Strain softening of materials and Luders-type deformations

Corona et al ( 2002 Int. J. Solids Struct. 39 3313 - 36) and Kyriakides and Miller ( 2000 ASME J. Appl. Mech. 67 645 - 54) pointed out that the strain-softening behaviour of materials was necessary for strain localization to occur in the materials, and the Luders-type deformations were treated as strain localization. In this case, however, the discontinuity of deformation gradient across interfaces between the sharp Luders bands and other regions outside the Luders bands was not considered. In the present paper it is shown that the strain-softening behaviour of materials ensures the non-convexity of the stress-work function of the materials, and, further on, two-phase deformations can occur in the materials. The Luders bands and other regions outside the Luders bands can be treated as two phases in equilibrium which coexist under the Maxwell stress, and the discontinuity of the deformation gradient across interfaces can be considered. As an illustration, the Luders-type deformations in fine-grained steel strips under uniaxial compression are analysed, and the Maxwell stress and inclination angle of the Luders bands are predicted which are consistent with experimental observations.