The study of elastic deformations in thin rods has recently seen renewed interest due to the close connection between these systems and coarse-grained models of widespread application in life- and material- sciences. Until now, the analysis has been restricted to the solution of equilibrium equations for continuous models characterized by constant bending and twisting elastic moduli and/or by isotropic rod section. However, more realistic models often require more general conditions: indeed this is the case whenever microscopic information issuing from atomistic simulations is to be transferred to analytic or semi-analytic coarse-grained or macroscopic models. In this talk we will show that integrable, indeed solvable, equations are obtained under quite general conditions and that regular (e.g. circular helical) solutions merge from reasonable choices of elastic stiffnesses. Moreover we will discuss the energy densities for the strained rod in order to describe the preferred static configurations and their stability. This work has been carried out in collaboration with Vincenzo Barone, Scuola Normale Superiore di Pisa (Italy); Silvana De Lillo and Gaia Lupo, Università di Perugia (Italy).
Bibliography:
[1] M. Argeri, V. Barone, S. De Lillo, G. Lupo, M. Sommacal, "Elastic rods in life- and material- sciences. A general integrable model", accepted for publication in Physica D.
[2] M. Argeri, V. Barone, S. De Lillo, G. Lupo, M. Sommacal, "Existence of energy minima for elastic thin rods in static helical configurations", accepted for publication on Theoretical and Mathematical Physics.