Prediction of Microelectronic Substrate Warpage Using Homogenized Thermomechanical Finite Element Models

2005 ◽  
Author(s):  
Parsaoran Hutapea ◽  
Joachim L. Grenestedt ◽  
Mitul Modi ◽  
Michael Mello ◽  
Kristopher Frutschy
Keyword(s):  
Finite Element ◽  
Effective Properties ◽  
Isothermal Condition ◽  
Numerical Approach ◽  
Thermomechanical Properties ◽  
Temperature Changes ◽  
Numerical Predictions ◽  
Homogenization Approach ◽  
Simple Bounds ◽  
Complex Features

High-density microelectronic substrates, used in organic CPU packages, are comprised of several polymer, fiber-weave, and copper layers and are filled with a variety of complex features such as traces, micro-vias, Plated-Through-Holes (PTH), and adhesion holes. When subjected to temperature changes, these substrates may warp, driven by the mismatch in Coefficients of Thermal Expansion (CTE) of the constituent materials. This study focused on predicting substrate warpage in an isothermal condition. The numerical approach consisted of three major steps: estimating homogenized (effective) thermomechanical properties of the features; calculating effective properties of discretized layers using the effective properties of the features; and assembling the layers to create 2D Finite Element (FE) plate models and to calculate warpage of the whole substrates. The effective properties of the features were extracted from 3D unit cell FE models, and closed-form approximate expressions were developed using the numerical results, curve fitting, and some simple bounds. The numerical approach was applied to predict warpage of production substrates, analyzed, and validated against experimentally measured stiffness and CTEs. In this paper, the homogenization approach, numerical predictions, and experimental validation are discussed.

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.

scholarly journals A Numerical Approach for the Design of RC Beams Subjected to Axial and Transverse Loads

2021 ◽  
Vol 1203 (3) ◽  
pp. 032108
Author(s):  
Amal Wahbi ◽  
Duc Toan Pham ◽  
Ghazi Hassen ◽  
Denis Garnier ◽  
Patrick de Buhan
Keyword(s):  
Finite Element ◽  
Limit Analysis ◽  
Optimization Method ◽  
Numerical Approach ◽  
Rc Beams ◽  
Present Contribution ◽  
Transverse Loads ◽  
Numerical Predictions ◽  
Analysis Theory ◽  
Mixed Modelling

Abstract The present contribution deals with a numerical approach for the design of RC beams subjected to axial and transverse loads. It is based on the finite-element implementation of the kinematic approach of the yield design (or limit analysis) theory combined with a “mixed modelling” where the concrete material is regarded as a classical two-dimensional continuum while the longitudinal reinforcements are modelled as one-dimensional elements working in tension-compression only. For the beams reinforced in shear, stirrups are incorporated in the analysis through a homogenization procedure. An optimization problem is formulated, then solved using conic quadratic optimization method. As a result, an upper bound estimate to the yield strength domain of RC beams may be drawn in the plane of axial and transverse loads. For illustrative purpose, calculations are conducted on typical RC beams with different longitudinal and transverse reinforcement degrees. Furthermore, it is shown that such numerical predictions prove to be in good agreement with the results derived from other numerical simulations of the same problem using a finite element-based limit analysis commercial software. In order to assess their practical validity, these predictions are also compared to some available experimental results published in the literature.

Thermomechanical Properties of CoNiCrAlY-BN-Polyester Composite Coatings Elaborated by Atmospheric Plasma Spraying

2014 ◽  
Vol 606 ◽  
pp. 167-170 ◽  
Author(s):  
Delphine Aussavy ◽  
Rodolphe Bolot ◽  
François Peyraut ◽  
Ghislain Montavon ◽  
Serge Selezneff
Keyword(s):  
Finite Element ◽  
Finite Element Modelling ◽  
Plasma Torch ◽  
Effective Properties ◽  
Composite Coatings ◽  
Thermomechanical Properties ◽  
Atmospheric Plasma Spraying ◽  
Atmospheric Plasma ◽  
Finite Element Software ◽  
Polyester Composite

This study concerns the mechanical properties of CoNiCrAlY-BN-Polyester composite coatings elaborated by Atmospheric Plasma Spray (APS) and used as abradable seals in the aeronautic industry. The objective is to determine the influence of the diameter of the plasma torch on the coating micrograph morphologies and on the resulting coating thermal and mechanical effective properties. The thermo-mechanical effective properties were then estimated by Finite Element modelling (thanks to the multipurpose finite element software ANSYS) based on coating microstructures captured by Scanning Electron Microscopy (SEM) and Optical Microscopy (OM)

scholarly journals Finite Element Analysis of Mixing Flow in a Circular Vessel with Concentric Three Blade Agitator

2021 ◽  
Vol 10 (2) ◽  
pp. 1056-1064
Keyword(s):  
Finite Element ◽  
Numerical Study ◽  
Research Work ◽  
Time Derivative ◽  
Galerkin Approximation ◽  
Isothermal Condition ◽  
Polar Coordinates ◽  
Mixing Process ◽  
Navier Stokes Equation ◽  
Numerical Predictions

