Characterization of Non-linear Polymer Properties to Predict Process Induced Warpage and Residual Stress of Electronic Packages

Nonlinear thermo-mechanical properties of advanced polymers are crucial to accurate prediction of the process induced warpage and residual stress of electronics packages. The Fiber Bragg grating (FBG) sensor based method is advanced and implemented to determine temperature and time dependent nonlinear properties. The FBG sensor is embedded in the center of the cylindrical specimen, which deforms together with the specimen. The strains of the specimen at different loading conditions are monitored by the FBG sensor. Two main sources of the warpage are considered: curing induced warpage and coefficient of thermal expansion (CTE) mismatch induced warpage. The effective chemical shrinkage and the equilibrium modulus are needed for the curing induced warpage prediction. Considering various polymeric materials used in microelectronic packages, unique curing setups and procedures are developed for elastomers (extremely low modulus, medium viscosity, room temperature curing), underfill materials (medium modulus, low viscosity, high temperature curing), and epoxy molding compound (EMC: high modulus, high viscosity, high temperature pressure curing), most notably, (1) zero-constraint mold for elastomers; (2) a two-stage curing procedure for underfill materials and (3) an air-cylinder based novel setup for EMC. For the CTE mismatch induced warpage, the temperature dependent CTE and the comprehensive viscoelastic properties are measured. The cured cylindrical specimen with a FBG sensor embedded in the center is further used for viscoelastic property measurements. A uni-axial compressive loading is applied to the specimen to measure the time dependent Young’s modulus. The test is repeated from room temperature to the reflow temperature to capture the time-temperature dependent Young’s modulus. A separate high pressure system is developed for the bulk modulus measurement. The time temperature dependent bulk modulus is measured at the same temperatures as the Young’s modulus. The master curve of the Young’s modulus and bulk modulus of the EMC is created and a single set of the shift factors is determined from the time temperature superposition. The supplementary experiments are conducted to verify the validity of the assumptions associated with the linear viscoelasticity. The measured time-temperature dependent properties are further verified by a shadow moiré and Twyman/Green test.

Circadian Phase Control - Genetic Algorithm and Non-linear Control Approach

This paper deals with the phase control for Neurospora circadian rhythm. The nonlinear control, given by tuning the parameters (considered as controlled variables) in Neurospora dynamical model, allows the circadian rhythms tracking a reference one. When there are many parameters (e.g. 3 parameters in this paper) and their values are unknown, the adaptive control law reveals its weakness since the parameters converging and control objective must be guaranteed at the same time. We show that this problem can be solved using the genetic algorithm for parameters estimation. Once the unknown parameters are known, the phase control is performed by chaos synchronization technique.

Diffusive models and chaos indicators for non-linear betatron motion in circular hadron accelerators

Understanding the complex dynamics of beam-halo formation and evolution in circular particle accelerators is crucial for the design of current and future rings, particularly those utilizing superconducting magnets such as the CERN Large Hadron Collider (LHC), its luminosity upgrade HL-LHC, and the proposed Future Circular Hadron Collider (FCC-hh). A recent diffusive framework, which describes the evolution of the beam distribution by means of a Fokker-Planck equation, with diffusion coefficient derived from the Nekhoroshev theorem, has been proposed to describe the long-term behaviour of beam dynamics and particle losses. In this thesis, we discuss the theoretical foundations of this framework, and propose the implementation of an original measurement protocol based on collimator scans in view of measuring the Nekhoroshev-like diffusive coefficient by means of beam loss data. The available LHC collimator scan data, unfortunately collected without the proposed measurement protocol, have been successfully analysed using the proposed framework. This approach is also applied to datasets from detailed measurements of the impact on the beam losses of so-called long-range beam-beam compensators also at the LHC. Furthermore, dynamic indicators have been studied as a tool for exploring the phase-space properties of realistic accelerator lattices in single-particle tracking simulations. By first examining the classification performance of known and new indicators in detecting the chaotic character of initial conditions for a modulated Hénon map and then applying this knowledge to study the properties of realistic accelerator lattices, we tried to identify a connection between the presence of chaotic regions in the phase space and Nekhoroshev-like diffusive behaviour, providing new tools to the accelerator physics community.

