Materials

Materials are declared under model.material. The section has two parts: a blocks mapping that assigns a material name to each element block, and one sub-dictionary per material name holding its properties.

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

The key neohookean in blocks must match a sibling key holding the property dictionary. The material name is matched after lowercase(strip(...)), so capitalisation and surrounding whitespace do not matter.

Meshes with more than one element block assign a material to each; see One material per element block below.

One material per element block

Each element block gets its own constitutive model and density. Name every block in blocks, and give each material a property dictionary:

model:
  type: solid mechanics
  material:
    blocks:
      lower: stiff
      upper: soft
    stiff:
      model: neohookean
      elastic modulus: 1.0e11
      Poisson's ratio: 0.25
      density: 1000.0
    soft:
      model: neohookean
      elastic modulus: 1.0e9
      Poisson's ratio: 0.25
      density: 1000.0

The value in blocks is a material label, and the dictionary it names carries a model key selecting the constitutive model. The label is arbitrary, which is what lets two blocks share a model with different properties — as stiff and soft do above.

If you omit model, the label itself is read as the model name. That is the older spelling and still works:

    blocks:
      my_block: neohookean
    neohookean:
      elastic modulus: 10.0e9
      Poisson's ratio: 0.25
      density: 1000.0

ERROR: [model.material.blocks] does not assign a material to "upper". Every
       element block in the mesh needs a material; there is no default.
       Mesh blocks: lower, upper.

ERROR: [model.material.blocks] assigns a material to "uppr" (did you mean
       "upper"?), which is not an element block in the mesh.
       Mesh blocks: lower, upper.

Material models

Elastic constants

Any two independent constants define an isotropic elastic material. Each YAML key below is an alias for the canonical name that ConstitutiveModels.jl expects; keys are matched case-insensitively.

Plasticity constants

Seth–Hill exponents

Density

density is read from the material dictionary and is not passed through the elastic-constant alias table; it is forwarded to ConstitutiveModels under its own name, which requires every model to carry density as the first entry of its property vector. That single copy is what the mass matrix and the explicit stable-time-step estimate both read — the physics object does not store a second one. If density is missing or zero, Carina emits a warning and continues with 0.0:

[WARNING] No density specified for material "neohookean"; using 0.0.

That is legal for quasi static, which never forms a mass matrix. For newmark and central difference it is a hard error, because a zero density makes the lumped mass matrix singular — every acceleration would be 0/0, and the run would fill the output file with NaN rather than report the missing property:

ERROR: The material assigned to block "cube" has density 0.0, but a dynamic
       time integrator requires a mass matrix. Set `density` in the
       [model.material] property dict.

Mixed materials and internal-variable output

Blocks may have different numbers of internal state variables — an elastic block next to a J2 plasticity block is fine. Per-block element output of internal variables works in that case, because Exodus element variables are written per block; the declared set of names is the union across blocks.

Nodal recovery of internal variables is different. It averages a quadrature-point quantity onto nodes, and a node on a block interface belongs to both blocks. If the blocks disagree about what a given state variable is — eqps in the plastic block, nonexistent in the elastic one — the projection has no meaning, so Carina refuses rather than averaging over one side:

ERROR: Nodal recovery of internal variables requires every element block to have
       the same state variables, but they differ: "lower" => []; "upper" =>
       [Fp_xx, ..., eqps]. Nodes on a block interface belong to both blocks, so
       there is no meaningful value to project there. Set `output.recovery:
       none`, or turn off `output.internal variables`; per-block element output
       of internal variables is unaffected.

Stress and deformation-gradient recovery are unaffected — those exist for every material.

Unknown property keys are ignored

Any key in the material dictionary that is neither density nor a recognised alias is dropped with a warning rather than an error:

[WARNING] Unknown material property key "youngs_modulus"; ignoring.

This is easy to miss in a long log. If a material behaves as though a property were never set, check for this warning first — note the example above uses underscores, which are not an accepted alias (Carina's keys use spaces).

The one case that cannot be missed is density, since misspelling it leaves the density at 0.0 and a dynamic run then aborts outright.

Example

model:
  type: solid mechanics
  material:
    blocks:
      specimen: j2 plasticity
    j2 plasticity:
      elastic modulus: 70.0e9
      Poisson's ratio: 0.36
      density: 2700.0
      yield stress: 250.0e6
      hardening modulus: 0.7e9