On patterns of deformation in phase transformations and Lüders bands

Materials which contain an unstable portion in the stress-strain relation frequently exhibit patterns of deformation characterized by alternating bands of large and small deformations. Certain metals produce these deformations as they undergo plastic straining or phase transformations. A rate-dependent material law including a field of imperfections is employed in a finite element model to produce a pattern of large and small deformations which resembles those observed experimentally. An essential feature of the formulation is the inclusion of a softening branch to the stress-strain curve to trigger the localization of strains, followed by a hardening branch to arrest it