Published Paper

Inserted: 23 mar 2025
Last Updated: 6 oct 2025

Journal: Journal of Elasticity
Volume: 157
Pages: article 71
Year: 2025
Doi: 10.1007/s10659-025-10161-5

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.

Keywords: linearized elasticity, edge dislocations, Wedge Disclinations, Airy Stress Function, Incompatible Kinematics

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