Strain Gradient Models for Growing Solid Bodies

2020 ◽  
pp. 281-302
Author(s):  
Zineeddine Louna ◽  
Ibrahim Goda ◽  
Jean-François Ganghoffer
Keyword(s):  
Strain Gradient ◽  
Solid Bodies ◽  
Gradient Models

Aifantis versus Lam strain gradient models of Bishop elastic rods

2019 ◽  
Vol 230 (8) ◽  
pp. 2799-2812 ◽  
Author(s):  
R. Barretta ◽  
S. Ali Faghidian ◽  
F. Marotti de Sciarra
Keyword(s):  
Strain Gradient ◽  
Elastic Rods ◽  
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 Finite-deformation second-order micromorphic theory and its relations to strain and stress gradient models

2017 ◽  
Vol 25 (7) ◽  
pp. 1429-1449 ◽  
Author(s):  
Samuel Forest ◽  
Karam Sab
Keyword(s):  
Strain Gradient ◽  
Finite Deformation ◽  
Stress Gradient ◽  
Higher Order ◽  
Second Order ◽  
Stress And Strain ◽  
Dynamical Equations ◽  
Generalized Continua ◽  
Micromorphic Theory ◽  
Gradient Models

Germain’s general micromorphic theory of order [Formula: see text] is extended to fully non-symmetric higher-order tensor degrees of freedom. An interpretation of the microdeformation kinematic variables as relaxed higher-order gradients of the displacement field is proposed. Dynamical balance laws and hyperelastic constitutive equations are derived within the finite deformation framework. Internal constraints are enforced to recover strain gradient theories of grade [Formula: see text]. An extension to finite deformations of a recently developed stress gradient continuum theory is then presented, together with its relation to the second-order micromorphic model. The linearization of the combination of stress and strain gradient models is then shown to deliver formulations related to Eringen’s and Aifantis’s well-known gradient models involving the Laplacians of stress and strain tensors. Finally, the structures of the dynamical equations are given for strain and stress gradient media, showing fundamental differences in the dynamical behaviour of these two classes of generalized continua.

scholarly journals A novel efficient mixed formulation for strain‐gradient models

2018 ◽  
Author(s):  
Stefanos‐Aldo Papanicolopulos ◽  
Fahad Gulib ◽  
Aikaterini Marinelli
Keyword(s):  
Strain Gradient ◽  
Mixed Formulation ◽  
Gradient Models
Sign in / Sign up

Export Citation Format

Share Document