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GitHubMechanical Neuroimaging Lab · Univ. of Delaware
Sentinel.jl

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Material Models ​

Type Hierarchy ​

Sentinel.AbstractMaterialModel Type
julia
AbstractMaterialModel

Abstract supertype for all MRE material constitutive models. Concrete subtypes drive dispatch for element integration, adjoint gradient computation, and optimization routines.

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Sentinel.IsotropicIncompressible Type
julia
IsotropicIncompressible <: AbstractMaterialModel

Rayleigh-damped viscoelastic isotropic incompressible material. Corresponds to Fortran mtrlmodel = 1.

The property list is consumed positionally; three layouts are accepted:

  • 3 properties (standard runfile layout): prop 1 = complex shear modulus μ* Pa, prop 2 = density (the element kernels do not read this slot –- density arrives via the assembly-level ρ argument), prop 3 = complex bulk modulus κ* Pa

  • 2 properties: prop 1 = μ_, prop 2 = κ_

  • 1 property: prop 1 = μ* (κ* defaults to 1e9 Pa)

Uses a mixed pressure-displacement formulation with elemental pressures.

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Sentinel.IsotropicCompressible Type
julia
IsotropicCompressible <: AbstractMaterialModel

Rayleigh-damped isotropic compressible viscoelastic material. Corresponds to Fortran mtrlmodel = 3.

The property list is consumed positionally; two layouts are accepted:

  • 3 properties (standard runfile layout): prop 1 = complex shear modulus μ* Pa, prop 2 = density (the element kernels do not read this slot –- density arrives via the assembly-level ρ argument), prop 3 = complex Lamé parameter λ* Pa (converted internally to bulk modulus κ = λ + 2μ/3)

  • 2 properties: prop 1 = μ_, prop 2 = complex bulk modulus κ_ Pa (used directly)

Supports both hex27 and tet4 elements.

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Sentinel.Orthotropic Type
julia
Orthotropic <: AbstractMaterialModel

Rayleigh-damped orthotropic viscoelastic material. Corresponds to Fortran mtrlmodel = 2.

Nine properties: the complex entries of the 6×6 orthotropic stiffness matrix in Voigt notation, in the order

11, 22, 33, 12, 13, 23, 44, 55, 66

Requires fiber direction field for principal axis definition.

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Sentinel.Poroelastic Type
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Poroelastic <: AbstractMaterialModel

Poroelastic material with fluid pressure as an additional nodal DOF. Corresponds to Fortran mtrlmodel = 4.

Material properties:

  • Solid frame elastic properties

  • Fluid viscosity η

  • Permeability κ

  • Porosity φ

DOF layout: [u_x(1..nn), u_y(1..nn), u_z(1..nn), p(1..nn)] Fixed extra properties: ρ_p (solid density), ρ_a (added mass), ρ_f (fluid density)

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Sentinel.TransverseIsotropicV1 Type
julia
TransverseIsotropicV1 <: AbstractMaterialModel

Transverse isotropic viscoelastic material, formulation 1 (absolute moduli). Corresponds to Fortran mtrlmodel = 5.

Properties (positional):

  • prop 1: complex shear modulus in the transverse (isotropic) plane Pa

  • prop 2: complex shear modulus in the fiber-aligned shear planes Pa

  • prop 3: complex tensile modulus along the fiber axis Pa

  • prop 4 (optional): complex bulk modulus κ* Pa (defaults to 1e9)

Requires fiber direction field (DTI-derived) for symmetry axis. Uses same assembly kernel as TransverseIsotropicV2 and GeneralizedAnisotropic.

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Sentinel.TransverseIsotropicV2 Type
julia
TransverseIsotropicV2 <: AbstractMaterialModel

Transverse isotropic viscoelastic material, formulation 2 (relative anisotropy ratios). Corresponds to Fortran mtrlmodel = 6.

Properties (positional):

  • prop 1: complex substrate (base) shear modulus μ Pa –- the transverse-plane shear modulus

  • prop 2: shear anisotropy ratio φ (complex, dimensionless); the fiber-plane shear modulus is μ(1 + φ)

  • prop 3: tensile anisotropy ratio ζ (complex, dimensionless); scales the tensile (normal-stress) terms

  • prop 4 (optional): complex bulk modulus κ* Pa (defaults to 1e9)

Requires fiber direction field (DTI-derived) for symmetry axis. Uses same assembly kernel as TransverseIsotropicV1 and GeneralizedAnisotropic.

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Sentinel.GeneralizedAnisotropic Type
julia
GeneralizedAnisotropic <: AbstractMaterialModel

Generalized anisotropic viscoelastic material. Corresponds to Fortran mtrlmodel = 7.

