Lattice structures are widely used in nowadays industries in combination with additive manufacturing technology to obtain components with a limited weight and tuneable mechanical properties. However, industries still find challenging a complete implementation of these metamaterials in the product development due to the complexity given by an accurate prediction of the mechanical and fatigue properties. To overcome this limitation, analytical and numerical techniques are developed, to help designers to achieve the desired performances. Finite Element simulations are a common tool utilized in this sense, where solid models can provide accurate results. Nevertheless, the implementation of this technique requires high computational costs, often not compatible with an iterative design process where versions of the component are constantly updated considering the feedback provided by actors having different backgrounds and product interactions. Accurate and computationally efficient simulations strategies are thus required. The proposed thesis investigates three possible simulations ideas able to describe the mechanical properties of the lattice-based components. Two main properties are studied: the lattice structure elastic behaviour, which is important to determine the in-service behaviour of the designed component and the fatigue resistance, which defines the component service duration. Homogenization technique is the first numerical method analysed and it is pivoted on the idea of substituting the intricate lattice geometries with a solid fictitious material displaying the same elastic properties. In this framework, a case study is analysed, where the design process of a total hip replacement prosthetic device is developed. The workflow starts with a preliminary experimental campaign on lattice specimens with the aim of determining the printing quality, the mechanical properties, and the biological characteristics. In this phase, a verification of the homogenization predictions is performed. On this base, the best specimens’ configurations are selected to design and manufacture the prosthetic device. The second simulation technique leverages on the observation of the onedimensional nature of the strut-based lattice structures. Lattice structures’ behaviour can thus be simulated through the usage of truss and beam elements, depending on the stretching or bending dominated nature of the lattice topologies. Based on this observation, two different paths are followed, the first one aiming to improve the fatigue life of lattice components by acting of their orientation in the printing chamber. It is known that printing orientation influences the surface quality of the components and, in lattice struts this effect can be directly linked to a variation in the fatigue life. An optimization algorithm is thus developed, aiming to optimize the fatigue resistance of the manufactured components. Following this idea, a control and an optimized lattice batch are printed and an improvement in the fatigue resistance is found, even if not as large as expected by the simulations. Improvements in the predictions can be observed if the as-build geometry of the struts is considered. The second path is devoted to the computation of the corrective coefficients able to properly describe the elastic properties of bending dominated lattice structures. One-dimensional simulations are normally too severe for bending dominated lattice topologies, and a compensation has to be provided to match the elastic properties calculated trough computational efficient beam models and lattice ones. To address this problem, an optimization routine is developed, where the compensation factors are computed comparing the elastic properties of the beam models and a homogenised solid model taken as reference. A benchmark testing between the beam model, - built with the so computed compensation coefficients - a homogenised, and a solid model is developed. Compensated beam models are found to be able to improve the predictions of lattice structures elastic properties if compared to the homogenization techniques, showing a comparable computational time. Nevertheless, a reduced accuracy is found in presence of dense lattice structures, where the hypothesis of one-dimensional is weaker. The third analysed simulation method aims to obtain a precise fatigue life estimation at the expense of computational time. Starting from an as-build geometry reconstructed trough CT-scan analysis, a finite element simulation built with solid elements is performed. To reduce the computational cost, an innovative finite element theory is adopted, the Finite Cell Method. A two-step simulation is performed, and thanks to the usage of the average strain energy density method, the fatigue life estimation can be obtained. An excellent agreement is found; however, a complete validation is required for this method before its safe implementation in the design process.

