Cauchy-Green

Definition

Name	Mesh>Cauchy-Green
Type	Stretching
Defined in	Faces

Stretching energy density is calculated as [Bra92, MFDSWS20, SOdlC12]:

\[U = \frac{E\,h}{2}\frac{1}{1+\nu}\left[Tr\left(C^2\right) + \frac{\nu}{1-\nu}\left(Tr C\right)^2\right]\]

where \(E\) is the 3D Young modulus constant, \(h\) is the membrane thickness, \(\nu\) is the Poisson ratio, and

\[C = \frac{1}{2}\left(FQ-I\right)\]

with \(F\) being the Gram matrix for the strained triangle, \(Q\) being the inverse of the Gram matrix for the unstretched triangle, and \(I\) is the identity matrix.

Python calling

evolver.add_force("Mesh>Cauchy-Green", {
    "E": {"1": str(E_value)},  # Elastic constant
    "h": {"1": str(h_value)},  # Thickness
    "nu": {"1": str(nu_value)} # Poisson ratio
})