Multiscale Plasticity: Reduction or Emergence?

During the twentieth century, plasticity, as an example of inelastic deformation of materials, has grown to become a distinct field in solid mechanics. As a research topic it combines material science with mathematical modelling at a hierarchy of length scales, and encompasses dislocations as well as tensorial constitutive equations. Because of its predictive powers in engineering, plasticity models have become a standard ingredient of an engineer's toolbox, but do we really understand what it is? This article looks back at plasticity from a more philosophical point of view with the aim of unraveling the fabric of plasticity. Does the current hierarchy of theories provide a reductionist explanation? Or rather, does it have a multiscale structure that expresses the emergent phenomena that are contained within plasticity? The conclusion of these considerations turns out to be that the challenge is still ahead of us.