Variational formulation of planar linearized elasticity with incompatible kinematics
Optimization and Control
2025-03-25 v1
Abstract
We present a variational characterization of mechanical equilibrium in the planar strain regime for systems with incompatible kinematics. For non-simply connected domains, we show that the equilibrium problem for a non-liftable strain-stress pair can be reformulated as a well-posed minimization problem for the Airy potential of the system. We characterize kinematic incompatibilities on internal boundaries as rotational or translational mismatches, in agreement with Volterra's modeling of disclinations and dislocations. Finally, we establish that the minimization problem for the Airy potential can be reduced to a finite-dimensional optimization involving cell formulas.
Cite
@article{arxiv.2503.18053,
title = {Variational formulation of planar linearized elasticity with incompatible kinematics},
author = {Pierluigi Cesana and Edoardo Fabbrini and Marco Morandotti},
journal= {arXiv preprint arXiv:2503.18053},
year = {2025}
}