Cases of brittle fractures in major bridges prompted AASHTO to publish its first fracture control plan in 1978. It focused on material and fabrication standards, and required periodic 24-month hands-on inspection of bridges with fracture critical members. The practical result of this plan was to significantly increase the life cycle cost of these bridges, rendering them uneconomical. Apart from the Point Pleasant Bridge that failed in 1967, no other bridge has collapsed in the USA following a fracture, even though large fractures have been observed in many other bridges. All these bridges showed some degree of redundancy and therefore could be reclassified as non-fracture critical if detailed analyses are carried out. The goal of this study is to provide guidance on redundancy evaluation of fracture critical bridges, specifically three girder bridges and twin box-girder bridges. The effect of various loading, analysis and geometric parameters on the post fracture response and the remaining load carrying capacity of the damaged bridge is evaluated through nonlinear finite element analysis of two well-documented structures: the Hoan Bridge and the twin box-girder bridge. Parameters such as damping definition, modelling of composite action, modelling of secondary elements, boundary conditions, and rate dependent material properties are found to be crucial in capturing the bridge response. A two-step methodology for system redundancy analysis of fracture critical bridges is proposed, leading to a reclassification of these elements as non-fracture critical for in-service inspection. The first step evaluates bridge capacity to withstand collapse following fracture based on whether the residual deformation is perceivable to people on or off the bridge. If the bridge satisfies the first step requirements, then the reserve load carrying capacity of the damaged bridge is evaluated in the second step. The Hoan Bridge failed to satisfy the proposed requirements in the first step and therefore its girders could not be reclassified as non-fracture critical. The twin box-girder bridge successfully resisted the collapse in two out three loading scenarios and displayed reserve load carrying capacity following full depth fracture in the exterior girder, and therefore can be reclassified as non-fracture critical for in-service inspection. / Ph. D.

The vestibular system of vertebrates consists of the utricle, saccule, and the semicircular canals. Head movement causes deformation of hair cell bundles in these organs, which translate this mechanical stimulus into an electrical response sent to the nervous system. This study consisted of two sections, both utilizing a Fortran-based finite element program to study hair cell bundle response. In the first part, the effects of variations in geometry and material properties on bundle mechanical response were studied. Six real cells from the red eared slider turtle utricle were modeled and their response to a gradually increased point load was analyzed. Bundle stiffness and tip link tension distributions were the primary data examined. The cells fell into two groups based on stiffness. All cells exhibited an increase in stiffness as the applied load was increased, but cells in the stiffer group showed a greater increase. Tip link tensions in the compliant group were approximately 3 times as high as those in the stiffer group. Cells in the stiffer group were larger, with more cilia, and also had a higher stereocilia/kinocilium height ratio than the cells in the other group. The stereocilia/kinocilium height ratio was the most important geometric factor in influencing bundle stiffness. Modeling a bundle as just its middle row of stereocilia resulted in some decrease in stiffness, but more significantly, a stiffness that was virtually constant as applied load increased. Tip link tension distributions showed serial behavior in the core rows of stereocilia and parallel behavior in the outer rows; this trend intensified if the tip link elastic modulus was increased. It was demonstrated that full three-dimensional modeling of bundles is critical for obtaining complete and accurate results. In the second part of the study, tip link ion gates were modeled. Sufficient tension in a tip link caused that link's ion gate to open, increasing the length of the link and causing its tension to decrease or the link to go slack. The two parameters that were varied were tip link elastic modulus and tip link gating distance d (change in length of the link). Bundle stiffness drops of up to 25% were obtained, but only when tip links went slack after gate opening; tip link slackening was dependent on tip link gating distance. Higher tip link modulus resulted in higher stiffness drops. Variable tip link modulus and tip link pre-tensioning were modeled. Variable tip link modulus resulted in increased bundle stiffness, especially under high applied loads, and in some cases, resulted in greater bundle stiffness drops when ion gates opened. Tip link pre-tensioning had no noticeable effect on bundle response. No evidence against inclusion of pre-tensioning or variable tip link elastic modulus was found. / Master of Science

Moisture damage is one of the major causes of deterioration of pavements. An example is the damage caused by flooding. While the effects of pore water pressure in pavement have been studied using finite element modeling, few of the models consider a realistic moving tire and the viscoelastic behavior of the asphalt layer. Consequently, a three-dimensional finite element simulation based on Biot consolidation theory and Schapery's non-linear viscoelasticity model, was developed to accurately simulate and analyze the detrimental effects of saturated layers in asphalt pavements. In addition, a parametric study is conducted to analyze the response of pavements with varying surface and base thickness, base and subgrade permeability, and vehicle speeds under different level of saturation. The results indicate that the effects of pore water pressure be considered in the design of pavements in flood-prone areas and in the proposal of flood management plans. Ultimately, the implementation of a "flood resilient" asphalt pavement could be effective in reducing the cost of road restoration and repair in flood-prone areas. / Master of Science / Moisture damage is one of the major causes of deterioration of pavements. An example is the damage caused by flooding. While the effects of pore water pressure in pavement have been studied using finite element modeling, few of the models have accurately modeled the behavior of the asphalt concrete and have not considered the realistic loading conditions. Consequently, a three-dimensional finite element simulation was developed to accurately simulate and analyze the detrimental effects of saturated layers in asphalt pavements. In addition, a parametric study is conducted to analyze the response of pavements with varying surface and base thickness, base and subgrade permeability, and vehicle speeds under different level of saturation. The results indicate that the effects of pore water pressure be considered in the design of pavements in flood-prone areas and in the proposal of flood management plans. Ultimately, the implementation of a "flood resilient" asphalt pavement could be effective in reducing the cost of road restoration and repair in flood-prone areas.

