Morphogenesis in plasticity: gradients, dislocation patterns & deformation bands - in recognition of Nasr Ghoniem’s research contributions

A personal, but quite general viewpoint on current morphogenic plasticity developments is given by elaborating on dislocation patterning and deformation bands with an eye on Nasr Ghoniem’s pioneering contributions to material instabilities. It is based on the gradient approach advocated by the author in the early 1980s and subsequently pursued by him and his co-workers, as well as other leading scientists, including Ghoniem himself. Since the physical origin of plastic flow in metals is due to the existence of dislocations, a brief discussion on the removal of classical elasticity singularities for this type of line defects is provided based on a gradient modification of Hooke’s law and its extension to also include fractional and fractal effects. The article will thus first briefly revisit early efforts on pattern-forming instabilities in plasticity and then discuss the need for combined gradient-stochastic models to capture plastic heterogeneity phenomena at small scales. It will continue with listing easy-to-use fractional/fractal dislocation solutions for potential implementation to respective dislocation-based computer simulations and conclude with a few remarks on possible extensions of the Laplacian-based gradient approach described herein to other multiscale/multiphysics phenomena. The last topic is an open issue that has not been pursued as yet in the material physics and mechanics community. Even though some of our new unpublished results are preliminary and sporadically shared with the community in conference presentations available at the internet, it is hoped that they can still inspire a much-needed collective collaboration and more elaborate interdisciplinary studies in the near future.