This study is to investigate the optimisation of the mixing process in two folds, such as, homogenisation of material and to predict the power consumption. This research work is extension of other studies conducted by different researchers. In all other research investigations, no one had employed agitator. The geometry features a cylindrical vessel fixed with a mechanically revolving stirrer along with fixed agitator. The flow is modelled for incompressible constant viscosity Newtonian fluid with isothermal condition. Simulated numerical predictions are achieved through so called a finite element algorithm. The governing equations considered here are two–dimensional equation continuity and time–dependent Navier–Stokes equation in cylindrical polar coordinates. Employed numerical scheme is constructed in multiple–stages. Where, time derivative is discretised in two step quadratic approximation of Taylor series expansion. Whereas, Galerkin approximation is employed for spatial discretisation. Whilst, at second step pressure correction is adopted through projection method. Whilst, implicitness is applied on only diffusion term to make algorithm in semi– implicit form of TGPC. The influences of inertia will be analysed through fluid inertia using dimensionless Reynolds number. The effects of rotational speed of stirrer with agitator will be explored. The computed results will be illustrated for pressure by isobars and flow structure through streamline contours plots. The keyaim of the numerical study is to estimate the improved possible design of the blenders, that enhance the mixing process

Utility of 2D Finite Element Simulations for Predicting Effective Thermomechanical Properties of Particle-Reinforced Composites

2018 ◽  
Author(s):  
Kamran Makarian ◽  
Sridhar Santhanam
Keyword(s):  
Finite Element ◽  
Failure Modes ◽  
Volume Fraction ◽  
Effective Properties ◽  
Coefficient Of Thermal Expansion ◽  
High Volume ◽  
Thermomechanical Properties ◽  
Reinforced Composites ◽  
Fe Simulations ◽  
Particle Reinforced Composites

In the last two decades, researchers have implemented two-dimensional (2D) Finite Element (FE) simulations of particle-reinforced composites for various purposes, including prediction of effective properties and failure modes. The present work aspires to examine the validity of the hypothesis that 2D FE simulations can provide accurate predictions for various thermomechanical properties of high volume fraction (VF) particle-reinforced composites. For this purpose, the random sequential adsorption (RSA) algorithm is implemented to generate FE simulations of various composites. The uniqueness in the methodology of the present work is in the generation of FE simulation of composites with more than two material types as reinforcement, as well as thorough and concurrent comparison of multiple thermal and mechanical properties. The adequacy of the simulations is verified statistically, and the results are compared to predictions from established schemes as well as certain experimental findings. These comparisons show that the predictive power of 2D FE simulations is lower for elastic properties, and higher for coefficient of thermal expansion (CTE) and thermal conductivity of particle-reinforced composites. The findings of this research can guide the researchers in making better decisions for implementing Finite Element Method (FEM) for designing high VF composites.

Rolling Resistance Calculation Procedure Using the Finite Element Method

2019 ◽  
Vol 48 (3) ◽  
pp. 224-248
Author(s):  
Pablo N. Zitelli ◽  
Gabriel N. Curtosi ◽  
Jorge Kuster
Keyword(s):  
Finite Element ◽  
Energy Dissipation ◽  
Rolling Resistance ◽  
Element Model ◽  
The Finite Element Method ◽  
Temperature Changes ◽  
Rubber Compounds ◽  
Different Temperatures ◽  
Materials Used ◽  
Account Temperature

ABSTRACT Tire engineers are interested in predicting rolling resistance using tools such as numerical simulation and tests. When a car is driven along, its tires are subjected to repeated deformation, leading to energy dissipation as heat. Each point of a loaded tire is deformed as the tire completes a revolution. Most energy dissipation comes from the cyclic loading of the tire, which causes the rolling resistance in addition to the friction force in the contact patch between the tire and road. Rolling resistance mainly depends on the dissipation of viscoelastic energy of the rubber materials used to manufacture the tires. To obtain a good rolling resistance, the calculation method of the tire finite element model must take into account temperature changes. It is mandatory to calibrate all of the rubber compounds of the tire at different temperatures and strain frequencies. Linear viscoelasticity is used to model the materials properties and is found to be a suitable approach to tackle energy dissipation due to hysteresis for rolling resistance calculation.

scholarly journals A Novel Finite Element Method Approach in the Modelling of Edge Trimming of CFRP Laminates

2021 ◽  
Vol 11 (11) ◽  
pp. 4743
Author(s):  
Fernando Cepero-Mejias ◽  
Nicolas Duboust ◽  
Vaibhav A. Phadnis ◽  
Kevin Kerrigan ◽  
Jose L. Curiel-Sosa
Keyword(s):  
Finite Element ◽  
Tool Wear ◽  
Cutting Tool ◽  
Machining Process ◽  
Machining Forces ◽  
General Terms ◽  
Numerical Predictions ◽  
Composite Damage ◽  
Edge Trimming ◽  
Optimal Cutting Parameters

