II.1.10.8 Combined strain criterion (2D)

The criterion is a strain criterion that uses a combination of several components of the strain tensor. This criterion can be considered as a Tsai-type criterion adapted to strain tensor. The combined strain failure index is calculated as follows:

in which the ${ϵ}_{11}^{\text{all}}$ and ${ϵ}_{22}^{\text{all}}$ allowables depend on the sign of ${ϵ}_{11}^{\text{Mech}}$ and ${ϵ}_{22}^{\text{Mech}}$ respectively. (The criterion is calculated from the mechanical or equivalent strain tensor components.) Ply or laminate passes the failure criterion if the two following conditions are respected:

The reserve factor is calculated as follows:

and the strength ratio is given by:

This criterion is referred to as “CombStrain2D” criterion in FeResPost.

FeResPost proposes a second version of the criterion where the “total” strain tensor $\left\{ϵ\right\}$ is used instead of the mechanical strain tensor $\left\{{ϵ}^{\text{Mech}}\right\}$. This version of the criterion is referred to as “CombTotalStrain2D” criterion in FeResPost.