scholarly journals Finite Element studies on indentation size effect using a higher order strain gradient theory

2013 ◽  
Vol 50 (6) ◽  
pp. 863-875 ◽  
Author(s):  
Suman Guha ◽  
Sandeep Sangal ◽  
Sumit Basu
Keyword(s):  
Finite Element ◽  
Size Effect ◽  
Strain Gradient ◽  
Indentation Size Effect ◽  
Higher Order ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Indentation Size

scholarly journals 1D HERMITE ELEMENTS FOR C1-CONTINUOUS SOLUTIONS IN SECOND GRADIENT ELASTICITY

2016 ◽  
Vol 7 ◽  
pp. 33-37 ◽  
Author(s):  
Christian Liebold ◽  
Wolfgang H. Müller
Keyword(s):  
Finite Element ◽  
Size Effect ◽  
Numerical Solution ◽  
Stiffness Matrix ◽  
Gradient Elasticity ◽  
Theory Of Elasticity ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Additional Material ◽  
Hermite Finite Elements

We present a modified strain gradient theory of elasticity for linear isotropic materials in order to account for the so-called size effect. Additional material length scale parameters are introduced and the problem of static beam bending is analyzed. A numerical solution is derived by means of a finite element approach. A global C1-continuous displacement field is applied in finite element solutions because the higher-order strain energy density additionally depends on second gradients of displacements. So-called Hermite finite elements are used that allow for merging gradients between elements. The element stiffness matrix as well as the global stiffness matrix of the problem is developed. Convergence, C1-continuity and the size effect in the numerical solution is shown. Experiments on bending stiffnesses of different sized micro beams made of the polymer SU-8 are performed by using an atomic force microscope and the results are compared to the numerical solution.

Higher order nonlocal viscoelastic strain gradient theory for dynamic buckling analysis of carbon nanocones

2020 ◽  
Vol 107 ◽  
pp. 106259
Author(s):  
M.S.H. Al-Furjan ◽  
Ahmad Farrokhian ◽  
Behrooz Keshtegar ◽  
Reza Kolahchi ◽  
Nguyen-Thoi Trung
Keyword(s):  
Strain Gradient ◽  
Higher Order ◽  
Buckling Analysis ◽  
Dynamic Buckling ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Carbon Nanocones ◽  
Viscoelastic Strain
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