Crystal plasticity model of shear and kink bands–energetic approach

We present a continuum crystal plasticity model of a lamellar deformation substructure of shear and kink bands. An evolutionary problem for the development of a spontaneous structural inhomogeneity is formulated in the framework of energetic solutions. Conti and Theil proved that in the case of an isothermal single-slip crystal, rigid plasticity with no hardening lamellaea form an optimal microstructure. Moreover, their model predicts the existence of a boundary layer which accommodates the lamellar substructure to displacement boundary conditions. It is suggested that the width of the shear and kink bands is a compromise: the minimization of bulk energy tends to decrease their size, while the energy of the band interfaces or the inner structure of the bands opposes this tendency.