Three-Dimensional Effects of Solder Joints in Micro-Scale BGA Assembly

1999 ◽  
Vol 121 (4) ◽  
pp. 297-302 ◽  
Author(s):  
J. Zhu
Keyword(s):  
Finite Element ◽  
Creep Strain ◽  
Solder Joints ◽  
Three Dimensional ◽  
Constitutive Law ◽  
Computational Time ◽  
Stress Strain ◽  
Micro Scale ◽  
Dimensional Effects ◽  
Solder Balls

Micro-scale BGA has attracted more and more interest due to their high performance/area ratio. This technology is especially important for mobile personal equipment, such as cellular phones and laptop computers. With the decrease of solder ball sizes, the reliability problem becomes the major concern for the package design, which requires more powerful tools to address this issue. Finite element method is a useful tool for packaging design and analysis. For some BGAs, the critical solder balls are sometimes not located at a symmetric plane and the deformations in three directions will affect the distribution of stress/strain in these solder balls. Therefore, a full three-dimensional analysis is necessary to address these effects. However, it is almost impossible to run a three-dimensional single finite element model to consider all design details even with simplified material properties, not to mention creep constitutive law. Therefore, the global/local modeling technique provides an alternate way, which can simplify the modeling work’ Significantly, reduce the computational time, and enhance the crucial information at critical locations. In this study, the global/local technique was used to study a micro-scale BGA assembly and to investigate the three-dimensional effects of stress/strain distribution inside the solder joints. It was found that the maximum creep strain is not located at the plane passing through the package center and solder joint axis. It was also found that the position of maximum creep strain will shift during first several cycles, but will stabilize after the fourth cycle. This result is also helpful in evaluating the reliability of the critical solder joints in micro-scale BGA assemblies.

Numerical analysis of the dynamic interaction between a non-pneumatic mechanical elastic wheel and soil containing an obstacle

2016 ◽  
Vol 231 (6) ◽  
pp. 731-742 ◽  
Author(s):  
Xianbin Du ◽  
Youqun Zhao ◽  
Qiang Wang ◽  
Hongxun Fu
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Interaction Model ◽  
Dynamic Interaction ◽  
Constitutive Law ◽  
Elastic Wheel ◽  
Non Linear ◽  
Dimensional Finite Element ◽  
Mechanical Elastic Wheel ◽  
Three Dimensional Finite Element

An innovative non-pneumatic tyre called the mechanical elastic wheel is introduced; significant challenges exist in the prediction of the dynamic interaction between this mechanical elastic wheel and soil containing an obstacle owing to its highly non-linear properties. To explore the mechanical properties of the mechanical elastic wheel and the soil, the finite element method is used, and a non-linear three-dimensional finite element wheel–soil interaction model is also established. Hyperelastic incompressible rubber, which is one of the main materials of the mechanical elastic wheel, is analysed using the Mooney–Rivlin model. The modified Drucker–Prager cap plasticity constitutive law is utilized to describe the behaviour of the soil, and the obstacle is represented as an elastic body. Simulations with different rotational speeds of the mechanical elastic wheel were conducted. The stress distribution and the displacement of the mechanical elastic wheel and the soil were obtained, and the effects of different rotational speeds on the displacement, the velocity and the acceleration of the hub centre are presented and discussed in detail. These results can provide useful information for optimization of the mechanical elastic wheel.

Plastic Deformation Theory Application in Finite Element Analysis

2012 ◽  
Vol 594-597 ◽  
pp. 2723-2726
Author(s):  
Wen Shan Lin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Deformation Theory ◽  
Three Dimensional ◽  
Constitutive Laws ◽  
Constitutive Law ◽  
Element Analysis ◽  
Finite Element Program ◽  
Theory Of Plasticity ◽  
Element Program

In the present study, the constitutive law of the deformation theory of plasticity has been derived. And that develop the two-dimensional and three-dimensional finite element program. The results of finite element and analytic of plasticity are compared to verify the derived the constitutive law of the deformation theory and the FEM program. At plastic stage, the constitutive laws of the deformation theory can be expressed as the linear elastic constitutive laws. But, it must be modified by iteration of the secant modulus and the effective Poisson’s ratio. Make it easier to develop finite element program. Finite element solution and analytic solution of plasticity theory comparison show the answers are the same. It shows the derivation of the constitutive law of the deformation theory of plasticity and finite element analysis program is the accuracy.

scholarly journals Field Variable Associations With Scratch Orientation Dependence of UHMWPE Wear: A Finite Element Analysis

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Matthew C. Paul ◽  
Liam P. Glennon ◽  
Thomas E. Baer ◽  
Thomas D. Brown
Keyword(s):  
Finite Element ◽  
Computational Models ◽  
Three Dimensional ◽  
Element Model ◽  
Field Variable ◽  
Orientation Dependence ◽  
Normal Strain ◽  
Stress Strain ◽  
Element Analysis ◽  
Local Direction

Scratches on the metal bearing surface of metal-on-polyethylene total joint replacements have been found to appreciably accelerate abrasive/adhesive wear of polyethylene, and constitute a source of the considerable variability of wear rate seen within clinical cohorts. Scratch orientation with respect to the local direction of relative surface sliding is presumably a factor affecting instantaneous debris liberation during articulation. A three-dimensional local finite element model was developed, of orientation-specific polyethylene articulation with a scratched metal counterface, to explore continuum-level stress/strain parameters potentially correlating with the orientation dependence of scratch wear in a corresponding physical experiment. Computed maximum stress values exceeded the yield strength of ultra-high molecular weight polyethylene (UHMWPE) for all scratch orientations but did not vary appreciably among scratch orientations. Two continuum-level parameters judged most consistent overall with the direction dependence of experimental wear were (1) cumulative compressive total normal strain in the direction of loading, and (2) maximum instantaneous compressive total normal strain transverse to the sliding direction. Such stress/strain metrics could be useful in global computational models of wear acceleration, as surrogates to incorporate anisotropy of local metal surface roughening.

