Cellular Structures: Assumptions and calculations

Assumptions used by model

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.

Calculations used by model

• Open-cell foam model
• Closed-cell foam model
• Triangulated lattice model
• Extruded honeycomb model
• Expanded honeycomb model
• Summary of calculated properties and data required

Open-cell foam model calculations

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

Closed-cell foam model calculations

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

Triangulated lattice model calculations

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

Extruded honeycomb model calculations

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

Expanded honeycomb model calculations

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

Summary of calculated properties and data required

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