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This paper presents the design of a graphics subroutine library, MacPac, as a contribution to the development of a standard for future graphics packages. The need for a new graphics standard, and hence the motivation for the development of MacPac, is illustrated through a detailed discussion of existing graphics standards and systems. MacPac is based on a design philosophy developed by Mark Green for the next generation of graphics packages. It addresses the hardware and software ideas of the 80's, incorporating and building upon the valuable and tested ideas of a number of existing graphics systems. The design languages used in the development of MacPac were created by Mark Green for the design of user interfaces. This work examines the effectiveness of these languages in the design of a graphics system. / Thesis / Master of Science (MS)

Many geological numerical models are initiated with a background stress state of zero. Often these numerical results are compared directly to geodetic data. Recent work (Kenner and Simons, 2004) has shown that modeled deformation rates can change as the model is cycled-up following repeated earthquakes or rifting events. In this study, we investigate model cycle-up in the context of time-dependent deformation following rifting during the 1975-1984 Krafla eruption in Iceland. We consider the number of rifting cycles required for complete cycle-up, variations in cycle-up time at different locations in the model, background stress magnitudes in fully cycled-up models, and errors incurred when the models are not properly cycled-up. The modeling is done using the commercial software ABAQUS. In ABAQUS a user-defined subroutine is used to apply repeated rifting events within the finite element model. We have generated various 3D models with different fault/rift geometries. The models include (1) a straight rift oriented perpendicular to the far-field velocity boundary conditions, (2) a rift oriented at an angle to the far-field velocities, (3) a model containing two intersecting rifts, one perpendicular to the far-field velocities and the other rift intersecting the first at an angle, and (4) overlapping rift segments in which the overlapped region is bounded by strike-slip faults.

A new user oriented optimization system is described which is particularly useful for integration into user oriented design packages. Four new subroutines have been developed for the system, one being for integer or mixed integer nonlinear problems. A description is given of the problem of handling constraints while solving optimization problems. The technique of integration into a design package is discussed. Solutions of four sample problems have been included to demonstrate use of the subroutines. / Thesis / Master of Engineering (ME)

In intraplate seismic zones (e.g. the New Madrid Seismic Zone, NMSZ, in the southcentral United States), the source of stress that drives earthquake is very complex. Data from the NMSZ indicate 3 earthquake of magnitude M~7, occurring at an approximate interval of 500 years during the last 2000 years. One hypothesis that satisfies these conditions proposes that short-lived bursts of earthquakes may result from perturbations in the local or regional stress field. This causes relaxation of a lower crustal weak zone which drive repeated earthquakes. The number of earthquakes is dependent on the geometry and rheology of the weak zone. Using finite element techniques which employ contact surfaces to model discrete faulting events and a maximum shear stress criteria evaluated at each node. We investigate the relevant parameter space, as it affects the concentration of stress at the base of the seismogenic fault and the number of earthquakes generated over a given time interval. Parameters that can be varied include earthquake stress drop, background tectonic stress, and maximum shear stress at failure. Results show that solutions are non-unique. With the addition of existing observational evidence, however, we can place bounds on the range of parameters which satisfy above observations.

