.dat)
amr.thermo.int	Integration interval (1)	1
amr.thermo.plot_int	Interval (in timesteps) between writing (Default negative value will cause the plot interval to be ignored.)	-1
amr.thermo.plot_dt	Interval (in simulation time) between writing (Default negative value will cause the plot dt to be ignored.)	-1.0
Instead of using AMR, prescribe an explicit, user-defined set of grids to work on. This is pretty much always used for testing purposes only.
explicitmesh.on	Use explicit mesh instead of AMR	0

Integrator::AllenCahn

src/Integrator/AllenCahn.H

This is a simple implementation of an Allen-Cahn equation governed by

\[\frac{\partial\alpha}{\partial t} = - L \Big(\frac{\lambda}{\epsilon}(2.0\alpha - 6\alpha^2 + 4\alpha^3) + \epsilon\,\kappa\,\Delta \alpha \Big)\]

where \(\alpha(x,t)\) is the order parameter.

Parameter	Type	Values
[prefix].refinement_threshold	Criterion for mesh refinement [0.01]	0.01
[prefix].ch.L	Value for \(L\) (mobility)	1.0
[prefix].ch.eps	Value for \(\epsilon\) (diffuse boundary width)	0.1
[prefix].ch.grad	Value for \(\kappa\) (Interface energy parameter)	1.0
[prefix].ch.chempot	Value for \(\lambda\) (Chemical potential coefficient)	1.0
[prefix].ch.direction	Force directional growth: 0=no growth, 1=only positive, -1=only negative	0 1 -1
[prefix].alpha.ic.type	Set the initial condition for the alpha field	sphere constant expression bmp png random psread

Integrator::CahnHilliard

src/Integrator/CahnHilliard.cpp src/Integrator/CahnHilliard.H

CahnHilliard

Integrator::Dendrite

src/Integrator/Dendrite.H

This is a BASIC phase field method for dendritic growth as described in “A Numerical Approach to Three-Dimensional Dendritic Solidification” by Ryo Kobayashi (1994) Reference: https://doi.org/10.1080/10586458.1994.10504577

Parameter	Type	Values
[prefix].alpha	Pre-multiplier of “m” barrier height	required
[prefix].delta	Anisotropy factor	required
[prefix].gamma	Anisotropic temperature coupling factor	required
[prefix].eps	Diffuse boundary width	required
[prefix].tau	Diffusive timescale	required
[prefix].heat.refinement_threshold	Refinement criteria for temperature	0.01
[prefix].phi.refinement_threshold	Refinement criteria for phi	0.01