Simulations of the welding process for butt and tee joints using finite element analyses are presented. The base metal is aluminum alloy 2519-T87 and the filler material is alloy 2319. The simulations are performed with the commercial software SYSWELD+®, which includes moving heat sources, material deposit, metallurgy of binary aluminum, temperature dependent material properties, metal plasticity and elasticity, transient heat transfer and mechanical analyses. One-way thermo-mechanical coupling is assumed, which means that the thermal analysis is completed first, followed by a separate mechanical analysis based on the thermal history. The residual stress state from a three-dimensional analysis of the butt joint is compared to previously published results. For the quasi-steady state analysis the maximum residual longitudinal normal stress was within 3.6% of published data, and for a fully transient analysis this maximum stress was within 13% of the published result. The tee section requires two weld passes, and both a fully three-dimensional (3-D) and a 3-D to 2-D solid-shell finite elements model were employed. Using the quasi-steady state procedure for the tee, the maximum residual stresses were found to be 90-100% of the room-temperature yield strength. However, the longitudinal normal stress in the first weld bead was compressive, while the stress component was tensile in the second weld bead. To investigate this effect a fully transient analysis of the tee joint was attempted, but the excessive computer times prevented a resolution of the longitudinal residual stress discrepancy found in the quasi-steady state analysis. To reduce computer times for the tee, a model containing both solid and shell elements was attempted. Unfortunately, the mechanical analysis did not converge, which appears to be due to the transition elements used in this coupled solid-shell model. Welding simulations to predict residual stress states require three-dimensional analysis in the vicinity of the joint and these analyses are computationally intensive and difficult. Although the state of the art in welding simulations using finite elements has advanced, it does not appear at this time that such simulations are effective for parametric studies, much less to include in an optimization algorithm. / Master of Science

The mechanical response tissue analyzer (MRTA) tests long bone quality through low frequency, low amplitude vibration in vivo. The MRTA measures complex stiffness over a range of low frequencies, offering a wealth of information on bone composition. Previous MRTA interpretation used lumped parameter algorithms focused on reliably estimating the bone's bending stiffness (EI). To interpret the stiffness response, the first finite element (FE) simulation of the MRTA test of a human tibia was developed to identify dominant parameters that will possibly make linear prediction algorithms more suitable for estimating bone quality. Five FE models were developed in stages by adding complexity. Starting with a solid mesh of the diaphysis, each model was created from its predecessor by sequentially adding: a medullary canal, linear elastic (LE) cancellous epiphyses, linear viscoelastic (LVE) cancellous and cortical bone, and a LVE skin layer. The models were simulated in vibration using a direct steady-state dynamics procedure in ABAQUS to calculate the complex stiffness response. Natural frequency analysis (ABAQUS) verified that the FE models accurately reproduced previous experimental and computational resonances for human tibiae. A solid, LE cortex roughly matched the dominant frequency from experimental MRTA raw data. Adding the medullary canal and LVE properties to bone did not greatly spread the peak or shift the resonant frequency. Adding the skin layer broadened the peak response to better match the MRTA experimental response. These results demonstrate a simulation of the MRTA response based upon published geometries and material data that captures the essence of the instrument. / Master of Science