Data driven regularization models of non-linear ill-posed inverse problems in imaging

Imaging technologies are widely used in application fields such as natural sciences, engineering, medicine, and life sciences. A broad class of imaging problems reduces to solve ill-posed inverse problems (IPs). Traditional strategies to solve these ill-posed IPs rely on variational regularization methods, which are based on minimization of suitable energies, and make use of knowledge about the image formation model (forward operator) and prior knowledge on the solution, but lack in incorporating knowledge directly from data. On the other hand, the more recent learned approaches can easily learn the intricate statistics of images depending on a large set of data, but do not have a systematic method for incorporating prior knowledge about the image formation model. The main purpose of this thesis is to discuss data-driven image reconstruction methods which combine the benefits of these two different reconstruction strategies for the solution of highly nonlinear ill-posed inverse problems. Mathematical formulation and numerical approaches for image IPs, including linear as well as strongly nonlinear problems are described. More specifically we address the Electrical impedance Tomography (EIT) reconstruction problem by unrolling the regularized Gauss-Newton method and integrating the regularization learned by a data-adaptive neural network. Furthermore we investigate the solution of non-linear ill-posed IPs introducing a deep-PnP framework that integrates the graph convolutional denoiser into the proximal Gauss-Newton method with a practical application to the EIT, a recently introduced promising imaging technique. Efficient algorithms are then applied to the solution of the limited electrods problem in EIT, combining compressive sensing techniques and deep learning strategies. Finally, a transformer-based neural network architecture is adapted to restore the noisy solution of the Computed Tomography problem recovered using the filtered back-projection method.

Non-linear modelling of microwave devices embedding nano-ferroelectric materials for real-time reconfigurable transmitarray

In this thesis work a nonlinear model for Interdigitated Capacitors (IDCs) based on ferroelectric materials, is proposed. Through the properties of materials such as Hafnium-Zirconium Oxide (HfZrO2), it is possible to realize tunable radiofrequency (RF) circuits. In particular, the model proposed in this thesis describes the use of an IDC, realized on a High-Resistivity silicon substrate, as a phase shifter for beam-steering applications. The model is obtained starting from already present experimental measurements, through which it is possible to identify a circuit model. The model is tested for both low power values and other power values using Harmonic Balance simulations, which show an excellent convergence of the model up to 40 dBm of input power. Furthermore, an array composed by two patches operating both at 2.55 GHz, which exploits the tunable properties of the HfZrO-based IDC is proposed. At 0dBm the model shows a 47° phase shift with polarization -1 V and 1 V which leads to a 11° steering of the main lobe of the array.

Morphometric and genetic changes in a population of Apis mellifera after 34 years of Africanization

Though the replacement of European bees by Africanized honey bees in tropical America has attracted considerable attention, little is known about the temporal changes in morphological and genetic characteristics in these bee populations. We examined the changes in the morphometric and genetic profiles of an Africanized honey bee population collected near where the original African swarms escaped, after 34 years of Africanization. Workers from colonies sampled in 1968 and in 2002 were morphometrically analyzed using relative warps analysis and an Automatic Bee Identification System (ABIS). All the colonies had their mitochondrial DNA identified. The subspecies that mixed to form the Africanized honey bees were used as a comparison for the morphometric analysis. The two morphometric approaches showed great similarity of Africanized bees with the African subspecies, Apis mellifera scutellata, corroborating with other markers. We also found the population of 1968 to have the pattern of wing venation to be more similar to A. m. scutellata than the current population. The mitochondrial DNA of European origin, which was very common in the 1968 population, was not found in the current population, indicating selective pressure replacing the European with the African genome in this tropical region. Both morphometric methodologies were very effective in discriminating the A. mellifera groups; the non-linear analysis of ABIS was the most successful in identifying the bees, with more than 94% correct classifications.

A simple way to introduce fibers into FEM models

This communication proposes a simple way to introduce fibers into finite element modelling. This is a promising formulation to deal with fiber-reinforced composites by the finite element method (FEM), as it allows the consideration of short or long fibers placed arbitrarily inside a continuum domain (matrix). The most important feature of the formulation is that no additional degree of freedom is introduced into the pre-existent finite element numerical system to consider any distribution of fiber inclusions. In other words, the size of the system of equations used to solve a non-reinforced medium is the same as the one used to solve the reinforced counterpart. Another important characteristic is the reduced work required by the user to introduce fibers, avoiding `rebar` elements, node-by-node geometrical definitions or even complex mesh generation. An additional characteristic of the technique is the possibility of representing unbounded stresses at the end of fibers using a finite number of degrees of freedom. Further studies are required for non-linear applications in which localization may occur. Along the text the linear formulation is presented and the bounded connection between fibers and continuum is considered. Four examples are presented, including non-linear analysis, to validate and show the capabilities of the formulation. Copyright (c) 2007 John Wiley & Sons, Ltd.

