My research is on the structural optimization of fibre-reinforced composite material (transversely isotropic material). I am currently working on a homogenization method for attaining the effective properties of fibre-reinforced composite materials. A lot of literature is available on how to compute the effective properties of composite material using homogenization.

However, I would like to understand if the attained effective properties of composite material is a convex function or not?

Considering only the linear (elastic) regime, how can one prove that composite's effective properties using the homogenization method are convex function or not?

I would be grateful if someone can help me to understand how I can approach the above problem or direct me to the relevant paper (if it exists).

Thank you for your time and attention.

  • $\begingroup$ Can you share more details or a reference for the homogenization method you are using? Since you want to know whether some function is convex, perhaps sharing the function you mean would be useful. $\endgroup$ Aug 27, 2021 at 3:53
  • $\begingroup$ Thank you for your reply, Brandon. The attached reference paper uses the asymptotic homogenization method to evaluate homogenized effective elasticity (i.e. stiffness) tensor ( Please refer to section 2.1 ). Please let me know if I still lack the necessary details while asking my query? $\endgroup$ Aug 28, 2021 at 11:24
  • $\begingroup$ sciencedirect.com/science/article/pii/… $\endgroup$ Aug 28, 2021 at 11:24
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    – Tyberius
    Dec 2, 2021 at 17:23