Thermomechanical Finite Element Analysis of Problems in Electronic Packaging Using the Disturbed State Concept: Part 1—Theory and Formulation

1998 ◽  
Vol 120 (1) ◽  
pp. 41-47 ◽  
Author(s):  
C. Basaran ◽  
C. S. Desai ◽  
T. Kundu
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Electronic Packaging ◽  
Constitutive Models ◽  
Cyclic Behavior ◽  
Element Analysis ◽  
Theoretical Formulation ◽  
Finite Element Procedure ◽  
Reliable Design ◽  
Number Of Cycles

Accurate prediction of the thermomechanical cyclic behavior of joints and interfaces in semiconductor devices is essential for their reliable design. In order to understand and predict the behavior of such interfaces there is a need for improved and unified constitutive models that can include elastic, inelastic, viscous, and temperature dependent microstructural behavior. Furthermore, such unified material models should be implemented in finite element procedures so as to yield accurate and reliable predictions of stresses, strains, deformations, microcracking, damage, and number of cycles to failure due to thermomechanical loading. The main objective of this paper is to present implementation of such an unified constitutive model in a finite element procedure and its application to typical problems in electronic packaging; details of the constitutive model are given by Desai et al. (1995). Details of the theoretical formulation is presented in this Part 1, while its applications and validations are presented in Part 2, Basaran et al. (1998).

An Inverse Procedure for Estimating the Anand Viscoplastic Constitutive Model Parameters for Copper Free-Air Ball

2015 ◽  
Author(s):  
Sai Sudharsanan Paranjothy ◽  
Ganesh Subbarayan ◽  
Dae Young Jung ◽  
Bahgat G. Sammakia
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Low Cost ◽  
Constitutive Models ◽  
Model Parameters ◽  
Element Analysis ◽  
Pad Cratering ◽  
Free Air ◽  
Inverse Finite Element Analysis ◽  
Force Displacement

Due to its superior mechanical and electrical properties, as well as low cost, Cu is gradually replacing Au as wire bonding material. However, since copper is a stiffer material, it requires greater bonding force, which in turn increases risk of bond pad cratering and inter-layer dielectric (ILD) fracture. A critical challenge to numerically modeling the pad cratering or ILD fracture is the availability of appropriate constitutive models for the Cu free-air balls (FAB). In this work we first present rate and temperature dependent force-displacement response of micron-sized Cu FAB characterized using a custom-built high-precision microtester. From the experimental force-displacement data, Anand viscoplastic constitutive model parameters are obtained using an inverse finite element analysis procedure, where the material parameters are iterated through an automated procedure until the finite element and experimental force-displacement responses match. The constitutive model parameters to describe the FAB behavior at low and intermediate strain rates and at high temperatures are obtained and reported in this paper.

Progressive failure analysis of scarf-repaired composite laminate based on damage constitutive model

2016 ◽  
Vol 233 (2) ◽  
pp. 180-188 ◽  
Author(s):  
Qiuyi Shen ◽  
Zhenghao Zhu ◽  
Yi Liu
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Composite Laminate ◽  
Damage Mechanics ◽  
Cohesive Zone Model ◽  
Load Capacity ◽  
Three Dimensional ◽  
Zone Model ◽  
State Variables ◽  
Element Analysis

A three-dimensional finite element model for scarf-repaired composite laminate was established on continuum damage model to predict the load capacity under tensile loading. The mixed-mode cohesive zone model was adopted to the debonding behavior analysis of adhesive. Damage condition and failure of laminates and adhesive were subsequently addressed. A three-dimensional bilinear constitutive model was developed for composite materials based on damage mechanics and applied to damage evolution and loading capacity analyses by quantifying damage level through damage state variables. The numerical analyses were implemented with ABAQUS finite element analysis by coding the constitutive model into material subroutine VUMAT. Good agreement between the numerical and experimental results shows the accuracy and adaptability of the model.

A Finite Element Procedure of a Cyclic Thermoviscoplasticity Model for Solder and Copper Interconnects

1998 ◽  
Vol 120 (1) ◽  
pp. 24-34 ◽  
Author(s):  
C. Fu ◽  
D. L. McDowell ◽  
I. C. Ume
Keyword(s):  
Finite Element ◽  
Electronic Packaging ◽  
Copper Interconnects ◽  
Implicit Time ◽  
Integration Scheme ◽  
Single Element ◽  
Ofhc Copper ◽  
Computation Efficiency ◽  
Backward Euler ◽  
Finite Element Procedure

A finite element procedure using a semi-implicit time-integration scheme has been developed for a cyclic thermoviscoplastic constitutive model for Pb-Sn solder and OFHC copper, two common metallic constituents in electronic packaging applications. The scheme has been implemented in the commercial finite element (FE) code ABAQUS (1995) via the user-defined material subroutine, UMAT. Several single-element simulations are conducted to compare with previous test results, which include monotonic tensile tests, creep tests, and a two-step ratchetting test for 62Sn36Pb2Ag solder; a nonproportional axial-torsional test and a thermomechanical fatigue (TMF) test for OFHC copper. At the constitutive level, we also provide an adaptive time stepping algorithm, which can be used to improve the overall computation efficiency and accuracy especially in large-scale FE analyses. We also compare the computational efforts of fully backward Euler and the proposed methods. The implementation of the FE procedure provides a guideline to apply user-defined material constitutive relations in FE analyses and to perform more sophisticated thermomechanical simulations. Such work can facilitate enhanced understanding thermomechanical reliability issue of solder and copper interconnects in electronic packaging applications.

