The Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hy- pothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus ob- tained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with stan- dard Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.
On the Kirchhoff-Love Hypothesis (Revised and Vindicated)
Ozenda, Olivier;Virga, Epifanio G.
2021-01-01
Abstract
The Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hy- pothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus ob- tained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with stan- dard Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
