Strain gradient finite element model for finite deformation theory: size effects and shear bands

2020 ◽  
Vol 65 (5) ◽  
pp. 1219-1246 ◽  
Author(s):  
Yooseob Song ◽  
George Z. Voyiadjis
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Strain Gradient ◽  
Finite Deformation ◽  
Size Effects ◽  
Deformation Theory ◽  
Shear Bands ◽  
Element Model ◽  
Finite Deformation Theory

Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory

2021 ◽  
pp. 146442072110050
Author(s):  
Mohamed-Ouejdi Belarbi ◽  
Abdelhak Khechai ◽  
Aicha Bessaim ◽  
Mohammed-Sid-Ahmed Houari ◽  
Aman Garg ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Beam Element ◽  
Functionally Graded ◽  
Sandwich Beams

In this paper, the bending behavior of functionally graded single-layered, symmetric and non-symmetric sandwich beams is investigated according to a new higher order shear deformation theory. Based on this theory, a novel parabolic shear deformation function is developed and applied to investigate the bending response of sandwich beams with homogeneous hardcore and softcore. The present theory provides an accurate parabolic distribution of transverse shear stress across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the functionally graded sandwich beam without using any shear correction factors. The governing equations derived herein are solved by employing the finite element method using a two-node beam element, developed for this purpose. The material properties of functionally graded sandwich beams are graded through the thickness according to the power-law distribution. The predictive capability of the proposed finite element model is demonstrated through illustrative examples. Four types of beam support, i.e. simply-simply, clamped-free, clamped–clamped, and clamped-simply, are used to study how the beam deflection and both axial and transverse shear stresses are affected by the variation of volume fraction index and beam length-to-height ratio. Results of the numerical analysis have been reported and compared with those available in the open literature to evaluate the accuracy and robustness of the proposed finite element model. The comparisons with other higher order shear deformation theories verify that the proposed beam element is accurate, presents fast rate of convergence to the reference results and it is also valid for both thin and thick functionally graded sandwich beams. Further, some new results are reported in the current study, which will serve as a benchmark for future research.

Nonlocal finite element model for the bending and buckling analysis of functionally graded nanobeams using a novel shear deformation theory

2021 ◽  
Vol 264 ◽  
pp. 113712 ◽  
Author(s):  
Mohamed-Ouejdi Belarbi ◽  
Mohammed-Sid-Ahmed Houari ◽  
Ahmed Amine Daikh ◽  
Aman Garg ◽  
Tarek Merzouki ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Buckling Analysis ◽  
Functionally Graded

scholarly journals Curvature reduces bending strains in the quokka femur

PeerJ ◽  
2017 ◽  
Vol 5 ◽  
pp. e3100 ◽  
Author(s):  
Kyle McCabe ◽  
Keith Henderson ◽  
Jess Pantinople ◽  
Hazel L. Richards ◽  
Nick Milne
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Linear Relationship ◽  
Strain Gradient ◽  
Stance Phase ◽  
Element Model ◽  
Knee Extensors ◽  
Bending Strain ◽  
Biarticular Muscles ◽  
The Relationship

This study explores how curvature in the quokka femur may help to reduce bending strain during locomotion. The quokka is a small wallaby, but the curvature of the femur and the muscles active during stance phase are similar to most quadrupedal mammals. Our hypothesis is that the action of hip extensor and ankle plantarflexor muscles during stance phase place cranial bending strains that act to reduce the caudal curvature of the femur. Knee extensors and biarticular muscles that span the femur longitudinally create caudal bending strains in the caudally curved (concave caudal side) bone. These opposing strains can balance each other and result in less strain on the bone. We test this idea by comparing the performance of a normally curved finite element model of the quokka femur to a digitally straightened version of the same bone. The normally curved model is indeed less strained than the straightened version. To further examine the relationship between curvature and the strains in the femoral models, we also tested an extra-curved and a reverse-curved version with the same loads. There appears to be a linear relationship between the curvature and the strains experienced by the models. These results demonstrate that longitudinal curvature in bones may be a manipulable mechanism whereby bone can induce a strain gradient to oppose strains induced by habitual loading.

STRAIN GRADIENT POLYCRYSTAL PLASTICITY ANALYSIS: FE MODELING AND SYNCHROTRON X-RAY DIFFRACTION

2010 ◽  
Vol 24 (01n02) ◽  
pp. 10-17 ◽  
Author(s):  
XU SONG ◽  
SHU YAN ZHANG ◽  
ALEXANDER M. KORSUNSKY
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Strain Gradient ◽  
Deformation Behaviour ◽  
Element Model ◽  
Model Parameters ◽  
Multiple Peaks ◽  
X Ray ◽  
Polycrystal Plasticity ◽  
Meso Scale

The results of a strain gradient finite element model of polycrystalline plastic deformation in an HCP alloy were analysed in terms of orientation-related meso-scale grain groups. The predictions for meso-scale elastic strains were post-processed to construct energy dispersive diffraction peak patterns. Synchrotron X-ray polycrystalline diffraction was thereafter employed to record experimentally multiple peaks from deformed samples of Ti -6 Al -4 V alloy. Model parameters were adjusted to provide the best simultaneous match to multiple peaks in terms of intensity, position and shape. The framework provides a rigorous means of validating polycrystal plasticity finite element model. The study represents an example of the parallel development of modelling and experimental tools that is useful for the study of statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) effects on the deformation behaviour of (poly)crystals.

A Finite Deformation Theory of Viscoplasticity Based on Overstress: Part II—Finite Element Implementation and Numerical Experiments

1990 ◽  
Vol 57 (3) ◽  
pp. 553-561 ◽  
Author(s):  
I. Nishiguchi ◽  
T.-L. Sham ◽  
E. Krempl
Keyword(s):  
Finite Element ◽  
Finite Deformation ◽  
Numerical Experiments ◽  
Deformation Theory ◽  
Integration Method ◽  
Time Integration ◽  
Second Order ◽  
Time Integration Method ◽  
Finite Element Implementation ◽  
Finite Deformation Theory

A one-step time integration method is developed for the finite deformation theory of viscoplasticity based on overstress (FVBO) described in Part I. This time integration method is based on a forward gradient approximation and it leads to explicit expressions of the tangent operators suitable for finite element implementation. Numerical experiments and closed-form solutions for a hypoelastic material in homogeneous deformation states are presented. The FVBO is applied to the modeling of second-order effects in torsion. The numerical results show that a modification of the Jaumann rate and second-order terms of the inelastic rate of deformation are necessary to model the observed effects.

A finite deformation theory of strain gradient plasticity

2002 ◽  
Vol 50 (1) ◽  
pp. 81-99 ◽  
Author(s):  
K.C. Hwang ◽  
H. Jiang ◽  
Y. Huang ◽  
H. Gao ◽  
N. Hu
Keyword(s):  
Strain Gradient ◽  
Finite Deformation ◽  
Deformation Theory ◽  
Strain Gradient Plasticity ◽  
Gradient Plasticity ◽  
Finite Deformation Theory

scholarly journals Avalanches, loading and finite size effects in 2D amorphous plasticity: results from a finite element model

2015 ◽  
Vol 2015 (2) ◽  
pp. P02011 ◽  
Author(s):  
Stefan Sandfeld ◽  
Zoe Budrikis ◽  
Stefano Zapperi ◽  
David Fernandez Castellanos
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Size Effects ◽  
Finite Size ◽  
Element Model ◽  
Finite Size Effects
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