Styrene-Butadiene Rubber (SBR) is a form of rubber compound that is widely used in the tire industry. This is due to some of their unique characteristics such as high strength, high elasticity and resilience, high abrasion resistance, ability to absorb and dissipate shocks and vibrations, low plastic deformation, high deformation at low levels of stresses, and high product life. One of the most important and often overlooked causes of SBR degradation and eventual tire failure is 'rubber aging.' It can be defined as an alteration in the mechanical, chemical, physical, or morphological properties of elastomers under the influence of various environmental factors during processing, storing and use. Some of these environmental factors are humidity, ozone, oxygen, temperature, radiation (UV rays), etc. This study focuses on the effects of two of these factors acting in tandem, oxygen and temperature. In the past, studies have been conducted to observe the effects of rubber aging on the mechanical and wear properties of rubber. Studies have also been conducted to study the reactions taking place in rubber during aging and changes in its chemical structure. These studies use different modelling techniques and experiments to quantify the effects of aging. In this study, a material aging model that can predict the hyperplastic response of styrene-butadiene rubber (SBR) was mathematically developed using an integrated testing and continuum damage model framework. Coupling between the mechanical changes of SBR to the change in the chemical properties, specifically crosslink density (CLD) was also investigated. SBR dogbone shaped samples were accelerated aged in an aging oven at various temperatures and aging periods. Subsequently, hyperelastic tests were conducted to obtain the high strain response taking the 'Mullin's effect' into consideration. These responses were calibrated to different hyperelastic material models and the Arruda-Boyce model was chosen, due to its stable behavior and optimal fit. An aging evolution function was developed based on the variation in the model coefficients. This damage model is able to predict the hyperelastic response of SBR as it ages. A user material subroutine (UMAT) was also implemented in Abaqus based on the obtained aging evolution function to predict the stress response of SBR for varied applications. Additionally, to couple the chemical variations with the hyperelastic response, the rubber structure and composition was probed using Fourier-transform infrared spectroscopy (FTIR). The degradation of additives and SBR polymer chains were analyzed microscopically to explain the impact on the macroscopic properties. This study helps to correlate the change in crosslink density to ameliorate mechanical properties, such as strain at break, modulus, and stiffness. The effects of aging on the viscoelastic properties of SBR were also studied. Dynamic Mechanical Analysis (DMA) was used to characterize the viscoelastic response. Master curves of storage and loss modulus were generated using the time-temperature superposition principle (TTSP). The friction coefficient was estimated from the storage and loss modulus using a simplified form of the Persson equation [1]. CLD was also estimated from DMA data. Wear experiments were conducted on the Dynamic Friction Tester (DFT) for various aging conditions. The estimated friction coefficient was compared to the one from the experiments. Archard's law was used to correlate the frictional energy to the volume loss during wear experiments. Correlation between the wear and the viscoelastic properties of SBR is also studied. Finally, the lifetime of SBR for various aging temperatures is predicted using various models. [1] M. Ciavarella, "A Simplified Version of Persson's Multiscale Theory for Rubber Friction Due to Viscoelastic Losses," J. Tribol., vol. 140, no. 1, 2018, doi: 10.1115/1.4036917. / Master of Science / Elastomers or rubbers are they are generally referred to are an indispensable part of human life. They are made up of long-chain polymer units linked to one other through crosslinks. This peculiar morphology of rubbers is what gives them their unique characteristics. There are as many as 40,000 known products that use some form of rubber as the primary raw material. Apart, from this, they are also widely used in aviation and aerospace, automobiles, dampers and absorbers, civil engineering, electronics, medical, toys, clothing, sports, footwear, and so on. This is due to some of their unique characteristics such as high strength, high elasticity and resilience, high abrasion resistance, ability to absorb and dissipate shocks and vibrations, low plastic deformation, high deformation at low levels of stresses, and high product life. Over the last couple of years, it has also played a pivotal role in personal protective equipment (PPE) and masks worn by billions of people and frontline workers all over the globe. The fact that rubber is included in the EU's list of critical raw materials highlights its global importance. However, over the past several years, the rubber supply has dwindled. COVID-19 also caused disruptions in the supply chain of rubber. As the effects of COVID-19 are fading, there has been a spike in the demand for rubber; the primary reason being automotive tires! Even though substantial research is being conducted to try and replace rubber as a raw material with synthetic alternatives such as polyurethane, the excellent blend of damping, friction and wear characteristics, heat dissipation provided by natural rubber cannot be replicated by any of these laboratory compounds. Hence, at this time, there is an increased need to conserve and improve the longevity of rubber compounds. Styrene-Butadiene Rubber (SBR) is a form of a rubber compound that is widely used in the tire industry. One of the most important and often overlooked causes of SBR degradation and eventual tire failure is 'rubber aging.' It can be defined as an alteration in the mechanical, chemical, physical, or morphological properties of elastomers under the influence of various environmental factors during processing, storing and use. Some of these environmental factors are humidity, ozone, oxygen, temperature, radiation (UV rays), etc. This study focuses on the effects of two of these factors acting in tandem, oxygen and temperature. In the past, studies have been conducted to observe the effects of rubber aging on the mechanical and wear properties of rubber. Studies have also been conducted to study the reactions taking place in rubber during aging and changes in its chemical structure. These studies use different modelling techniques and experiments to quantify the effects of aging. The present study aims to model changes in the hyperelastic (large stretching) behavior of SBR using a Continuum Damage Mechanics (CDM) approach. This mathematical model is translated into ABAQUS, a finite element analysis software to study the mechanical response of components with various geometries and loading conditions. Secondly, the effects of aging on the viscoelastic behavior of SBR is studied. This helps us to estimate the cross-link density (CLD) as well as the friction coefficient of SBR as it is aged. The impact of aging on the wear and friction properties of SBR is studied experimentally. Finally, using various mechanical and chemical models the lifetime of SBR is estimated for various aging temperatures. Thus, the end goal of the study is to drive the development of new rubber compounds that will help improve the service life of rubbers and also have a positive impact on the environment.

