Mathematics

The field theory of elastic bodies undergoing finite deformations (classical finite elasticity) is the point of departure for a variety of broader continuum field theories.  I will indicate a variety of approaches toward broadening finite elasticity with the common goal of including the effects of geometrical changes at more than one length scale.  My presentation will provide a detailed description of one such broadening, "elasticity with disarrangements" (Deseri & Owen, 2003), based on the multiscale geometry of structured deformations (Del Piero & Owen, 1993).  Here, the term "disarrangements" denotes non-smooth submacroscopic geometrical changes such as the formation of voids and the occurrence microscopic slips.  The talk will include an application of elasticity with disarrangements to the description of granular bodies ("elastic aggregates"), including the formulation of variational problems in the context of statics.  Central to a variety of applications of elasticity with disarrangements is the notion of "disarrangement phase", and I will discuss a notion of "stable disarrangement phase" that connects elasticity with disarrangements to theories of masonry-like (no-tension) materials.