Integrator::Flame

src/Integrator/Flame.cpp src/Integrator/Flame.H

Parameter	Type	Values
[prefix].timestep	Simulation timestep	1.0e-4
[prefix].pf.eps	Burn width thickness	0.0
[prefix].pf.kappa	Interface energy param	0.0
[prefix].pf.gamma	Scaling factor for mobility	1.0
[prefix].pf.lambda	Chemical potential multiplier	0.0
[prefix].pf.w1	Unburned rest energy	0.0
[prefix].pf.w12	Barrier energy	0.0
[prefix].pf.w0	Burned rest energy	0.0
[prefix].amr.ghost_cells	number of ghost cells in all fields	2
[prefix].geometry.x_len	Domain x length	0.001
[prefix].geometry.y_len	Domain y length	0.001
[prefix].pf.eta.bc.type	Boundary conditions for phase field order params	constant
[prefix].pf.eta.ic.type	phase field initial condition after comment	constant expression
[prefix].eta.ic.type	phase field initial condition	laminate constant expression bmp png
[prefix].thermal.on	IO::ParmParse pp(“thermal”); Whether to use the Thermal Transport Model	false
[prefix].elastic.on	Whether to use Neo-hookean Elastic model	0
[prefix].thermal.bound	System Initial Temperature	0.0
[prefix].elastic.traction	Body force	0.0
[prefix].elastic.phirefinement	Phi refinement criteria	1
[prefix].thermal.rho_ap	AP Density	required
[prefix].thermal.rho_htpb	HTPB Density	required
[prefix].thermal.k_ap	AP Thermal Conductivity	required
[prefix].thermal.k_htpb	HTPB Thermal Conductivity	required
[prefix].thermal.cp_ap	AP Specific Heat	required
[prefix].thermal.cp_htpb	HTPB Specific Heat	required
[prefix].thermal.q0	Baseline heat flux	0.0
[prefix].thermal.m_ap	AP Pre-exponential factor for Arrhenius Law	required
[prefix].thermal.m_htpb	HTPB Pre-exponential factor for Arrhenius Law	required
[prefix].thermal.E_ap	AP Activation Energy for Arrhenius Law	required
[prefix].thermal.E_htpb	HTPB Activation Energy for Arrhenius Law	required
[prefix].thermal.hc	Used to change heat flux units	1.0
[prefix].thermal.massfraction	Systen AP mass fraction	0.8
[prefix].thermal.mlocal_ap	AP mass flux reference value	0.0
[prefix].thermal.mlocal_htpb	HTPB mass flux reference value	0.0
[prefix].thermal.mlocal_comb	AP/HTPB mass flux reference value	0.0
[prefix].thermal.T_fluid	Temperature of the Standin Fluid	300.0
[prefix].thermal.disperssion1	K; dispersion variables are use to set the outter field properties for the void grain case.
[prefix].thermal.disperssion2	rho; dispersion variables are use to set the outter field properties for the void grain case.
[prefix].thermal.disperssion3	cp; dispersion variables are use to set the outter field properties for the void grain case.
[prefix].thermal.modeling_ap	Scaling factor for AP thermal conductivity (default = 1.0)	1.0
[prefix].thermal.modeling_htpb	Scaling factor for HTPB thermal conductivity (default = 1.0)	1.0
[prefix].thermal.temp.bc.type	Temperature boundary condition	constant
[prefix].laser.ic.type	laser initial condition	constant expression
[prefix].temp.ic.type	thermal initial condition	constant expression bmp png
[prefix].pressure.P	Constant pressure value	1.0
[prefix].pressure.a1	Surgate heat flux model paramater - AP	required
[prefix].pressure.a2	Surgate heat flux model paramater - HTPB	required
[prefix].pressure.a3	Surgate heat flux model paramater - Total	required
[prefix].pressure.b1	Surgate heat flux model paramater - AP	required
[prefix].pressure.b2	Surgate heat flux model paramater - HTPB	required
[prefix].pressure.b3	Surgate heat flux model paramater - Total	required
[prefix].pressure.c1	Surgate heat flux model paramater - Total	required
[prefix].pressure.mob_ap	Whether to include pressure to the arrhenius law	0
[prefix].pressure.dependency	Whether to use pressure to determined the reference Zeta	1
[prefix].pressure.h1	Surgate heat flux model paramater - Homogenized	1.81
[prefix].pressure.h2	Surgate heat flux model paramater - Homogenized	1.34
[prefix].pressure.r_ap	AP power pressure law parameter (r*P^n)	required
[prefix].pressure.r_htpb	HTPB power pressure law parameter (r*P^n)	required
[prefix].pressure.r_comb	AP/HTPB power pressure law parameter (r*P^n)	required
[prefix].pressure.n_ap	AP power pressure law parameter (r*P^n)	required
[prefix].pressure.n_htpb	HTPB power pressure law parameter (r*P^n)	required
[prefix].pressure.n_comb	AP/HTPB power pressure law parameter (r*P^n)	required
[prefix].variable_pressure	Whether to compute the pressure evolution	0
[prefix].homogeneousSystem	Whether to initialize Phi with homogenized properties	0
[prefix].amr.refinement_criterion	Refinement criterion for eta field	0.001
[prefix].amr.refinement_criterion_temp	Refinement criterion for temperature field	0.001
[prefix].amr.refinament_restriction	Eta value to restrict the refinament for the temperature field	0.1
[prefix].amr.phi_refinement_criterion	Refinement criterion for phi field [infinity]	1.0e100
[prefix].small	Lowest value of Eta.	1.0e-8
[prefix].phi.ic.type	IC type (psread, laminate, constant)	psread laminate expression constant bmp png
[prefix].phi.ic.psread.eps	value.ic_phicell = new IC::PSRead(value.geom, pp, “phi.ic.psread”); AP/HTPB interface length	1.0e-5
[prefix].phi.zeta_0	Reference interface length for heat integration	1.0e-5
[prefix].phi.ic.laminate.eps	value.ic_phicell = new IC::Laminate(value.geom, pp, “phi.ic.laminate”); AP/HTPB interface length	1.0e-5
[prefix].phi.zeta_0	Reference interface length for heat integration	1.0e-5
[prefix].phi.zeta_0	value.ic_phicell = new IC::Expression(value.geom, pp, “phi.ic.expression”); Reference interface length for heat integration	1.0e-5
[prefix].phi.zeta	AP/HTPB interface length	1.0e-5
[prefix].phi.zeta_0	value.ic_phicell = new IC::Constant(value.geom, pp, “phi.ic.constant”); Reference interface length for heat integration	1.0e-5
[prefix].phi.zeta	AP/HTPB interface length	1.0e-5
[prefix].phi.zeta_0	value.ic_phicell = new IC::BMP(value.geom, pp, “phi.ic.bmp”); Reference interface length for heat integration	1.0e-5
[prefix].phi.zeta	AP/HTPB interface length	1.0e-5
[prefix].phi.zeta_0	Reference interface length for heat integration	1.0e-5
[prefix].phi.zeta	AP/HTPB interface length	1.0e-5
[prefix].Tref	Initial temperature for thermal expansion computation	300.0

Integrator::Fracture

src/Integrator/Fracture.H

Parameter	Type	Values
IC for crack field
crack.ic.type	Type of crack {notch,ellipsoid}

Integrator::HeatConduction

src/Integrator/HeatConduction.H

This implements a basic heat conduction method in Alamo. The partial differential equation to be solved is

\[\frac{\partial T}{\partial t} = \alpha\,\Delta T\]

where \(T\) is temperature, \(t\) is time, and \(alpha\) is the thermal diffusivity. Integration is performed explicitly in time using forward Euler, and differentiation is performed using the finite difference method.

