Ply Homogenization Calculator

Introduction

This file containts functions to calculate the ply properties based upon the the properties of the constituents.

Note

Currently it does only convert mass fraction into volume fractions and the other way around. In the future a Rule of Mixture and a Tsai honogenization function will be added.

Routines

Calculate the ply properties from the properties of the constituents.

A.J.J. Lagerweij COHMAS Mechanical Engineering KAUST 2020

homogenization.isotropic2D(E, nu)

Determine stiffness & compliance matrix of 2D isotropic material.

Parameters:
  • E (float) – Young’s modulus.
  • nu (float) – Poisson’s ratio.
Returns:

  • C (matrix) – 3D stiffness matrix in Voigt notation (6x6).
  • S (matrix) – 3D compliance matrix in Voigt notation (6x6).
homogenization.isotropic3D(E, nu)

Determine stiffness & compliance matrix of 3D isotropic material.

Parameters:
  • E (float) – Young’s modulus.
  • nu (float) – Poisson’s ratio.
Returns:

  • C (matrix) – 3D stiffness matrix in Voigt notation (6x6).
  • S (matrix) – 3D compliance matrix in Voigt notation (6x6).
homogenization.massfrac_to_volfrac(fm1, rho1, rho2)

Caluculate the volume fraction from the mass fraction.

Parameters:
  • fm1 (float) – The mass fraction of material 1 defined as, fm1 = massa 1 / massa total.
  • rho1 (float) – The density of material 1.
  • rho2 (float) – The density of material 2.
Returns:

  • fv1 (float) – The fraction material 1 is used in volume.
  • fv2 (float) – The fraction material 2 is used in volume.
homogenization.orthotropic3D(E1, E2, E3, nu12, nu13, nu23, G12, G13, G23)

Determine stiffness & compliance matrix of a 3D orthotropic material.

This notation is in Voigt notation with engineering strain \(\gamma_{12}=2\varepsilon_{12}\).

Parameters:
  • E1 (float) – Young’s modulus in 1 direction.
  • E2 (float) – Young’s modulus in 2 direction.
  • E3 (float) – Young’s modulus in 3 direction.
  • nu12 (float) – Poisson’s ratio over 12.
  • nu13 (float) – Poisson’s ratio over 13.
  • nu23 (float) – Poisson’s ratio over 23.
  • G12 (float) – Shear modulus over 12.
  • G13 (float) – Shear modulus over 13.
  • G23 (float) – Shear modulus over 23.
Returns:

  • C (matrix) – 2D stiffness matrix in Voigt notaion (6x6).
  • S (matrix) – 2D compliance matrix in Voigt notation (6x6).
homogenization.reuss(S1, S2, volf)

Calculate the compliance matrix with the Reuss limit.

This lower limit of the rule of mixtures is generaly used for the transverse stiffness \(E_l\).

Parameters:
  • S1 (matrix) – The compliance matrix of material 1.
  • S2 (float) – The compliance matrix of material 2.
  • volf (matrix) – The volume fraction of material 1.
Returns:

  • C_hat (matrix) – The stiffess matrix of the mixed material.
  • S_hat (matrix) – The compliance matrix of the mixed material.
homogenization.trans_isotropic2D(E1, E2, nu12, G12)

Determine stiffness & compliance matrix of 2D plane stress transverse isotropic material.

This notation is in Voigt notation with engineering strain \(\gamma_{12}=2\varepsilon_{12}\).

Parameters:
  • E1 (float) – Young’s modulus in 1 direction.
  • E2 (float) – Young’s modulus in 3 direction.
  • nu12 (float) – Poisson’s ratio over 12.
  • G12 (float) – Shear modulus over 13.
Returns:

  • C (matrix) – 2D stiffness matrix in Voigt notaion (3x3).
  • S (matrix) – 2D compliance matrix in Voigt notation (3x3).
homogenization.trans_isotropic3D(E1, E2, nu12, nu23, G12)

Determine stiffness & compliance matrix of 3D transverse isotropic material.

This notation is in Voigt notation with engineering strain \(\gamma_{12}=2\varepsilon_{12}\).

Parameters:
  • E1 (float) – Young’s modulus in 1 direction.
  • E3 (float) – Young’s modulus in 3 direction.
  • nu12 (float) – Poisson’s ratio over 12.
  • nu23 (float) – Poisson’s ratio over 23.
  • G13 (float) – Shear modulus over 13.
Returns:

  • C (matrix) – 2D stiffness matrix in Voigt notaion (6x6).
  • S (matrix) – 2D compliance matrix in Voigt notation (6x6).
homogenization.voigt(C1, C2, volf)

Calculate the mixed stiffness matrix with the Voigt.

This upper limit of the rule of mixtures is generaly used for the longitudional stiffness \(E_l\).

Parameters:
  • C1 (matrix) – The stiffness matrix of material 1.
  • C2 (float) – The stiffness matrix of material 2.
  • volf (matrix) – The volume fraction of material 1.
Returns:

  • C_hat (matrix) – The stiffness matrix of the mixed material.
  • S_hat (matrix) – The compliance matrix of the mixed material.
homogenization.volfrac_to_massfrac(fv1, rho1, rho2)

Caluculate the mass fraction from the volume fraction.

Parameters:
  • fv1 (float) – The volume fraction of material 1 defined as, fv1 = volume 1 / volume total.
  • rho1 (float) – The density of material 1.
  • rho2 (float) – The density of material 2.
Returns:

  • fm1 (float) – The fraction material 1 is used in mass
  • fm2 (float) – The fraction material 2 is used in mass.