EFFECT – Efficient finite element code

The theme of this dissertation is the finite element method applied to mechanical structures. A new finite element program is developed that, besides executing different types of structural analysis, also allows the calculation of the derivatives of structural performances using the continuum method of design sensitivities analysis, with the purpose of allowing, in combination with the mathematical programming algorithms found in the commercial software MATLAB, to solve structural optimization problems. The program is called EFFECT – Efficient Finite Element Code. The object-oriented programming paradigm and specifically the C ++ programming language are used for program development. The main objective of this dissertation is to design EFFECT so that it can constitute, in this stage of development, the foundation for a program with analysis capacities similar to other open source finite element programs. In this first stage, 6 elements are implemented for linear analysis: 2-dimensional truss (Truss2D), 3-dimensional truss (Truss3D), 2-dimensional beam (Beam2D), 3-dimensional beam (Beam3D), triangular shell element (Shell3Node) and quadrilateral shell element (Shell4Node). The shell elements combine two distinct elements, one for simulating the membrane behavior and the other to simulate the plate bending behavior. The non-linear analysis capability is also developed, combining the corotational formulation with the Newton-Raphson iterative method, but at this stage is only avaiable to solve problems modeled with Beam2D elements subject to large displacements and rotations, called nonlinear geometric problems. The design sensitivity analysis capability is implemented in two elements, Truss2D and Beam2D, where are included the procedures and the analytic expressions for calculating derivatives of displacements, stress and volume performances with respect to 5 different design variables types. Finally, a set of test examples were created to validate the accuracy and consistency of the result obtained from EFFECT, by comparing them with results published in the literature or obtained with the ANSYS commercial finite element code.

Development of Abutment Design Standards for Local Bridge Designs, Volume 1 of 3, Development of Design Methodology, August 2004

Several superstructure design methodologies have been developed for low volume road bridges by the Iowa State University Bridge Engineering Center. However, to date no standard abutment designs have been developed. Thus, there was a need to establish an easy to use design methodology in addition to generating generic abutment standards and other design aids for the more common substructure systems used in Iowa. The final report for this project consists of three volumes. The first volume (this volume) summarizes the research completed in this project. A survey of the Iowa County Engineers was conducted from which it was determined that while most counties use similar types of abutments, only 17 percent use some type of standard abutment designs or plans. A literature review revealed several possible alternative abutment systems for future use on low volume road bridges in addition to two separate substructure lateral load analysis methods. These consisted of a linear and a non-linear method. The linear analysis method was used for this project due to its relative simplicity and the relative accuracy of the maximum pile moment when compared to values obtained from the more complex non-linear analysis method. The resulting design methodology was developed for single span stub abutments supported on steel or timber piles with a bridge span length ranging from 20 to 90 ft and roadway widths of 24 and 30 ft. However, other roadway widths can be designed using the foundation design template provided. The backwall height is limited to a range of 6 to 12 ft, and the soil type is classified as cohesive or cohesionless. The design methodology was developed using the guidelines specified by the American Association of State Highway Transportation Officials Standard Specifications, the Iowa Department of Transportation Bridge Design Manual, and the National Design Specifications for Wood Construction. The second volume introduces and outlines the use of the various design aids developed for this project. Charts for determining dead and live gravity loads based on the roadway width, span length, and superstructure type are provided. A foundation design template was developed in which the engineer can check a substructure design by inputting basic bridge site information. Tables published by the Iowa Department of Transportation that provide values for estimating pile friction and end bearing for different combinations of soils and pile types are also included. Generic standard abutment plans were developed for which the engineer can provide necessary bridge site information in the spaces provided. These tools enable engineers to design and detail county bridge substructures more efficiently. The third volume provides two sets of calculations that demonstrate the application of the substructure design methodology developed in this project. These calculations also verify the accuracy of the foundation design template. The printouts from the foundation design template are provided at the end of each example. Also several tables provide various foundation details for a pre-cast double tee superstructure with different combinations of soil type, backwall height, and pile type.