Parameter	Type	Values
[prefix].heat.alpha	Diffusion coefficient \(\alpha\). This is an example of a required input variable - - program will terminate unless it is provided.	required
[prefix].heat.refinement_threshold	Criterion for mesh refinement. This is an example of a default input variable. The default value is provided here, not in the definition of the variable.	0.01
[prefix].ic.type	Initial condition type.	constant sphere expression
[prefix].bc.temp.type	Select BC object for temperature	constant expression

Integrator::Mechanics

src/Integrator/Mechanics.H

This is a general purpose integrator that focuses on solving elasticity/mechanics equations in the absence of other multiphysics simulations. It is enabled by alamo.program=mechanics if used on its own, in which case there is no prefix. If it is being used by another integrator, see that integrator to determine the value of [prefix] (often equal to elastic).

This integrator inherits from Integrator::Base::Mechanics; see documentation for that integrator for additional parameters.

Model setup There are two basic tools for setting up a mechanics problem in this integrator.

The eta field: this is used to mix models of different types. Use nmodels to specify how many material models to use, and then specify each model as model1, model2, etc. The type of moel is specified using the alamo.program.mechanics.model input.

Once you have done this, you must determine the spatial distribution of each model. This is done by choosing an IC for the eta field with ic.type. The IC::Expression is the most general and recommended. The models are then mixed linearly, i.e.

\[W_{\textrm{eff}} = \sum_{i=1}^N W_i\,\eta_i(\mathbf{x})\]

See the Eshelby test for an example of model mixing.
The psi field: this is used specifically for cases where a “void” region is desired. Its usage is similar to the eta case, and is conceptually similar in that it scales the model field to near-zero in order to mimic the (lack of) mechanical behavior in an empty region. It is important to use psi here, for reasons that are discussed in detail in this paper. The initialization of psi is similar to that for eta.

See the PlateHole and RubberPlateHole for canonical exmaples. The Integrator::Fracture and Integrator::TopOp integrators are examples of integrators that leverage the psi property.

Body forces currently have limited support due to the relatively low number of times they are needed. See the Integrator::Base::Mechanics documentation for detail. See the TrigTest test for examples of current body force implementation.

Boundary conditions are implemented using the BC::Operator::Elastic classes. See the documentation on these classes for more detail. See any of the mechanics-based tests for examples of boundary condition application.

Parameter	Type	Values
[prefix].nmodels	Number of elastic model varieties	1
[prefix].eta_ref_threshold	Refinement threshold for eta field	0.01
[prefix].ref_threshold	Refinement threshold for strain gradient	0.01
[prefix].model_neumann_boundary	Explicity impose neumann condition on model at domain boundaries (2d only)	false
[prefix].ic.type	Select the initial condition for eta	constant ellipse voronoi bmp png expression psread
[prefix].eta.reset_on_regrid	Whether to re-initialize eta when re-gridding occurs. Default is false unless eta ic is set, then default is. true.	true
[prefix].psi.ic.type	Select initial condition for psi field	ellipse constant expression psread png
[prefix].psi.reset_on_regrid	Whether to re-initialize psi when re-gridding occurs. Default is false unless a psi ic is set, then default is true.	true
[prefix].trac_normal.ic.type	Read in IC for the “normal traction” field (applied at diffuse boundaries)	ellipse constant expression psread

Integrator::PhaseFieldMicrostructure

src/Integrator/PhaseFieldMicrostructure.cpp src/Integrator/PhaseFieldMicrostructure.H

file PhaseFieldMicrostructure.H

Parameter	Type	Values
[prefix].pf.number_of_grains	Number of grain fields (may be more if using different IC)	2
[prefix].pf.M	Mobility	required
[prefix].pf.mu	Phase field \(\mu\)	required
[prefix].pf.gamma	Phase field \(\gamma\)	required
[prefix].pf.sigma0	Initial GB energy if not using anisotropy	required
[prefix].pf.l_gb	Mobility	required
[prefix].pf.elastic_df	Determine whether to use elastic driving force	false
[prefix].pf.elastic_mult	Multiplier of elastic energy	1.0
[prefix].pf.threshold.value	Value used for thresholding kinetic relation	0.0
[prefix].pf.threshold.chempot	Whether to include chemical potential in threshold	false
[prefix].pf.threshold.boundary	Whether to include boundary energy in threshold	false
[prefix].pf.threshold.corner	Whether to include corner regularization in threshold	false
[prefix].pf.threshold.lagrange	Whether to include lagrange multiplier in threshold	false
[prefix].pf.threshold.mechanics	Whether to include mechanical driving force in threshold	false
[prefix].pf.threshold.type	Type of thresholding to use	continuous chop
[prefix].amr.max_level	Maximum AMR level	required
[prefix].amr.ref_threshold	Phase field refinement threshold	0.1
[prefix].mechanics.tstart	Elasticity	0.0
[prefix].lagrange.on	Lagrange multiplier method for enforcing volumes	false
[prefix].lagrange.lambda	Lagrange multiplier value	required
[prefix].lagrange.vol0	Prescribed volume	required
[prefix].lagrange.tstart	Lagrange multipler start time	0.0
[prefix].sdf.on	synthetic driving force (SDF)	false
[prefix].sdf.val	value of SDF for each grain
[prefix].sdf.tstart	time to begin applying SDF	0.0
[prefix].anisotropy.on	Turn on	false
[prefix].anisotropy.beta	Regularization para m	required
[prefix].anisotropy.tstart	Time to turn on anisotropy	required
[prefix].anisotropy.timestep	Modify timestep when turned on	required
[prefix].anisotropy.plot_int	Modify plot_int when turned on	-1
[prefix].anisotropy.plot_dt	Modify plot_dt when turned on	-1.0
[prefix].anisotropy.thermo_int	Modify thermo int when turned on	-1
[prefix].anisotropy.thermo_plot_int	Modify thermo plot int when turned on	-1
[prefix].anisotropy.elastic_int	Frequency of elastic calculation	-1
[prefix].anisotropy.regularization	Type of regularization to use	k12 wilmore
[prefix].anisotropy.type	Type of GB to use	abssin sin read sh
[prefix].bc.eta.type	Boundary condition for eta	constant
[prefix].ic.type	Initial condition for the order parameter eta	constant perturbedinterface voronoi expression sphere ellipse random
[prefix].anisotropic_kinetics.on	Anisotropic mobility	0
[prefix].anisotropic_kinetics.tstart	simulation time when anisotropic kinetics is activated	0.0
[prefix].anisotropic_kinetics.mobility	file containing anisotropic mobility data	file path
[prefix].anisotropic_kinetics.threshold	file containing anisotropic mobility data	file path

