Model

The required top-level model section declares the physics and its material.

model:
  type: solid mechanics
  material:
    blocks:
      my_block: neohookean
    neohookean:
      elastic modulus: 10.0e9
      Poisson's ratio: 0.25
      density: 1000.0

type is checked but not yet dispatched on

Every example writes type: solid mechanics, and you should keep writing it. Carina builds a solid-mechanics physics object unconditionally — there is no branch on this key anywhere in the source — so omitting type produces the same run as writing it.

What the key does do is constrain you to a physics that exists. Any other value aborts:

Unknown model.type = "thermal". Supported: "solid mechanics".
Thermal and coupled physics are not implemented.

That matters more than it looks. Heat conduction and true multiphysics are design goals, not present capabilities; without this check, an input file written in anticipation of them would run as solid mechanics and report nothing.

Keys under model are validated, so materials: for material: warns before it reaches the missing-section error below.

material

The material sub-section is required and must contain a blocks mapping. See Materials for the full list of models, property keys, and aliases — including the important limitation that Carina currently applies a single material to the whole mesh.

volumetric projection

With this key the volumetric strain θ(J) is replaced, element by element, by its L² projection onto polynomials of degree 0 (constant) or 1 (linear) in the reference coordinates. This is the mean-dilatation formulation of research/tet15-p1/note.tex, the reduction of the three-field functional in the motion, the volumetric strain and the pressure with the two auxiliary fields in one discontinuous space. The formulation is intended for the TETRA15 element with linear; it runs on any element. The projection couples the quadrature points of an element, so the kernels are assembled by element; the assembled matrix keeps the sparsity of the displacement mesh.

The element has two forms, selected by volumetric form:

• split: for a material with an exact volumetric-isochoric split and a quadratic volumetric energy κ/2 θ² (currently j2 plasticity, with θ = J − 1). The volumetric energy is evaluated at the projected strain, and the isochoric response and the internal variables at the quadrature points without projection.
• general: for any material. With J̃ = θ⁻¹(Ph θ(J)), the inverse of θ applied to the projection Ph θ(J) of the pointwise θ(J), the material is evaluated at the deformation gradient F̃ = (J̃/J)^{1/3} F, whose isochoric part is that of F and whose volume ratio is J̃; its internal variables are updated there. The element is the stationarity of the integral of the stored energy W(F̃). The pressure that enters the residual is the projection of the material's mean stress at F̃ (note, section "General materials"). The element matrix and the diagonal kernels of the preconditioners are assembled in closed form, with the material's own tangent at F̃ evaluated once per quadrature point; the matrix-free action is the forward-mode derivative of the element residual along the vector.

When volumetric form is absent, the split form is used for a material with the split and the general form otherwise. general may be given for a material with the split: for j2 plasticity with volumetric strain: J - 1 the two forms give the same energy, residual, tangent and internal variables to rounding.

volumetric strain selects θ(J): log J or J - 1 (case and white space are ignored). In the general form the default is log J. The two choices give different elements, which converge to the same solution under refinement; the energies of one element differ by 5.6% at 20% strain (note, Remark "The volumetric variable is a modeling choice"). In the split form θ is the material's own volumetric strain, and the key, if present, must name it: the projected pressure κ θ̄ of the split form is the stationarity condition of κ/2 θ² written in the material's θ.

model:
  type: solid mechanics
  volumetric projection: linear
  volumetric form: general
  volumetric strain: log J
  material:
    blocks:
      cube: neohookean
    neohookean:
      elastic modulus: 1.0e9
      Poisson's ratio: 0.45
      density: 1000.0

Errors from this section

All of these abort the run at startup:

The property-dict one is the common mistake. A blocks entry such as my_block: neohookean requires a sibling key neohookean: holding the properties — the name in blocks is a reference, not a definition. The error lists the property dicts you did write, which usually makes the mismatch obvious.

The block name on the left of that entry (my_block) is checked against the element blocks in the mesh file. It is only used for the startup log line — the material is applied to the whole mesh either way — so a mistyped block name used to produce a correct-looking run with a wrong label.