Development of Abutment Design Standards for Local Bridge Designs, Volume 3 of 3, Verification of Design Methodology, August 2004

Several superstructure design methodologies have been developed for low volume road bridges by the Iowa State University Bridge Engineering Center. However, to date no standard abutment designs have been developed. Thus, there was a need to establish an easy to use design methodology in addition to generating generic abutment standards and other design aids for the more common substructure systems used in Iowa. The final report for this project consists of three volumes. The first volume summarizes the research completed in this project. A survey of the Iowa County Engineers was conducted from which it was determined that while most counties use similar types of abutments, only 17 percent use some type of standard abutment designs or plans. A literature review revealed several possible alternative abutment systems for future use on low volume road bridges in addition to two separate substructure lateral load analysis methods. These consisted of a linear and a non-linear method. The linear analysis method was used for this project due to its relative simplicity and the relative accuracy of the maximum pile moment when compared to values obtained from the more complex non-linear analysis method. The resulting design methodology was developed for single span stub abutments supported on steel or timber piles with a bridge span length ranging from 20 to 90 ft and roadway widths of 24 and 30 ft. However, other roadway widths can be designed using the foundation design template provided. The backwall height is limited to a range of 6 to 12 ft, and the soil type is classified as cohesive or cohesionless. The design methodology was developed using the guidelines specified by the American Association of State Highway Transportation Officials Standard Specifications, the Iowa Department of Transportation Bridge Design Manual, and the National Design Specifications for Wood Construction. The second volume introduces and outlines the use of the various design aids developed for this project. Charts for determining dead and live gravity loads based on the roadway width, span length, and superstructure type are provided. A foundation design template was developed in which the engineer can check a substructure design by inputting basic bridge site information. Tables published by the Iowa Department of Transportation that provide values for estimating pile friction and end bearing for different combinations of soils and pile types are also included. Generic standard abutment plans were developed for which the engineer can provide necessary bridge site information in the spaces provided. These tools enable engineers to design and detail county bridge substructures more efficiently. The third volume (this volume) provides two sets of calculations that demonstrate the application of the substructure design methodology developed in this project. These calculations also verify the accuracy of the foundation design template. The printouts from the foundation design template are provided at the end of each example. Also several tables provide various foundation details for a pre-cast double tee superstructure with different combinations of soil type, backwall height, and pile type.

Development of Abutment Design Standards for Local Bridge Designs, Volume 2 of 3, Design Manual, August 2004

Several superstructure design methodologies have been developed for low volume road bridges by the Iowa State University Bridge Engineering Center. However, to date no standard abutment designs have been developed. Thus, there was a need to establish an easy to use design methodology in addition to generating generic abutment standards and other design aids for the more common substructure systems used in Iowa. The final report for this project consists of three volumes. The first volume summarizes the research completed in this project. A survey of the Iowa County Engineers was conducted from which it was determined that while most counties use similar types of abutments, only 17 percent use some type of standard abutment designs or plans. A literature review revealed several possible alternative abutment systems for future use on low volume road bridges in addition to two separate substructure lateral load analysis methods. These consisted of a linear and a non-linear method. The linear analysis method was used for this project due to its relative simplicity and the relative accuracy of the maximum pile moment when compared to values obtained from the more complex non-linear analysis method. The resulting design methodology was developed for single span stub abutments supported on steel or timber piles with a bridge span length ranging from 20 to 90 ft and roadway widths of 24 and 30 ft. However, other roadway widths can be designed using the foundation design template provided. The backwall height is limited to a range of 6 to 12 ft, and the soil type is classified as cohesive or cohesionless. The design methodology was developed using the guidelines specified by the American Association of State Highway Transportation Officials Standard Specifications, the Iowa Department of Transportation Bridge Design Manual, and the National Design Specifications for Wood Construction. The second volume (this volume) introduces and outlines the use of the various design aids developed for this project. Charts for determining dead and live gravity loads based on the roadway width, span length, and superstructure type are provided. A foundation design template was developed in which the engineer can check a substructure design by inputting basic bridge site information. Tables published by the Iowa Department of Transportation that provide values for estimating pile friction and end bearing for different combinations of soils and pile types are also included. Generic standard abutment plans were developed for which the engineer can provide necessary bridge site information in the spaces provided. These tools enable engineers to design and detail county bridge substructures more efficiently. The third volume provides two sets of calculations that demonstrate the application of the substructure design methodology developed in this project. These calculations also verify the accuracy of the foundation design template. The printouts from the foundation design template are provided at the end of each example. Also several tables provide various foundation details for a pre-cast double tee superstructure with different combinations of soil type, backwall height, and pile type.