Integrator::SutureCrack

src/Integrator/SutureCrack.H

Parameter	Type	Values
IC for crack field
crack.ic.type	Crack type to use {notch}

Integrator::ThermoElastic

src/Integrator/ThermoElastic.H

Parameter	Type	Values
[prefix].alpha	Diffusion coefficient

Integrator::TopOp

src/Integrator/TopOp.H

Parameter	Type	Values
[prefix].psi.ic.type	Initial condition for psi field	ellipse constant
[prefix].eta_ref_threshold	Refinement threshold based on eta	0.01
[prefix].alpha	\(\alpha\) parameter	1.0
[prefix].beta	\(\beta\) parameter	1.0
[prefix].gamma	\(\gamma\) parameter	1.0
[prefix].volume0frac	Prescribed volume fraction	0.5
[prefix].volume0	Prescribed total vlume	0.5

Integrator::Base

Integrator::Base::Mechanics

src/Integrator/Base/Mechanics.H

Parameter	Type	Values
[prefix].type	Type of mecahnics to use. Static: do full implicit solve. Dynamic: evolve dynamic equations with explicit dynamics Disable: do nothing.	disable static dynamic
[prefix].time_evolving	Treat mechanics fields as changing in time. [false] You should use this if you care about other physics driven by the output of this integrator.	false
[prefix].plot_disp	Include displacement field in output	true
[prefix].plot_rhs	Include right-hand side in output	true
[prefix].plot_psi	Include \(\psi\) field in output	true
[prefix].plot_stress	Include stress in output	true
[prefix].plot_strain	Include strain in output	true
[prefix].viscous.mu_dashpot	Dashpot damping (damps velocity)	0.0
[prefix].viscous.mu_newton	Newtonian viscous damping (damps velocity gradient)	0.0
[prefix].velocity.ic.type	Initializer for RHS	none expression
[prefix].bc.type	Select the mechanical boundary conditions	constant tensiontest expression
[prefix].print_model	Print out model variables (if enabled by model)	false
[prefix].rhs.type	Initializer for RHS	none trig constant
[prefix].interval	Timestep interval for elastic solves (default - solve every time)	0
[prefix].max_coarsening_level	Maximum multigrid coarsening level (default - none, maximum coarsening)	-1
[prefix].print_residual	Whether to include residual output field	false
[prefix].elastic_ref_threshold	Whether to refine based on elastic solution	0.01
[prefix].zero_out_displacement	Set this to true to zero out the displacement before each solve. (This is a temporary fix - we need to figure out why this is needed.)	false
[prefix].tstart	Time to start doing the elastic solve (by default, start immediately)	-1.0

Model

src/Model/Model.H

In Alamo, any type of constitutive behavior is encapsulated in a “Model”. There is a broad range of model types, and so there is no abstract Model class. Rather, the base Model classes are stored in subsets of Model.

Model::Interface

Model::Interface::Crack

Model::Interface::Crack::Constant

src/Model/Interface/Crack/Constant.H

Parameter	Type	Values
[prefix].G_c	Fracture energy
[prefix].zeta	Lengthscale regularization
[prefix].mobility	Mobility (speed)
[prefix].threshold	Threshold
[prefix].gtype	Type of g function to use {square, multiwell, 4c3, squarep, squarepexp, cubicm}
[prefix].wtype	Type o w function to use {square, multiwell, multiwell2, 4c3}

