Sixty years of configurational mechanics (1950–2010)

In the last 60 years, starting with works by Peach, Koehler and Eshelby, an original branch of continuum physics has developed that consists in providing means of evaluating the evolution of particular material zones of bodies under the action of external loadings. These zones are essentially more or less localized regions of the bodies in which irreversible changes of properties occur through a re-organization of material components. This is interpreted as changes of local configuration in the accepted view of the continuum mechanics of deformable solids. The present conspectus reviews the formidable progress achieved in this “configurational mechanics” in the period 1950–2010 from an historical and personal perspective. In this general view phenomena such as fracture, phase transformations, the presence of material heterogeneities, and more generally the expansion of structural defects of different types find a natural unified framework. Here the emphasis is placed on the original works, the various breakthroughs and their contributors, the connection with the notion of “material” force, the modern – but often unfamiliar – concept of mechanics on the material manifold, a strategy of post-processing to evaluate driving forces, and a methodology imported from mathematical physics. Unavoidable ingredients are those of Eshelby stress tensor, material momentum in dynamics, and material forces of inhomogeneity. Differing views on the type of selected approach are exposed. Although this synthesis is necessarily concise, the perused landscape is wide dealing not only with the paradigmatic case of pure elasticity but also with extensions to generalized continua, couple-field theory and anelastic behaviors of the considered materials. The most recent successful advances concern the applications to numerical schemes and mechano-biology, the former with an unexpected efficacy, and the latter to the price of a natural complexity.May the (configurational) force be with you.(adapted from the script of “Star Wars”)