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The new “modified Tsai-Hill failure criterion” introduced in Shimoda et al. ( SAMO , 2020) does not possess a convex fracture envelope for all possible set of its coefficients. An extended version of the “modified Tsai-Hill failure criterion” is introduced. The extended version encompasses several known failure criterions for the anisotropic materials. The convexity of the fracture envelope for composite materials and metallic alloys is briefly discussed. Albeit the convexity of the failure envelope is not necessary from the physical viewpoint, the convexity is favorable for the application of optimization methods.

structural and multidisciplinary optimization

Comment on “Minimization of maximum failure criterion of laminated composite shell structure by optimizing distributed-material orientation” by Shimoda M., Muramatsu Y., Tsukihara R.