Model::Interface::Crack::Sin

src/Model/Interface/Crack/Sin.H

Parameter	Type	Values
[prefix].Gc0	Min Gc (fracture energy) value
[prefix].Gc1	Max Gc (fracture energy)value
[prefix].theta0	Angle offset
[prefix].zeta	Regularization
[prefix].mobility	Crack mobiilty
[prefix].threshold	Threshold for kinetics
[prefix].gtype	Type of g function to use {square, multiwell, 4c3, squarep, squarepexp, cubicm}
[prefix].wtype	Type o w function to use {square, multiwell, multiwell2, 4c3}

Model::Interface::GB

Model::Interface::GB::AbsSin

src/Model/Interface/GB/AbsSin.H

Parameter	Type	Values
[prefix].theta0	Angle offset (degrees)
[prefix].sigma0	Minimum energy
[prefix].sigma1	Energy multiplier

Model::Interface::GB::Read

src/Model/Interface/GB/Read.H

Parameter	Type	Values
[prefix].filename	Filename containing GB data	file path

Model::Interface::GB::SH

src/Model/Interface/GB/SH.H

Parameter	Type	Values
[prefix].theta0	Theta offset (degrees)
[prefix].phi0	Phi offset (radians)
[prefix].sigma0	Minimum energy value
[prefix].sigma1	Energy multiplier
[prefix].regularization	Type of regularization to use: {wilhelm,k23}

Model::Interface::GB::Sin

src/Model/Interface/GB/Sin.H

Parameter	Type	Values
[prefix].theta0	Theta offset (degrees)
[prefix].sigma0	Minimum energy
[prefix].sigma1	Energy multiplier
[prefix].n	Frequency number (integer)

Model::Solid

src/Model/Solid/Solid.H

Solid models are used with the Integrator::Mechanics integrator, which implements the Solver::Nonlocal::Newton elasticity solver. All solid models inherit from the Model::Solid base class, which requires all of the necessary components to be used in a mechanics solve. Model classes have basically two functions:

Provide energy (W), stress (DW), and modulus (DDW) based on a kinematic variable
Evolve internal variables in time.

Model::Solid::Affine

src/Model/Solid/Affine/Affine.H

“Affine” generally means “linear with an offset”. Here we use “affine” to refer to models that are elastic with an eigenstrain, i.e.

\[\sigma = \mathbb{C}(\varepsilon - \varepsilon_0)\]

The quantity \(\varepsilon_0\) is any kind of eigenstrain - examples include thermal strain, plastic strain, or viscous strain. This class can be used directly, where the eigenstrain is read in or set by the integrator. There are also classes (particularly visco/plastic models) that inherit from this type of model.

Model::Solid::Affine::Hexagonal

src/Model/Solid/Affine/Hexagonal.H

This model implements an affine hexagonal material:

\[W_{aff}(\nabla\mathbf{u}) = W_{lin}(\nabla\mathbf{u} - \mathbf{F}_0)\]

where \(W_{aff}\) is the present model, \(\mathbf{F}_0\) is the eigenstrain, and \(W_{lin}\) is the cubic model defined in Model::Solid::Linear::Hexagonal.

Parameter	Type	Values
[prefix].F0	Eigenstrain matrix. Can be defined in 2D or 3D.

Model::Solid::Affine::Isotropic

src/Model/Solid/Affine/Isotropic.H

Parameter	Type	Values
[prefix].lame	Lame modulus
[prefix].shear	Shear modulus
[prefix].E	Elastic modulus
[prefix].nu	Poisson’s ratio
[prefix].E	Young’s modulus
[prefix].shear	Shear modulus
[prefix].E	Young’s modulus
[prefix].lame	Lame parameter
[prefix].nu	Poisson’s ratio
[prefix].shear	Shear modulus
[prefix].lambda	Lame parameter
[prefix].nu	Poisson’s ratio
[prefix].bulk	Bulk modulus
[prefix].shear	Shear modulus
[prefix].F0	Eigendeformation gradient

Model::Solid::Affine::J2

src/Model/Solid/Affine/J2.H

This models an isotropic elastic-perfectly-plastic, non-time-dependent solid model.

The energy and derivatives are:

\begin{gather} W = \frac{1}{2}(\varepsilon - \varepsilon_p):\mathbb{C}(\varepsilon-\varepsilon_p) \\ DW = \mathbb{C}(\varepsilon-\varepsilon_p) \\ DDW = \mathbb{C} \end{gather}

where \(\mathbb{C}\) is an isotropic Set::Matrix4 and \(\varepsilon_p\) is is stored in the F0 eigenstrain.

The plastic strain is evolved according to the following:

Calculate the deviatoric stress \(\sigma_v=\sigma - \frac{1}{3}tr(\sigma)\mathbf{I}\)
Calculate \(J_2=\sqrt{\frac{3}{2}\sigma_v:\sigma_v}\)
If \(J_2<\sigma_0\) then quit - no plasticity occurs
Calculate \(\Delta\sigma = (1-\frac{\sigma_0}{J_2})\), which projects the stress back on the yield surface.
Convert to change in plastic strain, \(\Delta\varepsilon=\mathbb{C}^{-1}\Delta\sigma\)
Update plastic strain: \(\varepsilon_p += \Delta\varepsilon\)

Notes:

This does not implement any kind of hardening model. Rate hardening, isotropic hardening, and kinematic hardening have yet to be implemneted.

