Anisotropic stiffness degradation triggers onset of strain localization

In Rizzi and Loret (1997), the strain localization of elastic-plastic solids with transversely isotropic elasticity was analysed. The critical hardening modulus at the onset of strain localization has been observed to tend to zero when the elastic stiffness approaches the boundary of the domain defining its positive definiteness. We provide here an analytical explanation for this behaviour using a spectral decomposition of the elastic stiffness.