Properties (positional):

  • prop 1: complex shear modulus in the transverse plane Pa

  • prop 2: complex principal directional Young's modulus along axis 1 (fiber direction) Pa

  • prop 3: complex principal directional Young's modulus in the transverse direction Pa

The stiffness matrix is used directly in global coordinates –- no fiber rotation is applied. Uses same assembly kernel (genanisoforwardassemble) as models 5 and 6.

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Sentinel.material_model Function
julia
material_model(model::Int) -> AbstractMaterialModel

Convert the Fortran integer model flag to the corresponding Julia type singleton.

Examples

julia
julia> material_model(1)
IsotropicIncompressible()

julia> material_model(4)
Poroelastic()
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Sentinel.model_index Function
julia
model_index(::AbstractMaterialModel) -> Int

Return the Fortran integer index for a material model type.

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Sentinel.has_pressure_dofs Function
julia
has_pressure_dofs(::AbstractMaterialModel) -> Bool

Return true if the material model includes pressure degrees of freedom.

  • Incompressible models (1, 2, 5, 6, 7) use elemental pressure DOFs for the mixed formulation.

  • Poroelastic (4) uses nodal pressure DOFs.

  • Compressible (3) has no pressure DOFs.

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Sentinel.pressure_dof_type Function
julia
pressure_dof_type(::AbstractMaterialModel) -> Symbol

Return :elemental or :nodal to indicate pressure DOF placement. Returns :none for models without pressure DOFs.

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Sentinel.uses_fiber_directions Function
julia
uses_fiber_directions(::AbstractMaterialModel) -> Bool

Return true if the material model requires a fiber direction field (e.g., from DTI).

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Material Data ​

Sentinel.Material Type
julia
Material

Complete material description for a single zone, including all properties, error tracking, and multi-mesh parameterization. Corresponds to the Fortran material derived type.

Fields

  • model: integer model identifier (1–7), or use material_model(model) for dispatch

  • numprop: number of material properties

  • nreg: number of regularization terms

  • nummeas: number of measurement points for error analysis

  • prop: vector of SingleProperty, length numprop

  • nummtrlmesh: number of material meshes (for multi-resolution parameterization)

  • meshind: (2, numprop, nummtrlmeshstructs) — mesh index for real/imag per property

  • res8: (nummtrlmesh, 3) — resolution of each material mesh [dx, dy, dz]

  • nodval: nodal material property values for tet mesh, (nn, numprop) complex

  • psource: pressure source for poroelastic model, (np, numdispsets) complex

  • rhop, rhoa, rhof: poroelastic density parameters (model=4 only)

  • toterrinit, totalerror, disperror, toterrprev: error tracking scalars

  • numerrupdate: iteration counter for error updates

  • calcvar: flag — compute property estimate variances

  • errinit: flag — whether toterrinit has been initialized

  • regerror: per-regularization-term error, length nreg

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Sentinel.SingleProperty Type
julia
SingleProperty

Stores the values of one scalar material property across all parameter nodes/elements. Corresponds to the Fortran singleproperty derived type.

Fields

  • basis: parameterization basis — 1 = nodal, 2 = elemental

  • nvpp: number of values per point (e.g., 3 for power-law: θ₀_r, α_r, ω₀_r)

  • scalar: 4-element scaling vector [s_r, s_i, α_r, α_i] for power-law normalization

  • npr: number of parameter points for the real part

  • npi: number of parameter points for the imaginary part

  • rvalue: real property values, size (npr, nvpp) — stored as normalized values

  • ivalue: imaginary property values, size (npi, nvpp) — stored as normalized values

  • rvariance: variance of real estimates, size (npr, nvpp)

  • ivariance: variance of imaginary estimates, size (npi, nvpp)

  • rupdate: flags indicating updated real parameter points, length npr

  • iupdate: flags indicating updated imaginary parameter points, length npi

  • rcount: update counts for real parameter points, length npr

  • icount: update counts for imaginary parameter points, length npi

  • rgp: number of Gauss points affected by each real property value, length npr

  • igp: number of Gauss points affected by each imaginary property value, length npi

  • rmesh: index of the material mesh that real property is defined on (1-based)

  • imesh: index of the material mesh that imaginary property is defined on (1-based)

Notes

The scalar vector enables dimensionless parameterization:

  • scalar[1] scales real values: μ_r = scalar[1] * rvalue[j, k]

  • scalar[2] scales imag values: μ_i = scalar[2] * ivalue[j, k]

  • scalar[3], scalar[4] are α scalings for power-law frequency dependence

For non-power-law (standard) properties, nvpp = 1 and only one set of values exists. For power-law properties, nvpp = 3 with values [θ₀, α, ω₀] per point.

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