Parameter	Type	Values
[prefix].sigma0	J2 Yield criterion	1.0
[prefix].hardening	Hardening coefficient (negative value disables rate hardening)	-1.0
[prefix].ratecoeff	Rate coefficient (negative value disables rate hardening)	-1.0

Model::Solid::Affine::J2Plastic

src/Model/Solid/Affine/J2Plastic.H

Parameter	Type	Values
[prefix].lambda	Lame constant
[prefix].mu	Shear modulus
[prefix].E	Young’s modulus
[prefix].nu	Poisson’s ratio
[prefix].yield	Yield strength
[prefix].hardening	Hardening constant
[prefix].theta	Hardening theta

Model::Solid::Finite

Model::Solid::Finite::CrystalPlastic

src/Model/Solid/Finite/CrystalPlastic.H

A basic and relatively untested implementation of finite-deformation FCC crystal plasticity. Use with caution.

Inherits from PseudoLinear::Cubic to provide elastic response.

Plastic flow modeled as:

\[\mathbf{F}^p\mathbf{F}^{p-1} = \sum \dot{\gamma}_n \mathbf{a}_n\otimes\mathbf{N}_n\]

where \(\mathbf{F}=\mathbf{F}^e\mathbf{F}^p\) and \(\gamma_n\) are slips on system \(n\).

Power law rate hardening is used in the integration of slips:

\[\dot{\gamma}_n = \dot{\gamma}_0 \Big(\frac{\tau}{\tau_{crss}}\Big)^m \operatorname{sign}(\tau)\]

Parameter	Type	Values
[prefix].tau_crss	Critical resolved shear stress \(\tau_{crss}\)
[prefix].gammadot0	Rate hardening coefficient \(\dot{\gamma}_0\)	1.0
[prefix].m_rate_inv	Inverse of the hardening exponent \(\frac{1}{m}\)	0.5
[prefix].tstart	Time to activate plastic slip	0.0

Model::Solid::Finite::NeoHookeanPredeformed

src/Model/Solid/Finite/NeoHookeanPredeformed.H

Parameter	Type	Values
[prefix].F0	Large-deformation eigendeformation (Identity = no deformation)
[prefix].eps0	Small-deformation eigendeformation (Zero = no deformation)

Model::Solid::Finite::NeoHookean

src/Model/Solid/Finite/NeoHookean.H

Parameter	Type	Values
[prefix].shear	Shear modulus
[prefix].kappa	Bulk modulus
[prefix].mu	Alternative input for shear modulus
[prefix].kappa	Bulk modulus
[prefix].shear	Shear modulus
[prefix].lame	Lame parameter
[prefix].E	Young’s modulus
[prefix].nu	Poisson’s ratio

Model::Solid::Finite::PseudoAffine

Model::Solid::Finite::PseudoAffine::Cubic

src/Model/Solid/Finite/PseudoAffine/Cubic.H

Parameter	Type	Values
[prefix].F0	Large-strain eigendeformation (Identity = no deformation)
[prefix].eps0	Small-strain eigendeformation (Zero = no deformation)

Model::Solid::Finite::PseudoLinear

Model::Solid::Finite::PseudoLinear::Cubic

src/Model/Solid/Finite/PseudoLinear/Cubic.H

Parameter	Type	Values
[prefix].C11	Set::Scalar C11 = 1.68, C12 = 1.21, C44 = 0.75; Elastic constant (default: 1.68)
[prefix].C12	Elastic constant (default: 1.21)
[prefix].C44	Elastic constant (default: 0.75)
[prefix].phi1	Bunge Euler angle \(\phi_1\)
[prefix].Phi	Bunge Euler angle \(\Phi\)
[prefix].phi2	Bunge Euler angle \(\phi_2\)

Model::Solid::Linear

Model::Solid::Linear::Cubic

src/Model/Solid/Linear/Cubic.H

This class implements basic cubic elasticity. For a discussion on cubic elasticity, please see this link.

Parameter	Type	Values
[prefix].C11	Elastic constant	1.68
[prefix].C12	Elastic constant	1.21
[prefix].C44	Elastic constant	0.75
[prefix].anglefmt	specify whether using radians or degrees	radians degrees
[prefix].phi1	Bunge Euler angle \(\phi_1\) about x axis	0.0
[prefix].Phi	Bunge Euler angle \(\Phi\) about z axis	0.0
[prefix].phi2	Bunge Euler angle \(\phi_2\) about x axis	0.0

