PATTERN-FORMATION IN PLASTICITY

The approach of gradient-dependent constitutive equations as advocated by the author and his co-workers to address pattern-forming instabilities in plastic deformation is reviewed and new results are presented for both micro- and macro-plasticity phenomena. Dislocation patterning in thin films is considered and spatial features of shear bands and interfaces are discussed with some emphasis on the interpretation and measurement of the gradient-coefficients. Following the author's original suggestion [1] first outlined in 1982 at an international symposium on ''Defects, Fracture and Fatigue,'' a number of papers have introduced an internal length scale into the form of gradient-dependent constitutive equations. This makes it possible to capture material heterogeneity and deal with mesh-size sensitivity exhibited by finite element calculations in the material softening regime for deformation, damage and dislocation problems. Moreover, it allows for the description of ''size effects'', a topic of increasing interest in the mechanics of materials community. The present paper, which is dedicated to Professor Edelen, elaborates on the above issues and it may be considered as a continuation of another contribution dedicated to Professor Eringen and published in this journal in 1992 [20].