Isotropic materials

Isotropic materials are the simplest and most widely used type of materials. Isotropic materials have material properties that are independent of direction. In other words, an isotropic material's properties are the same in any or all directions.

For an isotropic material, the components of the elastic constant tensor are the same for all orientations. The isotropic tensor of elastic constants, cijkl, has only two independent constants and can be written as:

The constants, λ and μ are called the Lame constants and δij is the Kronecker delta function. The constant μ is also the shear modulus and is frequently designated as G. It is common to express the elastic constant matrix in terms of the elastic modulus, E, and Poisson's ratio, ν.

The relationships between the various commonly used constants for isotropic materials are summarized in the following table.

To fully characterize an isotropic material, a coefficient of thermal expansion, α, is required to compute thermal strains. The thermal strains in an isotropic material are computed from:

ΔT is the difference between the material temperature and the strain-free reference temperature.

See Thermal material properties for more information on specifying thermal properties for orthotropic materials.

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Understanding stress-strain yield stress input for Samcef

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Isotropic Material Definition dialog box (Simcenter Samcef Structure)

Viscoelastic properties in the Material dialog box (Simcenter Samcef)

Viscoplastic properties in the Material dialog box (Simcenter Samcef)

Yield criterion in the Elastoplastic Material dialog box (Simcenter Samcef)

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