Model::Solid::Linear::Hexagonal

src/Model/Solid/Linear/Hexagonal.H

This class implements elasticity for a linear material with hexagonal symmetry. The elastic modulus tensor \(\mathbb{C}\) has major and minor symmetry but not cubic symmetry, so the symmetry class for this material is Set::Sym::MajorMinor. The five elastic constants in the unrotated system are \(C_{11},C_{12},C_{13},C_{33},C_{44}\), and the resulting elastic modulus tensor is

\[\begin{split}\mathbb{C} &= \begin{bmatrix} C_{0000} & C_{0011} & C_{0022} & C_{0012} & C_{0020} & C_{0001} \\ C_{1100} & C_{1111} & C_{1122} & C_{1112} & C_{1120} & C_{1101} \\ C_{2200} & C_{2211} & C_{2222} & C_{2212} & C_{2220} & C_{2201} \\ C_{1200} & C_{1211} & C_{1222} & C_{1212} & C_{1220} & C_{1201} \\ C_{2000} & C_{2011} & C_{2022} & C_{2012} & C_{2020} & C_{2001} \\ C_{0100} & C_{0111} & C_{0122} & C_{0112} & C_{0120} & C_{0101} \end{bmatrix} \\ &= \begin{bmatrix} C_{11} & C_{12} & C_{12} & & & \\ C_{12} & C_{11} & C_{13} & & & \\ C_{12} & C_{13} & C_{33} & & & \\ & & & C_{44} & & \\ & & & & 0.5(C_{11}-C_{12}) & \\ & & & & & 0.5(C_{11}-C_{12}) \end{bmatrix}\end{split}\]

Rotations can be specified using Bunge euler angles to generate a rotation matrix \(\mathbf{R}\). The rotated modulus tensor \(\mathbb{C}^{rot}\) is then

\[\mathbb{C}^{rot}_{psqt} = \mathbb{C}_{ijkl}R_{pi}R_{qj}R_{sk}R_{tl}\]

Parameter	Type	Values
[prefix].C11	Elastic constant	required
[prefix].C12	Elastic constant	required
[prefix].C13	Elastic constant	required
[prefix].C33	Elastic constant	required
[prefix].C44	Elastic constant	required
[prefix].phi1	Bunge Euler angle \(\phi_1\)	0.0
[prefix].Phi	Bunge Euler angle \(\Phi\)	0.0
[prefix].phi2	Bunge Euler angle \(\phi_2\)	0.0

Model::Solid::Linear::Isotropic

src/Model/Solid/Linear/Isotropic.H

This model implements an isotropic linear elastic material. See this link for more information about the theory.

Free energy for a linear material is defined as

\[W(\nabla\mathbf{u}) = \frac{1}{2}\nabla\mathbf{u}\cdot\mathbb{C}\,\nabla\mathbf{u}\]

For an isotropic material, stress and strain are related through

\[\mathbb{C}_{ijkl} = \lambda \delta_{ij}\varepsilon_{kk} + 2\mu\varepsilon_{ij}\]

where \(\lambda\) and \(\mu\) are the Lame constant and shear modulus, respectively. Users can specify these either through (lame and shear) OR (lambda and mu) OR (E and nu).

Class methods:

Isotropic(): Basic constructor. Does nothing, and leaves all values initiated as NAN.
Isotropic(Solid<Set::Sym::Isotropic> base) Basic constructor. Does nothing gut allows for inheritance.
Isotropic(Set::Scalar a_mu, Set::Scalar a_lambda) BAD old-fashioned constructor. Do not use!
~Isotropic() Simple destructor. Don’t need to change it.
void Define(Set::Scalar a_mu, Set::Scalar a_lambda) BAD old-fashioned way of doing things. Use Parse instead.
Set::Scalar W(const Set::Matrix & gradu) const override Returns elastic free energy density
Set::Matrix DW(const Set::Matrix & gradu) const override Returns first derivative of free energy, the stress tensor
Set::Matrix4<...> DDW(const Set::Matrix & ) const override Returns second derivative of free energy, the modulus tensor
virtual void Print(std::ostream &out) const override Prints the modulus tensor object to output stream (usually the terminal)
static Isotropic Random() Static method that generates a random yet acceptable model.
static Isotropic Zero() Static method that generates a “zero” element (so that there is no effect under addition)
static void Parse(Isotropic & value, IO::ParmParse & pp) Parser where all the IO occurs

Parameter	Type	Values
[prefix].planestress	Whether or not to use the plane stress approximation.
[prefix].lame	Lame parameter
[prefix].shear	Shear modulus (redundant with “mu”)
[prefix].lambda	Lame parameter
[prefix].mu	Shear modulus (redundant with “shear”)
[prefix].E	Elastic modulus
[prefix].nu	Poisson’s ratio

Model::Solid::Linear::Laplacian

src/Model/Solid/Linear/Laplacian.H

Parameter	Type	Values
alpha	Coefficient for the Laplacian	1.0

Numeric

Numeric::Interpolator

src/Numeric/Interpolator/Interpolator.H

This namespace has evolved to contain some general Interpolator routines that are actually unrelated. The Numeric::Interpolator::Linear is an I/O utility. The Numeric::Interpolator::NodeBilinear is a low-level AMReX override that the average user (or even coder) will probably not need to touch.

Numeric::Interpolator::Linear

src/Numeric/Interpolator/Linear.H

This is a general-purpose routine for specifying time-interpolated quantities in an input file. Interpolators obey the following syntax:

(t1,t2,..,tn;v1,v2,...,vn)

where tn are times and vn are values at those times.

Note: do not include whitespace in an interpolator, this will mess with the parser.

Interpolators can usually be used in place of regular numbers, but only when supported by the calling parse function.

