In determining the calculations for the cellular structures model, the following assumptions have been made:
The cell structure is uniform and perfect (i.e. cell walls and lattice struts have uniform thickness, all cells are the same size, and the cell geometry for foams and lattices is isotropic). The exception is expanded honeycombs, where 1/3 of the cell walls have double thickness.
For anisotropy present in honeycombs the relevant property is defined as in-plane or through-thickness. Also for expanded honeycombs where there is anisotropy within the plane the lowest value is taken (i.e. for shear modulus).
The gas 'contained' within the structure is air.
The equations used by the open-cell foam model are summarized below. For more information on the derivation of these equations see derivation of calculations.
For a definition of the symbols used, see symbols.
Young's modulus
Shear modulus
Bulk modulus
Poisson's ratio
Compressive strength
Yield strength
Tensile strength
Flexural strength
Fracture toughness
l / a is the ratio of the cell size of the foam to the flaw size in the material. The default value for l / a = 10.
Thermal conductivity
where thermal conductivity of gas
Thermal expansion and specific heat capacity are the same as the bulk material
Electrical resistivity
Dielectric constant
Dielectric loss tangent is set equal to that for the bulk material
The equations used by the closed-cell foam model are summarized below. For more information on the derivation of these equations see derivation of calculations.
For a definition of the symbols used, see symbols.
Young's modulus
Shear modulus
Bulk modulus
Poisson's ratio
Compressive strength
Yield strength
Tensile strength
Flexural strength
Fracture toughness
l / a is the ratio of the cell size of the foam to the flaw size in the material. The default value for l / a = 10.
Thermal conductivity
where thermal conductivity of gas
Thermal expansion and specific heat capacity are the same as the bulk material
Electrical resistivity
Dielectric constant
Dielectric loss tangent is set equal to that for the bulk material
The equations used by the triangulated lattice model are summarized below. For more information on the derivation of these equations, see derivation of calculations.
For a definition of the symbols used, see symbols.
Young's modulus
Shear modulus
Bulk modulus
Poisson's ratio
Compressive strength
Yield strength
Tensile strength
Flexural strength
Fracture toughness
l / a is the ratio of the cell size of the foam to the flaw size in the material. Default value for l / a = 10.
Thermal conductivity
where thermal conductivity of gas
Thermal expansion and specific heat capacity are same as the bulk material
Electrical resistivity
Dielectric constant
Dielectric loss tangent is set equal to that for the bulk material
The equations used by the extruded honeycomb model are summarized below. For more information on the derivation of these equations see derivation of calculations.
For a definition of the symbols used, see symbols.
Young's modulus (in-plane)
Shear modulus
Bulk modulus
Poisson's ratio
Compressive strength
Yield strength (through-thickness)
Tensile strength (through-thickness)
Flexural strength
Fracture toughness
l / a is the ratio of the cell size of the foam to the flaw size in the material. The default value for l / a = 10 .
Thermal conductivity
where thermal conductivity of gas
Thermal expansion and specific heat capacity are the same as the bulk material
Electrical resistivity
Dielectric constant
Dielectric loss tangent is set equal to that for the bulk material
The equations used by the expanded honeycomb model are summarized below. For more information on the derivation of these equations see derivation of calculations.
For a definition of the symbols used, see symbols.
Young's modulus (in-plane)
Shear modulus
Bulk modulus
Poisson's ratio
Compressive strength
Yield strength (through-thickness)
Tensile strength (through-thickness)
Flexural strength
Fracture toughness
l / a is the ratio of the cell size of the foam to the flaw size in the material. The default value for l / a = 10.
Thermal conductivity
where thermal conductivity of gas
Thermal expansion and specific heat capacity are the same as the bulk material
Electrical resistivity
Dielectric constant
Dielectric loss tangent is set equal to that for the bulk material
Calculated Property | Bulk Material properties required by calculation |
---|---|
Density | Density |
Young's modulus | Young's modulus |
Flexural modulus | - |
Shear modulus | Young's modulus (Shear modulus required for honeycombs) |
Bulk modulus | Young's modulus |
Poisson's ratio | - |
Yield strength | Yield strength |
Tensile strength | Tensile strength |
Compressive strength | Compressive
strength Young's modulus |
Flexural strength | Yield strength Young's modulus |
Fracture toughness | Fracture toughness |
Specific heat capacity | Specific heat capacity |
Thermal expansion coefficient | Thermal expansion coefficient |
Thermal conductivity | Thermal conductivity |
Electrical resistivity | Electrical resistivity |
Dielectric constant | Dielectric constant |
Dielectric loss tangent | Dielectric loss tangent |
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