Variational Approach to Ordered Structures

In 1993, an important paper by E. Kroener on the configurational forces in the theory of material defects appeared in the Proceedings of the 7nth International Symposium on Continuum Models of Discrete Systems. The paper was mainly concerned with an application of the Noether Theorem to the continuum theory of liquid crystals. From the proposed variational procedure an energy-stress tensor emerges, as one of the results. Remarkably, this tensor exactly coincides with the so-called Ericksen tensor for liquid crystals. The publication of Kroener’s paper revivified the quarrel on the physical interpretation of such a tensor ( as whether a Cauchy-like or an Eshelby-like tensor). However, independently of the controversy and of the physical interpretation of the result, the variational approach emphasized by Kroener represented a stimulating contribution toward a better understanding of the notion of configurational force versus that of physical force. The variational procedure was revisited and reproposed by others ( and among them this writer) in subsequent papers either in liquid crystals or in structured materials or in electromagnetic elastic materials. Some comments on the variational methods for introducing configurational forces are expounded hereby