scholarly journals Second Gradient Models and Concrete Structures

2017 ◽  
pp. 185-191
Author(s):  
G. Jouan ◽  
M. Soufflet ◽  
P. Kotronis ◽  
F. Collin
Keyword(s):  
Concrete Structures ◽  
Second Gradient ◽  
Second Gradient Models ◽  
Gradient Models

scholarly journals Homogenization of frame lattices leading to second gradient models coupling classical strain and strain-gradient terms

2019 ◽  
Vol 24 (12) ◽  
pp. 3976-3999 ◽  
Author(s):  
Houssam Abdoul-Anziz ◽  
Pierre Seppecher ◽  
Cédric Bellis
Keyword(s):  
Displacement Field ◽  
Strain Gradient ◽  
Periodic Structures ◽  
Three Dimensional ◽  
Discrete Systems ◽  
Effective Energy ◽  
Classical Strain ◽  
Second Gradient ◽  
Second Gradient Models ◽  
Gradient Models

We determine in the framework of static linear elasticity the homogenized behavior of three-dimensional periodic structures made of welded elastic bars. It has been shown that such structures can be modeled as discrete systems of nodes linked by extensional, flexural/torsional interactions corresponding to frame lattices and that the corresponding homogenized models can be strain-gradient models, i.e., models whose effective elastic energy involves components of the first and the second gradients of the displacement field. However, in the existing models, there is no coupling between the classical strain and the strain-gradient terms in the expression of the effective energy. In the present article, under some assumptions on the positions of the nodes of the unit cell, we show that classical strain and strain-gradient strain terms can be coupled. In order to illustrate this coupling we compute the homogenized energy of a particular structure that we call asymmetrical pantographic structure.

scholarly journals An identification method to calibrate higher-order parameters in local second-gradient models

2015 ◽  
Vol 343 (7-8) ◽  
pp. 443-456 ◽  
Author(s):  
Simon Raude ◽  
Richard Giot ◽  
Alexandre Foucault ◽  
Roméo Fernandes
Keyword(s):  
Higher Order ◽  
Order Parameters ◽  
Identification Method ◽  
Second Gradient ◽  
Second Gradient Models ◽  
Gradient Models
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