Nonlinear Incompressible Finite Element for Simulating Loading of Cardiac Tissue—Part II: Three Dimensional Formulation for Thick Ventricular Wall Segments

1988 ◽  
Vol 110 (1) ◽  
pp. 62-68 ◽  
Author(s):  
A. Horowitz ◽  
I. Sheinman ◽  
Y. Lanir
Keyword(s):  
Finite Element ◽  
Cardiac Tissue ◽  
Large Deformations ◽  
Three Dimensional ◽  
Shear Stiffness ◽  
Cardiac Mechanics ◽  
Nonlinear Finite Element ◽  
Constitutive Law ◽  
Ventricular Wall ◽  
Collagenous Matrix

A three dimensional incompressible and geometrically as well as materially nonlinear finite element is formulated for future implementation in models of cardiac mechanics. The stress-strain relations in the finite element are derived from a recently proposed constitutive law which is based on the histological composition of the myocardium. The finite element is formulated for large deformations and considers incompressibility by introducing the hydrostatic pressure as an additional variable. The results of passive loading cases simulated by this element allow to analyze the mechanical properties of ventricular wall segments, the main of which are that the circumferential direction is stiffer than the longitudinal one, that its shear stiffness is considerably lower than its tensile and compressive stiffness, and that, due to its mechanically prominent role, the collagenous matrix may affect the myocardial perfusion.

scholarly journals The Biomechanical Effect of Different Denture Base Materials on the Articular Disc in Complete Denture Wearers: A Finite Element Analysis

2015 ◽  
Vol 3 (3) ◽  
pp. 455-461
Author(s):  
Mohamed M. El-Zawahry ◽  
Ahmed A. El-Ragi ◽  
Mohamed I. El-Anwar ◽  
Eman Mostafa Ahmed Ibraheem
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Base Material ◽  
Acrylic Resin ◽  
Complete Denture ◽  
Articular Disc ◽  
Stress Strain ◽  
Element Analysis ◽  
Denture Base ◽  
Base Materials

AIM: The objective of the present study was to evaluate the effect of different denture base materials on the stress distribution in TMJ articular disc (AD) in complete denture wearers.MATERIAL AND METHODS: Two three dimensional Finite Element (FEA) models of an individual temporomandibular joint (TMJ) were built on the basis CT scan. The FEA model consisted of four parts: the condyle, the articular disc, the denture base, and the articular eminence skull. Acrylic resin and chrome-cobalt denture base materials were studied. Static loading of 300N was vertically applied to the central fossa of the mandibular second premolar. Stress and strain were calculated to characterize the stress/strain patterns in the disc.RESULTS: The maximum tensile stresses were observed in the anterior and posterior bands of (AD) on load application with the two denture base materials. The superior boundaries of the glenoid fossa showed lower stress than those on the inferior boundaries facing the condyle.CONCLUSIONS: Within the limitations of the present study it may be concluded that: The denture base material may a have an effect in stress-strain pattern in TMJ articular disc. The stiffer denture base material, the better the distribution of the load to the underling mandibular supporting structures & reducing stresses induced in the articular disc.

scholarly journals Stress-strain state of a three-layer cylindrical shell under internal axisymmetric pulse load

2020 ◽  
pp. 145-151
Author(s):  
Viktor Gaidaichuk ◽  
Kostiantyn Kotenko
Keyword(s):  
Finite Element ◽  
Cylindrical Shell ◽  
Strain State ◽  
Layer Structure ◽  
Three Dimensional ◽  
Pulse Load ◽  
Geometrical Parameters ◽  
Time Interval ◽  
Stress Strain ◽  
Stress Strain State

The problem of dynamic deformation of a three-layer cylindrical shell under non-stationary loads in the case of rigid clamping of the shell ends is considered. The article presents the results of assessing the stress-strain state of a three-layer cylindrical shell, taking into account its structural feature, the ratio of the sheathing thickness and the physical and mechanical characteristics of a one-piece polymer filler. Calculations were performed by software complex Nastran. The values of displacements and stresses were calculated by the algorithm of direct transient dynamic process. The step duration of the time interval was 0.0000025 s, and the total number of steps was 200. The choice of the type of three-dimensional finite element was due to obtaining more detailed and accurate calculation results. The finite element model included 19000 three-dimensional finite elements and numbered 20800 nodes. The influence of geometrical parameters of shell layers with different physical and mechanical properties of one-piece filler on the stress-strain state under axisymmetric internal impulse load is investigated. Numerical results on the dynamics of the three-layer structure, obtained by the finite element method, allow to characterize the stress-strain state of the three-layer elastic structure of the cylindrical type at any time in the studied time interval. Optimization of the shell design is recommended. Changing the ratio of the thickness of the internal and external shells of the shell significantly affects the stress-strain state of the shell and its performance. Increasing the thickness of the internal layer of the shell significantly contributes to the increase of the latter. Comparison of the given results with materials of other similar researches and positions, testify to objectivity of the made approach.

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