The interest in the use of aluminum as a structural material in marine applications has increased greatly in recent years. This increase is primarily due to the low weight of aluminum compared to other structural materials as well as its ability to resist corrosion. However, a critical issue in the use of any structural material for naval applications is its response to fire. Past experience has shown that finite element programs can produce accurate predictions of failure of structural components. Parameter studies conducted within finite element programs are often easier to implement than corresponding studies conducted experimentally. In this work, the compression-controlled failures of aluminum plates subjected to an applied mechanical load and an applied heat flux (to simulate fire) were predicted through the use of finite element analysis. Numerous studies were completed on these finite element models. Thicknesses of the plates were varied as well as the applied heat flux and the applied compressive stresses. The effect of surface emissivity along with the effect of insulation on the exposed surface of the plate was also studied. The influence of the initial imperfection of the plates was also studied. Not only were the physical conditions of the model varied but the element type of both the solid and shell models as well as the mesh density were also varied. Two different creep laws were used to curve fit raw creep data to understand the effects of creep in the buckling failure of the aluminum plates. These predictions were compared with experiments (from a previous study) conducted on aluminum plates of approximately 800mm in length, 200mm in width, 6-9mm in thickness and clamped at both ends to create fixed boundary conditions. A hydraulic system and a heater were used to apply the compressive load and the heat flux respectively. Comparisons between predicted and experimental results reveal that finite element analysis can accurately predict the compression-controlled failure of aluminum plates subjected to simulated fire. However, under certain combinations of the applied heat flux and compressive stress, the mesh density as well as the choice of element may have a significant impact on the results. Also, it is undetermined which creep curve-fitting model produces the most accurate results due to the influence of other parameters such as the initial imperfection. / Master of Science

This thesis presents the results of a research effort aimed at investigating the crash performance of w-beam guardrail barriers in vehicle-roadside crashes using the finite element method. The developed roadside barrier models can be used to assess the occupant injury risk, vehicle performance, and damage to guardrail barriers during a roadside accident. The finite element models of w-beam guardrail barriers may also help evaluate the crash performance of the w-beam barriers with minor damage in vehicle-barrier crashes. Thus, the results can be used to develop repair guidelines to assist highway personnel in identifying levels of minor barrier damage and deterioration. Finite element models of the weak post w-beam guardrail barriers were developed and simulated using LS-DYNA. The simulation results were validated against full scale crash tests of pickup trucks and passenger cars impacting w-beam guardrail barriers. The maximum dynamic deflection of the guardrail, exit velocity and angle of the vehicle, and occupant injury risk were calculated and compared to the tests. Kinematics of the vehicle and guardrail were assessed qualitatively as well as quantitatively. The analysis showed that simulation results were in good agreement with test data. Additionally, the models were validated against pendulum tests conducted the Federal Outdoor Impact Laboratory (FOIL). Simulation results of pendulum tests showed that the test section taken from the current full scale models performed very similarly to that in the real pendulum tests. The developed finite element models were subsequently used to examine the crash performance of weak post w-beam guardrail barriers with minor damage under vehicle impacts. Only rail/post deflection based minor damage to weak post w-beam guardrail barriers was considered in this study. Simulations were completed to obtain the damaged profiles of the guardrail systems; the damaged weak post guardrail barriers were impacted by the pickup model at mid-span for the second time. The impacting vehicle remained stable in all of these simulations. No conclusions could be drawn however whether these second impacts could have resulted in rail tearing or rupture. / Master of Science

This thesis suggests a formulation for updating physically meaningful parameters in analytical finite element(FE) models using scanning laser Doppler vibrometer(SLDV) dynamic response data. The update formulation is demonstrated in several computer simulations. The formulation is the result of incorporating an analytical FE model into an experimental model. The experimental model efficiently utilizes SLDV data to fully exploit the instrument's capability to automatically make measurements at many locations. The data in the experimental model is posed in a manner consistent with an analytical FE model's representation for harmonic response, simplifying comparison between the two. The experimental model, which uses finite element shape functions as a basis for a least squares fit to the data, can be solved to give a velocity field based only on that data. The function resulting from inserting the analytical model into the experimental model is an expression of the prediction error of the FE model as compared to the test data. This function is minimized using a quasi-Newton optimization routine, reducing the error and resulting in an updated model. Computer simulations of the update algorithm indicate that: 1. Analytically supplied derivatives and variable scaling are required by the optimization routine to consistently converge, 2. The percentage error of updated parameters falls within two standard deviations of the data's percentage error, 3. Error in the position of the laser results in the update algorithm's failure, and, 4. Error in the parameters not included in the update will appear as error in the updated parameters' solution. / Master of Science

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