For instance, the BC::Operator::Elastic::TensionTest allows the user to specify fixed displacement; for instance, to specify a value of 0.1:

bc.tenstion_test.disp = 0.1

However, it may be desirable to change the value over time. In this case, one may specify an interpolator string instead:

bc.tenstion_test.disp = (1.0,1.5,2.0;0.0,0.1,0.0)

This will cause the displacement value to be zero for t<1.0; ramp to 0.1 as 1.0<t<2.0; ramp back to 0.0 as 2.0<t<3.0; and then remain at the constant value of 3.0 for t>3.0.

Parameter	Type	Values
[prefix].str	Interpolator string used when Parsed from queryclass.

Numeric::Interpolator::NodeBilinear

src/Numeric/Interpolator/NodeBilinear.H

Provide an interpolator function that can work with templated fields.

Warning: This is a low-level class used to add templating functionality to unerlying AMReX classes. Edit at your own risk!

Operator

Operator::Elastic

src/Operator/Elastic.cpp src/Operator/Elastic.H

Parameter	Type	Values
[prefix].small	Regularization offset value used in near-singular elastic solves. It should be small - if it is too large, you will get better convergence but less correct values!

Set

src/Set/Set.cpp src/Set/Set.H

The Set namespace defines the Alamo datatypes. This includes scalars (Set::Scalar), vectors (Set::Vector), and nD tensors (Set::Tensor). Scalars are an alias for AMReX Real. Vectors and tensors are an alias for the Tuxfamily Eigen vectors and matrices, and so you can use Eigen operations on them (like A.determinant(), etc.) See the Eigen documentation for more.

The Set namespace defines the Matrix4 datatype for fourth order tensors. These can have isotropic, major, minor, majorminor, etc., symmetries.

The Set namespace also defines the Field datatype, which is where most data is stored. It is templated so that Set::Field<Set::Scalar> is a field of scalars, Set::Field<Set::Vector> is a vector field, etc. One can also have, for instance, a field of models, like Set::Field<Model::Solid::Linear::Iostropic>.

Set::Matrix4_Isotropic

src/Set/Matrix4_Isotropic.H

The isotropic tensor is defined to be

\[C_{ijkl} = \mu(d_{il}d_{jk} + d_{ik}d_{jl}) + \lambda d_{ij} d_{kl}\]

The inverse (“compliance”) tensor is

\[S_{ijkl} = ((1+\nu)/2E)(d_{il}d_{jl} + d_{ik}d_{jl}) - (\nu/E)d_{ij}d_{kl}\]

Replacing E, nu with Lame constants gives:

\[S_{ijkl} = (1/(4 \mu))(d_{il}d_{jl} + d_{ik}d_{jl}) + (\lambda/(2*\mu*(3\lambda+2\mu))) * d_{ij} * d_{kl}\]

For reference: http://solidmechanics.org/text/Chapter3_2/Chapter3_2.htm: https://en.wikipedia.org/wiki/Lam%C3%A9_parameters

Solver

Solver::Nonlocal

Solver::Nonlocal::Linear

src/Solver/Nonlocal/Linear.H

Parameter	Type	Values
[prefix].max_iter	Max number of iterations to perform before erroring out
[prefix].bottom_max_iter	Max number of iterations on the bottom solver
[prefix].max_fmg_iter	Max number of F-cycle iterations to perform
[prefix].fixed_iter	Number of fixed iterations to perform before exiting gracefully
[prefix].verbose	Verbosity of the solver (1-5)
[prefix].pre_smooth	Number of smoothing operations before bottom solve (2)
[prefix].post_smooth	Number of smoothing operations after bottom solve (2)
[prefix].final_smooth	Number of final smoothing operations when smoother is used as bottom solver (8)
[prefix].bottom_smooth	Additional smoothing after bottom CG solver (0)
[prefix].bottom_solver	The method that is used for the multigrid bottom solve (cg, bicgstab, smoother)
[prefix].bottom_tol_rel	Relative tolerance on bottom solver
[prefix].bottom_tol_abs	Absolute tolerance on bottom solver
[prefix].tol_rel	Relative tolerance
[prefix].tol_abs	Absolute tolerance
[prefix].omega	Omega (used in gauss-seidel solver)
[prefix].average_down_coeffs	Whether to average down coefficients or use the ones given. (Setting this to true is important for fracture.)
[prefix].normalize_ddw	Whether to normalize DDW when calculating the diagonal. This is primarily used when DDW is near-singular - like when there is a “void” region or when doing phase field fracture.
[prefix].dump_on_fail	If set to true, output diagnostic multifab information whenever the MLMG solver fails to converge. (Note: you must also set `amrex.signalhandling=0` and `amrex.throw_exception=1` for this to work.)
[prefix].abort_on_fail	If set to false, MLMG will not die if convergence criterion is not reached. (Note: you must also set `amrex.signalhandling=0` and `amrex.throw_exception=1` for this to work.)

Solver::Nonlocal::Newton

src/Solver/Nonlocal/Newton.H

Parameter	Type	Values
[prefix].nriters	Number of newton-raphson iterations.
[prefix].nrtolerance	Tolerance to use for newton-raphson convergence

Util

src/Util/Util.cpp src/Util/Util.H

Parameter	Type	Values

plot_file	Name of directory containing all output data