scholarly journals Size Dependence of Residual Thermal Stresses in Micro Multilayer Ceramic Capacitors by Using Finite Element Unit Cell Model Including Strain Gradient Effect

2013 ◽  
Vol 49 (6) ◽  
pp. 743-750
Author(s):  
W. G. Jiang ◽  
C. A. Xiong ◽  
X. G. Wu
Keyword(s):  
Finite Element ◽  
Strain Gradient ◽  
Size Dependence ◽  
Thermal Stresses ◽  
Cell Model ◽  
Unit Cell ◽  
Unit Cell Model ◽  
Multilayer Ceramic Capacitors ◽  
Gradient Effect ◽  
Multilayer Ceramic

scholarly journals Validity of Finite Element Unit Cell Model for Studying Yield Condition of Isotropic Porous Materials.

1995 ◽  
Vol 61 (591) ◽  
pp. 2435-2441
Author(s):  
Tomoyuki Sasaki ◽  
Moriaki Goya ◽  
Kiyohiro Miyagi ◽  
Shousuke Itomura ◽  
Toshiyasu Sueyoshi
Keyword(s):  
Finite Element ◽  
Porous Materials ◽  
Cell Model ◽  
Yield Condition ◽  
Unit Cell ◽  
Unit Cell Model

Strain Gradient Finite Element Analysis of Size Dependence of Thermal Stresses in Through-Silicon Vias (TSVs)

2011 ◽  
Vol 199-200 ◽  
pp. 1920-1923
Author(s):  
Wu Gui Jiang ◽  
Cheng Xu ◽  
Jian Fei Yu ◽  
Jian Shan Wang
Keyword(s):  
Finite Element ◽  
Strain Gradient ◽  
Size Dependence ◽  
Thermal Stresses ◽  
Radius Ratio ◽  
Constitutive Law ◽  
Element Analysis ◽  
Through Silicon Vias ◽  
Size Scale ◽  
Silicon Vias

Through-Silicon Vias (TSVs) technology, which is widely used in three-dimensional (3D) Microsystems packaging, has been investigated by using a strain gradient finite element method (FEM). A thermomechanical strain gradient constitutive law was embedded into the commercial software ABAQUS to consider the size dependence of thermal stresses in TSVs. Our numerical results show that when both thicknesses of SiO2 dielectric layer and Si substrate are kept to a constant, for a given via depth/radius ratio, the Mises stress decreases with the decrease in the radius above 100 nm, and then it increases markedly with the further decrease in the via radius below 100 nm, which is not consistent with the results obtained by the conventional FEM. It is also shown that as the whole size of the TSV structures is scaled down proportionally, for a given via depth/radius ratio, the peak Mises stresses are almost size scale- independent above 100 nm and exhibit a strong size scale effect below 100 nm.

Finite element analyses on bending fatigue of three-dimesional five-directional braided composite T-beam with mixed unit-cell model

2017 ◽  
Vol 52 (9) ◽  
pp. 1139-1154 ◽  
Author(s):  
Yiwei Ouyang ◽  
Baozhong Sun ◽  
Bohong Gu
Keyword(s):  
Finite Element ◽  
Cell Model ◽  
Unit Cell ◽  
Finite Element Analyses ◽  
Unit Cell Model ◽  
Joint Region ◽  
Bending Fatigue ◽  
Braided Composite ◽  
T Beam ◽  
Interior Cell

This paper reports the bending fatigue behavior of three-dimensional five-directional braided T-shaped composite from finite element analyses and experimental characterizations. The braided composite microstructure was divided into five types of unit cell models, that is, interior cell, surface cell, corner cell, interior cell in joint region, and corner cell in joint region. A user-defined material subroutine was developed to characterize the unit cells properties, damage accumulation, and failure criterion of the T-beam under different stress levels. The stiffness degradation curves and bending displacement curves were obtained from the finite element analysis to show the three stages of fatigue developments, that is, matrix cracks, interface debonding, and fiber breaking. The stress and strain concentration areas were found in the middle of the flange and the web of the T-beam composites. The high strength reinforced fibers are recommended to add in the middle of the flange and the web for improving the bending fatigue resistance. And also, we hope the mixed unit-cell model could be extended to the other braided composite structures under quasi-static or cyclic loadings.

scholarly journals Thermo-Viscoelastic Response of 3D Braided Composites Based on a Novel FsMsFE Method

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 271
Author(s):  
Jun-Jun Zhai ◽  
Xiang-Xia Kong ◽  
Lu-Chen Wang
Keyword(s):  
Finite Element ◽  
Cell Model ◽  
Structural Parameters ◽  
Thermal Relaxation ◽  
Viscoelastic Behavior ◽  
Unit Cell ◽  
Time Dependent ◽  
3D Braided Composites ◽  
Equivalent Time ◽  
Representative Unit Cell

A homogenization-based five-step multi-scale finite element (FsMsFE) simulation framework is developed to describe the time-temperature-dependent viscoelastic behavior of 3D braided four-directional composites. The current analysis was performed via three-scale finite element models, the fiber/matrix (microscopic) representative unit cell (RUC) model, the yarn/matrix (mesoscopic) representative unit cell model, and the macroscopic solid model with homogeneous property. Coupling the time-temperature equivalence principle, multi-phase finite element approach, Laplace transformation and Prony series fitting technology, the character of the stress relaxation behaviors at three scales subject to variation in temperature is investigated, and the equivalent time-dependent thermal expansion coefficients (TTEC), the equivalent time-dependent thermal relaxation modulus (TTRM) under micro-scale and meso-scale were predicted. Furthermore, the impacts of temperature, structural parameters and relaxation time on the time-dependent thermo-viscoelastic properties of 3D braided four-directional composites were studied.

A two-dimensional analytical unit cell model for redox flow battery evaluation and optimization

2021 ◽  
Vol 506 ◽  
pp. 230192
Author(s):  
Yunxiang Chen ◽  
Jie Bao ◽  
Zhijie Xu ◽  
Peiyuan Gao ◽  
Litao Yan ◽  
...  
Keyword(s):  
Cell Model ◽  
Unit Cell ◽  
Two Dimensional ◽  
Redox Flow Battery ◽  
Unit Cell Model ◽  
Flow Battery
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