femCalc - Mat

MAT, $i$ , NEOHOOK, $μ$ , $κ$ , $ρ$

Defines the Neo-Hookean slightly compressible hyperelastic material by the formula:

ψ = \frac{μ}{2} (J^{- \frac{2}{3}} I_{1} - 3) + \frac{κ}{2}  {(J - 1)}^{2}

The last parameter $ρ$ denotes the material density. Parameter $i$ denotes the block’s number.

MAT, $i$ , GENT, $μ$ , $J_{m}$ , $κ$ , $ρ$

Defines the Gent slightly compressible hyperelastic material by the formula:

ψ = - \frac{μ J_{m}}{2} \ln (1 - \frac{J^{- \frac{2}{3}} I_{1} - 3}{J_{m}}) + \frac{κ}{2} (\frac{J^{2} - 1}{2} - \ln J)

The last parameter $ρ$ denotes the material density. Parameter $i$ denotes the block’s number.

MAT, $i$ , ANISOGENT, $μ$ , $μ^{aniso}$ , $J_{m}^{aniso}$ $m$ , $κ$ , $β$ , $ρ$

Defines the anisotropic Gent slightly compressible hyperelastic material by the formula:

ψ = \frac{μ}{2} (J^{- \frac{2}{3}} I_{1} - 3) + \frac{κ}{2}  {(J - 1)}^{2} - μ^{aniso} J_{m}^{aniso} \ln (1 - {\frac{J_{4}}{J_{m}^{aniso}}}^{2})

J_{4} = \frac{I_{4} + I_{6}}{2}

I_{4} = a_{0}^{T} \cdot C a_{0}

I_{6} = g_{0}^{T} \cdot C g_{0}

where $a_{0}$ , $g_{0}$ are two fiber directions. Unit fiber directions $a_{0}$ , $g_{0}$ are defined by angle $β$ and the local coordinate system of an element. Angle $β$ has to be entered in degrees. The last parameter $ρ$ denotes the material density. Parameter $i$ denotes the block’s number .

MAT, i, NEOHOOK, μ, κ, ρ

MAT, i, GENT, μ, Jm, κ, ρ

MAT, i, ANISOGENT, μ, μaniso, Jmaniso m, κ, β, ρ

MAT, $i$ , NEOHOOK, $μ$ , $κ$ , $ρ$

MAT, $i$ , GENT, $μ$ , $J_{m}$ , $κ$ , $ρ$

MAT, $i$ , ANISOGENT, $μ$ , $μ^{aniso}$ , $J_{m}^{aniso}$ $m$ , $κ$ , $β$ , $ρ$