Special Session 124: Mathematical methods for heterogeneous media

Variational formulation of planar linearized elasticity with incompatible kinematic
Marco Morandotti
Politecnico di Torino
Italy
Co-Author(s):    Pierluigi Cesana and Edoardo Fabbrini
Abstract:
We address mechanical equilibrium in the planar strain regime for systems with incompatible kinematic from a variational standpoint. We show that, for non-simply connected domains, the equilibrium problem for a non-liftable strain-stress pair can be reformulated as a well-posed minimization problem for the Airy potential. We characterize the additional compatibility conditions on the internal boundaries of the domain as Volterra dislocations or disclination. Finally, we establish that the minimization problem for the Airy potential can be reduced to a finite-dimensional optimization involving cell formulas.