Despite the phenomena of fracture and fatigue having been the focus of academic research for more than 150 years, it remains in effect an empirical science lacking a complete and comprehensive set of predictive solutions. In this regard, the focus of the research in this thesis is on the development of new cohesive-zone models for fracture and fatigue that are afforded an ability to capture strain-rate effects. For the case of monotonic fracture in ductile material, different combinations of material response are examined with rate effects appearing either in the bulk material or localised to the cohesive-zone or in both. The development of a new rate-dependent CZM required first an analysis of two existing methods for incorporating rate dependency, i.e.either via a temporal critical stress or a temporal critical separation. The analysis revealed unrealistic crack behaviour at high loading rates. The new rate-dependent cohesive model introduced in the thesis couples the temporal responses of critical stress and critical separation and is shown to provide a stable and realistic solution to dynamic fracture. For the case of fatigue, a new frequency-dependent cohesive-zone model (FDCZM) has been developed for the simulation of both high and low-cycle fatigue-crack growth in elasto-plastic material. The developed model provides an alternative approach that delivers the accuracy of the loading-unloading hysteresis damage model along with the computational efficiency of the equally well-established envelope load-damage model by incorporating a fast-track feature. With the fast-track procedure, a particular damage state for one loading cycle is 'frozen in' over a predefined number of cycles. Stress and strain states are subsequently updated followed by an update on the damage state in the representative loading cycle which again is 'frozen in' and applied over the same number of cycles. The process is repeated up to failure. The technique is shown to be highly efficient in terms of time and cost and is particularly effective when a large number of frozen cycles can be applied without significant loss of accuracy. To demonstrate the practical worth of the approach, the effect that the frequency has on fatigue crack growth in austenitic stainless-steel 304 is analysed. It is found that the crack growth rate (da/dN) decreases with increasing frequency up to a frequency of 5 Hz after which it levels off. The behaviour, which can be linked to martensitic phase transformation, is shown to be accurately captured by the new FDCZM.

Indiana University-Purdue University Indianapolis (IUPUI) / Additively manufactured (AM) metals have been increasingly fabricated for structural applications. However, a major hurdle preventing their extensive application is lack of understanding of their mechanical properties. To address this issue, the objective of this research is to develop a computational model to simulate the creep behavior of nickel alloy 718 manufactured using the laser powder bed fusion (L-PBF) additive manufacturing process. A finite element (FE) model with a subroutine is created for simulating the creep mechanism for 3D printed nickel alloy 718 components. A continuum damage mechanics (CDM) approach is employed by implementing a user defined subroutine formulated to accurately capture the creep mechanisms. Using a calibration code, the material constants are determined. The secondary creep and damage constants are derived using the parameter fitting on the experimental data found in literature. The developed FE model is capable to predict the creep deformation, damage evolution, and creep-rupture life. Creep damage and rupture is simulated as defined by the CDM theory. The predicted results from the CDM model compare well with experimental data, which are collected from literature for L-PBF manufactured nickel alloy 718 of creep deformation and creep rupture, at different levels of temperature and stress. Using the multi-regime Liu-Murakami (L-M) and Kachanov-Rabotnov (K-R) isotropic creep damage formulation, creep deformation and rupture tests of both the secondary and tertiary creep behaviors are modeled. A single element FE model is used to validate the model constants. The model shows good agreement with the traditionally wrought manufactured 316 stainless steel and nickel alloy 718 experimental data collected from the literature. Moreover, a full-scale axisymmetric FE model is used to simulate the creep test and the capacity of the model to predict necking, creep damage, and creep-rupture life for L-PBF manufactured nickel alloy 718. The model predictions are then compared to the experimental creep data, with satisfactory agreement. In summary, the model developed in this work can reliably predict the creep behavior for 3D printed metals under uniaxial tensile and high temperature conditions.