Ultralujasta teräksestä valmistetun henkilönostimen teleskooppipuomin kehittäminen

Tässä työssä kehitettiin palo- ja pelastuskäyttöön tarkoitettuun henkilönostimeen teleskooppipuomin profiilit. Profiilien valmistusmateriaalina oli kuumavalssattu, ultraluja säänkestävä rakenneteräs. Työssä kehitettiin standardien ja ohjeiden pohjalta laskentapohja, jolla voidaan tutkia teleskooppipuomin jaksojen tukireaktioita, taivutus- ja vääntömomentteja ja leikkaus ja normaalivoimia. Laskentapohjassa voidaan varioida eri kuormitusten suuntia, teleskooppipuomin sivusuuntaista ulottumaa ja nostokulmaa. Profiilien alustavassa mitoituksessa hyödynnettiin paikallisen lommahduksen huomioon ottavia standardeja ja suunnitteluohjeita. Eri poikkileikkausten ominaisuuksia verrattiin keskenään ja profiili valittiin yhdessä kohdeyrityksen kanssa. Alustavan mitoituksen yhteydessä muodostettiin apuohjelma valitulle poikkileikkaukselle, jolla voitiin tutkia profiilin eri muuttujien vaikutusta mm. paikalliseen lommahdukseen ja jäykkyyteen. Laskentapohjaan sisällytettiin myös optimointirutiini, jolla voitiin minimoida poikkileikkauksen pinta-ala ja tätä kautta profiilin massa. Lopullinen mitoitus suoritettiin elementtimenetelmällä. Mitoituksessa tutkittiin alustavasti mitoitettujen profiilien paikallista lommahdusta lineaarisen stabiilius- ja epälineaarisen analyysin pohjalta. Profiilien jännityksiä tutkittiin tarkemmin mm. varioimalla kuormituksia ja osittelemalla elementtien normaalijännityksiä. Diplomityössä kehitetyllä ja analysoidulla teleskooppipuomilla voitiin keventää jaksojen painoja 15-30 %. Sivusuuntainen ulottuma parani samalla lähes 20 % ja nimelliskuorma kasvoi 25 %.

Harustetun 110 kV kannatuspylvään konseptin kehittäminen

Diplomityössä kehitettiin harustetun 110 kV kannatuspylvään konsepti tuotteeksi. Pylväs on säänkestävästä teräksestä valmistettu putkipalkkirakenteinen I-pylväs. Tavoitteena oli suunnitella rakenteesta kokonaistaloudellisesti edullinen. Rakenteen suunnittelussa otettiin huomioon valmistus-, kuljetus- ja varastointi- sekä rakentamisnäkökohtia. Työssä perehdyttiin pylväsrakenteiden yksityiskohtiin, putkipalkkien liitosmenetelmiin ja pylvään jalan nivelöintiratkaisuihin. Säänkestävä rakennemateriaali otettiin huomioon rakennesuunnittelussa. Rakenteen lujuusteknisen suunnittelun apuna käytettiin epälineaarista elementtimenetelmää. Pylväsrakenteen käyttäytyminen mallinnettiin geometrisesti epälineaariseksi, ja liitosdetaljien analysointia varten kehitettiin epälineaarisia materiaalimalleja. Rakenteen värähtelykäyttäytyminen analysoitiin myös elementtimenetelmällä. Lopputuloksena saatiin aikaan pylväs, joka täyttää sille asetetut vaatimukset. Pylväs on helposti valmistettava, kuljetettava ja pystytettävä.

An Anisotropic Model of Damage and Unilateral Effect for Brittle Materials

This work deals with the initial applications and formulation of an aniscitropic plastic-damage constitutive model proposed for non-linear analysis of reinforced concrete structures submitted to a loading with change of the sign. The original constitutive model is based on the fundamental hypothesis of energy equivalence between real and continuous medium following the concepts of the Continuum Damage Mechanics. The concrete is assumed as an initial elastic isotropic medium presenting anisotropy, permanent strains and bimodularity (distinct elastic responses whether traction or compression stress states prevail) induced by damage evolution. In order to take into account the bimodularity, two damage tensors governing the rigidity in tension or compression regimes are introduced. Then, some conditions are introduced in the original version of the model in order to simulate the damage unilateral effect. The three-dimensional version of the proposed model is analyzed in order to validate its formulation when compared to micromechanical theory. The one-dimensional version of the model is applied in the analyses of a reinforced concrete beam submitted to a loading with change of the sign. Despite the parametric identification problems, the initial applications show the good performance of the model.