Analytical and Numerical Predictions of Thermoelastic Properties of Carbon Single-Walled Nanotubes

Aerospace ◽  
2005 ◽  
Author(s):  
Vinod P. Veedu ◽  
Davood Askari ◽  
Mehrdad N. Ghasemi-Nejhad
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Graphene Sheet ◽  
Effective Properties ◽  
Constitutive Models ◽  
Thermoelastic Properties ◽  
Asymptotic Homogenization ◽  
Element Analysis ◽  
Single Walled Nanotubes ◽  
Numerical Predictions

The objective of this paper is to develop constitutive models to predict thermoelastic properties of carbon single-walled nanotubes using analytical, asymptotic homogenization, and numerical, finite element analysis, methods. In our approach, the graphene sheet is considered as a non-homogeneous network shell layer which has zero material properties in the regions of perforation and whose effective properties are estimated from the solution of the appropriate local problems set on the unit cell of the layer. Our goal is to derive working formulas for the entire complex of the thermoelastic properties of the periodic network. The effective thermoelastic properties of carbon nanotubes were predicted using asymptotic homogenization method. Moreover, in order to verify the results of analytical predictions, a detailed finite element analysis is followed to investigate the thermoelastic response of the unit cells and the entire graphene sheet network.

Finite Element Analysis of Hyperelastic Components

1998 ◽  
Vol 51 (5) ◽  
pp. 303-320 ◽  
Author(s):  
D. W. Nicholson ◽  
N. W. Nelson ◽  
B. Lin ◽  
A. Farinella
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Recent Literature ◽  
Constitutive Models ◽  
Review Article ◽  
Considerable Extent ◽  
Arc Length ◽  
Numerical Techniques ◽  
Element Analysis ◽  
Current Review

Finite element analysis of hyperelastic components poses severe obstacles owing to features such as large deformation and near-incompressibility. In recent years, outstanding issues have, to a considerable extent, been addressed in the form of the hyperelastic element available in commercial finite element codes. The current review article, which updates and expands a 1990 article in Rubber Reviews, is intended to serve as a brief exposition and selective survey of the recent literature. Published simulations are listed. Rubber constitutive models and the measurement of their parameters are addressed. The underlying incremental variational formulation is sketched for thermomechanical response of compressible, incompressible and near-incompressible elastomers. Coupled thermomechanical effects and broad classes of boundary conditions, such as variable contact, are encompassed. Attention is given to advanced numerical techniques such as arc length methods. Remaining needs are assessed. This review article contains 142 references.

Nonlinear Finite Element Analysis of Super-Long Pile and Soil Interaction in Soft Soil

2011 ◽  
Vol 201-203 ◽  
pp. 1601-1605 ◽  
Author(s):  
Shang Ping Chen ◽  
Wen Juan Yao ◽  
Sheng Qing Zhu
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Soft Soil ◽  
Three Dimensional ◽  
Nonlinear Behavior ◽  
Element Model ◽  
Element Analysis ◽  
Friction Resistance ◽  
Tip Resistance ◽  
Side Friction

In this paper, a nonlinear three-dimensional finite element model for super-long pile and soil interaction is established. In this model, contact elements are applied to simulate the nonlinear behavior of interaction of super-long pile and soil. A nonlinear elastic constitutive model for concrete is employed to analyze stress-strain relation of pile shaft under the axial load and the Duncan-Chang’s nonlinear constitutive model is used to reflect nonlinear and inelastic properties of soil. The side friction resistance, axial force, pile-tip resistance, and developing trend of soil plastic deformation are obtained and compared with measured results from static load tests. It is demonstrated that a super-long pile has the properties of degradation of side friction resistance and asynchronous action between side and pile-tip resistance, which is different from piles with a short to medium length.

Analytical and Experimental Investigation on Sound Transmission of Double Thin Plates with Magnetic Negative Stiffness

2018 ◽  
Vol 10 (05) ◽  
pp. 1850054 ◽  
Author(s):  
Akintoye Olumide Oyelade ◽  
Yi Chen ◽  
Ruojun Zhang ◽  
Gengkai Hu
Keyword(s):  
Finite Element ◽  
Transmission Loss ◽  
Sound Transmission ◽  
Interaction Force ◽  
Negative Stiffness ◽  
Thin Plates ◽  
Acoustic Metamaterials ◽  
Element Analysis ◽  
Theoretical Formulation ◽  
Wave Condition

Transmission loss of acoustic metamaterials (AM) made of double thin plates with magnetic (negative) stiffness was analyzed using theory, finite element analysis and experimental techniques. The theoretical formulation was done using a rectangular duct below the first cut off frequency, the model is then validated against finite element method and experiment. Two cubic magnets were used, their interaction force and the resulted magnetic stiffness were calculated. The sound transmission loss (STL) of the structure is calculated for plane wave condition, the addition of magnetic mass shifts STL peaks to the lower frequency compared to a structure without mass. The slight increase in STL for small negative stiffness in experiment is not enough to cancel the effect of air compressibility. However, a significant enhancement could be expected if negative stiffness can be made large enough in the double thin plates. The developed AM can be employed as a prospective sound engineering control at low frequency.

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