This diploma work describes below mentioned issues: a plan of construction technology of component called “DC shield” which consists of a block A and a block B, definition of the tasks for “TPV”. Specification of material, production and checking of a semi-product. Determination of the bases, technologies of working and cutting materials. Determination of the manufacturing machines, working out of processing and composition of a tool set. Definition of the jigs, characteristic of the basic changes. Composition of a program and composition of the subroutine systems. Determination of a checking range, measuring and a process of packaging. Economical evaluation with taking account of environmental aspects of the production.

Fiber-reinforced rubberlike materials (FRRM) commonly used in tires undergo large deformations, and exhibit different response in tension and compression along the fiber direction. Assuming that the response of a fiber-reinforced rubberlike material can be modeled as transversely isotropic with the fiber direction as the axis of transverse isotropy, we express the stored energy function, W, in terms of the five invariants of the right Cauchy-Green strain tensor and the fiber direction, and account for different response in tension and compression along the fiber direction. It has been shown in the literature that in shear-dominated deformations, the 5th invariant, I5, significantly contribution to the stress-strain curve. We have implemented the constitutive relation in the commercial software, LS-DYNA. The numerical solutions of several boundary value problems studied here agree with their analytical solutions derived by using Ericksen's inverse approach, in which a part of the solution is assumed and unknowns in the presumed solution are then found by analyzing the pertinent boundary value problem. However, computed results have not been compared with experimental findings. For W of the FRRMs an expression that is a complete quadratic function of the five invariants is also examined. Homogeneous deformations such as simple extension, simple shear, and biaxial loading problems are studied to delineate the mechanical behaviors of FRRMs. Consistency with the infinitesimal deformation theory requires that linear terms in the 4th and 5th invariants, I4 and I5, be included in the expression for W. Stability analysis of deformations reveals the qualitative changes triggered by the second order terms of the quadratic function. Analytical solutions for inflation, extension and twist deformations caused by internal pressure, end torque, and axial force for a pressurized cylindrical laminate are derived using Ericksen's inverse method. Effects of fiber orientations on the mechanical behaviors of a +/-α angle-ply cylindrical tube are investigated using the derived analytical solutions. The T-peel test, widely used for characterizing adhesion across a plethora of adhesives, adherends, and geometries, results in a range of responses that may complicate meaningful interpretation of the test data. This research effort, involving several specific specimen types, was undertaken to investigate concerns that commonly used configurations may not always result in plateaus in the force-displacement response. We experimentally and numerically study debonding of T-peel specimens having 75 mm bond length and 0.81 mm thick adherends made of either 6061 aluminum (Al) or one of the three steels (G70 70U hot dip galvanized, E60 elctrogalvanized (EGZ), 1010 cold-rolled steel (CRS) bonded with either LORD® 406 or Maxlok™ acrylic adhesive. For the EGZ and the Al adherends, specimens with a bond length of 250 mm and adherend thickness of 1.60 mm are also examined. Effects of adherend materials and thicknesses, bond lengths, and adhesives on test results are examined using three metrics to interpret the T-peel bond performance. We find a limited correlation between the commonly used "T-peel strength" and the energy dissipated per unit debond area. For those two metrics, the relative performances of the CRS and the Al specimens are quite different. Quasi-static plane strain deformations of the test specimens are analyzed by the finite element method (FEM) and a cohesive zone model using the commercial software, ABAQUS, to help interpret the test data. Numerical results provided energies required to elastically and plastically deform the adherends, and help determine the transition from non-self-similar to self-similar debonding. The FE simulations also facilitate determination of the fraction of the crosshead displacement at which self-similar debonding occurs. Results reported herein should help practitioners select appropriate specimen dimensions for extracting meaningful data for adhesive performance. / Ph. D.