Element Kernels

Interface

Sentinel.element_stiffness! Function

element_stiffness!(Ke, cv_disp, cv_press, cell_coords, ::AbstractMaterialModel,
                   props_at_gp, ω) -> Ke

Compute the complex element stiffness matrix Ke for one element.

Arguments

• Ke: preallocated (ndofs, ndofs) complex matrix, zeroed before entry

• cv_disp: Ferrite CellValues for displacement field (updated via reinit!)

• cv_press: Ferrite CellValues for pressure field (or nothing if not used)

• cell_coords: node coordinates for the current cell (from Ferrite)

• model: AbstractMaterialModel singleton that selects the physics kernel

• props_at_gp: material properties evaluated at each Gauss point (produced by evaluate_material_at_gauss_points)

• ω: angular frequency [rad/s]

Returns

The modified Ke matrix (also modified in-place).

Notes

Each material model must implement this method. The default fallback throws a MethodError with a descriptive message if a model hasn't been implemented yet.

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Gauss Point Material

Sentinel.GaussPointMaterial Type

GaussPointMaterial

Material properties evaluated at a single Gauss point, ready for use in element integration kernels.

Fields

• μ: complex shear modulus G* [Pa]

• κ: complex bulk modulus K* Pa

• C: full 6×6 complex stiffness tensor (for anisotropic models)

• fiber: fiber direction unit vector (for TI/orthotropic models)

• ρ: density [kg/m³]

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Sentinel.PoroelasticNodeMaterial Type

PoroelasticNodeMaterial

Material properties for one node of a tet4 poroelastic element. Properties vary nodally within the element (contrast with GaussPointMaterial which varies per Gauss point on hex27).

Fields

• G: complex shear modulus G* Pa

• lambda: complex Lamé first parameter λ* Pa

• kappa_poro: hydraulic conductivity κ [m²/(Pa·s)] — already converted from log₁₀

• eta: porosity φ (dimensionless, 0–1) (Fortran: etak)

• rhop: solid frame (drained) density [kg/m³]

• rhof: fluid density [kg/m³]

• rhoa: added (apparent) mass density [kg/m³]

The three density fields are physically constant per material zone but are embedded here so the element_stiffness! signature stays uniform with the other kernels (no extra arguments needed).

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Tet4 Helpers

Sentinel.tet4_basis Function

tet4_basis(coords) -> (dpx, dpy, dpz, vol)

Compute constant shape function gradients and element volume for a linear tetrahedron (tet4) from its 4 node coordinates.

Ports the Fortran TETBASIS subroutine from tet4.f90.

Arguments

• coords: length-4 indexable collection of node positions, each a Vec{3} or 3-element vector with [1]=x, [2]=y, [3]=z components.

Returns

• dpx::SVector{4,Float64}: ∂N_i/∂x for nodes 1–4

• dpy::SVector{4,Float64}: ∂N_i/∂y for nodes 1–4

• dpz::SVector{4,Float64}: ∂N_i/∂z for nodes 1–4

• vol::Float64: element volume (positive)

Notes

The Fortran builds the matrix H where column i = [1, x_i, y_i, z_i]ᵀ, computes its determinant dH, and extracts gradients from the adjugate: dpx[i] = Adj[i,2]/dH, dpy[i] = Adj[i,3]/dH, dpz[i] = Adj[i,4]/dH vol = |dH| / 6

Properties:

• Gradients satisfy partition-of-unity: ∑dpx = ∑dpy = ∑dpz = 0

• ∫φᵢ dΩ = vol/4 for each linear basis function

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Sentinel.voigt_strain Function

voigt_strain(∇u::Tensor{2,3}) -> SVector{6, Float64}

Compute the Voigt notation strain vector from the displacement gradient: ε = [∂u/∂x, ∂v/∂y, ∂w/∂z, ∂u/∂y+∂v/∂x, ∂u/∂z+∂w/∂x, ∂v/∂z+∂w/∂y]

This is the symmetric part of ∇u in Voigt notation.

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