Asymptotic Properties of the Nitzberg-Mumford Variational Model for Segmentation with Depth

2006 ◽  
pp. 75-84 ◽  
Author(s):  
Giovanni Bellettini ◽  
Riccardo March
Keyword(s):  
Asymptotic Properties ◽  
Variational Model

A Multiscale Variational Model for Image Decomposition

2014 ◽  
Vol 35 (5) ◽  
pp. 1190-1195
Author(s):  
Jian Bai ◽  
Xiang-chu Feng ◽  
Xu-dong Wang
Keyword(s):  
Image Decomposition ◽  
Variational Model

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe 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 $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis 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 obtained 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 standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

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