Variational formulation of planar linearized elasticity with incompatible kinematics
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916660439416832 |
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| author | Cesana, Pierluigi Fabbrini, Edoardo Morandotti, Marco |
| author_facet | Cesana, Pierluigi Fabbrini, Edoardo Morandotti, Marco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18053 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational formulation of planar linearized elasticity with incompatible kinematics Cesana, Pierluigi Fabbrini, Edoardo Morandotti, Marco Optimization and Control 49J45, 49J10, 74B15 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. |
| title | Variational formulation of planar linearized elasticity with incompatible kinematics |
| topic | Optimization and Control 49J45, 49J10, 74B15 |
| url | https://arxiv.org/abs/2503.18053 |