Use of tensorial polynomial strength function for strength prediction in laminated polymeric composites

It has been shown recently that a strength function, expressed by a tensorial polynomial for an anisotropic material, can be only of the form

F₄(σ) + F₂(σ) + F₁(σ) ≤ 1

where F_i(σ) are the respective polynomials of order i of the σ tensor components. Some further work in this field is now presented. It will be seen that a notable simplification has been achieved, bringing down the initial number of components of an 8th rank tensor from 3⁸ = 6561 to a more managable number of 42 for orthotropic materials and 11 for the planar case. It is also shown that the three F_i(σ) polynomials cannot exist simulataneously, leading either to the known Tsai and Wu proposal or a new tensorial form. Some considerations to strength theory for isotropic materials are given as well. Finally, applicability of strength theories for composite laminates is discussed, with some suggestions for practical use.