Shear localization in semi-solid deformation: A bifurcation theory approach

Considering the granular nature of the semi-solid deformation, a new criterion for the onset of instability in the semi-solid materials was developed, which is capable of incorporating the thixotropic behavior, Reynold's dilatancy and the internal friction between agglomerates. It is based on the bifurcation theory approach and on the Pan analysis which shows that the onset of instability in rate-dependent materials can be identified on the basis of the rate-independent localization criterion. The localization criterion correlates the critical net hardening modulus to strain hardening as well as to strain rate hardening. The results reveal that the localization is inhibited when the fraction of solid skeleton is lower than a critical value.