Universal measures of strength anisotropy based on local failure

Many materials are anisotropic, which means that their properties are not identical in all directions. Researchers have widely investigated measures of stiffness anisotropy but have not paid sufficient attention to measures of strength anisotropy. In this study, several universal measures of strength anisotropy are proposed by using the failure stress/strain ratio and failure energy ratio. Furthermore, a curve for 2D cases and a coloured spherical surface for 3D cases are suggested to fully characterize the strength anisotropy under any loading, such as uniaxial tension and pure shear. The degrees of strength anisotropy of several common periodic truss structures are compared, and the isoface-centred cubic (FCC) structure is found to have the smallest strength anisotropy among them. Interestingly, a periodic structure with stiffness isotropy can be easily constructed, but constructing a periodic structure with strength isotropy is almost impossible, at least for truss structures. The trend shows that when a structure has more bars with a uniformly distributed orientation, it has a smaller degree of strength anisotropy.