Before revision: A substitution of the incremental constitutive law (1) and of the strain compatibility ( 3 ) into the continuity of incremental tractions ( 2 ) yields the necessary condition for strain localization: Since the second-order tensor defined for every vector as is the so-called ‘acoustic tensor’ , defining the condition of propagation of acceleration waves, we can conclude that the condition for strain localization coincides with the condition of singularity (propagation at null speed) of an acceleration wave.
After revision: A substitution of the incremental constitutive law (1) and of the strain compatibility ( 3 ) into the continuity of incremental tractions ( 2 ) yields the necessary condition for strain localization: Since the second-order tensor defined for every vector as is the so-called 'acoustic tensor' , defining the condition of propagation of acceleration waves, we can conclude that the condition for strain localization coincides with the condition of singularity (propagation at null speed) of an acceleration wave.