Nowadays, the development of robust finite element models is vital to research cost-effectively the optimal cutting parameters of a composite machining process. However, various factors, such as the high computational cost or the complicated nature of the interaction between the workpiece and the cutting tool significantly hinder the modelling of these types of processes. For these reasons, the numerical study of common machining operations, especially in composite machining, is still minimal. This paper presents a novel approach comprising a mixed multidirectional composite damage mode with composite edge trimming operation. An ingenious finite element framework which infer the cutting edge tool wear assessing the incremental change of the machining forces is developed. This information is essential to replace tool inserts before the tool wear could cause severe damage in the machined parts. Two unidirectional carbon fibre specimens with fibre orientations of 45∘ and 90∘ manufactured by pre-preg layup and cured in an autoclave were tested. Excellent machining force predictions were obtained with errors below 10% from the experimental trials. A consistent 2D FE composite damage model previously performed in composite machining was implemented to mimic the material failure during the machining process. The simulation of the spring back effect was shown to notably increase the accuracy of the numerical predictions in comparison to similar investigations. Global cutting forces simulated were analysed together with the cutting tool tooth forces to extract interesting conclusions regarding the forces received by the spindle axis and the cutting tool tooth, respectively. In general terms, vertical and normal forces steadily increase with tool wear, while tangential to the cutting tool, tooth and horizontal machining forces do not undergo a notable variation.

scholarly journals Image-based semi-multiscale finite element analysis using elastic subdomain homogenization

Meccanica ◽  
2021 ◽  
Author(s):  
J. Jansson ◽  
K. Salomonsson ◽  
J. Olofsson
Keyword(s):  
Finite Element ◽  
Analytical Method ◽  
Effective Properties ◽  
Reference Model ◽  
Computational Time ◽  
Component Level ◽  
Element Analysis ◽  
Model Fidelity ◽  
Multiscale Finite Element ◽  
Anisotropic Elastic

AbstractIn this paper we present a semi-multiscale methodology, where a micrograph is split into multiple independent numerical model subdomains. The purpose of this approach is to enable a controlled reduction in model fidelity at the microscale, while providing more detailed material data for component level- or more advanced finite element models. The effective anisotropic elastic properties of each subdomain are computed using periodic boundary conditions, and are subsequently mapped back to a reduced mesh of the original micrograph. Alternatively, effective isotropic properties are generated using a semi-analytical method, based on averaged Hashin–Shtrikman bounds with fractions determined via pixel summation. The chosen discretization strategy (pixelwise or partially smoothed) is shown to introduce an uncertainty in effective properties lower than 2% for the edge-case of a finite plate containing a circular hole. The methodology is applied to a aluminium alloy micrograph. It is shown that the number of elements in the aluminium model can be reduced by $$99.89\%$$ 99.89 % while not deviating from the reference model effective material properties by more than $$0.65\%$$ 0.65 % , while also retaining some of the characteristics of the stress-field. The computational time of the semi-analytical method is shown to be several orders of magnitude lower than the numerical one.

A FINITE ELEMENT ANALYSIS OF EFFECTIVE THERMOELECTROELASTIC PROPERTIES OF COMPOSITES WITH A DOUBLY PERIODIC ARRAY OF PIEZOELECTRIC FIBERS

2009 ◽  
Vol 23 (06n07) ◽  
pp. 1689-1694 ◽  
Author(s):  
PENG YAN ◽  
CHIPING JIANG
Keyword(s):  
Finite Element ◽  
Effective Properties ◽  
Cell Model ◽  
Periodic Array ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Uniform Temperature Field ◽  
Periodic Microstructures ◽  
Doubly Periodic Array ◽  
Electrical Loads

This work deals with modeling of 1-3 thermoelectroelastic composites with a doubly periodic array of piezoelectric fibers under arbitrary combination of mechanical, electrical loads and a uniform temperature field. The finite element method (FEM) based on a unit cell model is extended to take into account the thermoelectroelastic effect. The FE predictions of effective properties for several typical periodic microstructures are presented, and their influences on effective properties are discussed. A comparison with the Mori-Tanaka method is made to estimate the application scope of micromechanics. The study is useful for the design and assessment of composites.

Analysis and Modeling of Defects in Unsupported Overhanging Features in Micro-Stereolithography

2016 ◽  
Author(s):  
Vito Basile ◽  
Francesco Modica ◽  
Irene Fassi
Keyword(s):  
Finite Element ◽  
Numerical Models ◽  
Numerical Approach ◽  
Fe Analysis ◽  
Test Cases ◽  
Layer By Layer ◽  
Failure Condition ◽  
Micro Scale ◽  
Part Geometry ◽  
Shape Component

In the present paper, a numerical approach to model the layer-by-layer construction of cured material during the Additive Manufacturing (AM) process is proposed. The method is developed by a recursive mechanical finite element (FE) analysis and takes into account forces and pressures acting on the cured material during the process, in order to simulate the behavior and investigate the failure condition sources, which lead to defects in the final part geometry. The study is focused on the evaluation of the process capability Stereolithography (SLA), to build parts with challenging features in meso-micro scale without supports. Two test cases, a cantilever part and a bridge shape component, have been considered in order to evaluate the potentiality of the approach. Numerical models have been tuned by experimental test. The simulations are validated considering two test cases and briefly compared to the printed samples. Results show the potential of the approach adopted but also the difficulties on simulation settings.

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