Parameter estimation in a growth model for a biological population

The motivating problem concerns the estimation of the growth curve of solitary corals that follow the nonlinear Von Bertalanffy Growth Function (VBGF). The most common parameterization of the VBGF for corals is based on two parameters: the ultimate length L∞ and the growth rate k. One aim was to find a more reliable method for estimating these parameters, which can capture the influence of environmental covariates. The main issue with current methods is that they force the linearization of VBGF and neglect intra-individual variability. The idea was to use the hierarchical nonlinear model which has the appealing features of taking into account the influence of collection sites, possible intra-site measurement correlation and variance heterogeneity, and that can handle the influence of environmental factors and all the reliable information that might influence coral growth. This method was used on two databases of different solitary corals i.e. Balanophyllia europaea and Leptopsammia pruvoti, collected in six different sites in different environmental conditions, which introduced a decisive improvement in the results. Nevertheless, the theory of the energy balance in growth ascertains the linear correlation of the two parameters and the independence of the ultimate length L∞ from the influence of environmental covariates, so a further aim of the thesis was to propose a new parameterization based on the ultimate length and parameter c which explicitly describes the part of growth ascribable to site-specific conditions such as environmental factors. We explored the possibility of estimating these parameters characterizing the VBGF new parameterization via the nonlinear hierarchical model. Again there was a general improvement with respect to traditional methods. The results of the two parameterizations were similar, although a very slight improvement was observed in the new one. This is, nevertheless, more suitable from a theoretical point of view when considering environmental covariates.

Effect of Laser Shock Peening on Fatigue Crack Propagation of Aeronautical Structures

Laser Shock Peening (LSP) is a surface enhancement treatment which induces a significant layer of beneficial compressive residual stresses up to several mm underneath the surface of metal components in order to improve the detrimental effects of crack growth behavior rate in it. The aim of this thesis is to predict the crack growth behavior of thin Aluminum specimens with one or more LSP stripes defining a compressive residual stress area. The LSP treatment has been applied as crack retardation stripes perpendicular to the crack growing direction, with the objective of slowing down the crack when approaching the LSP patterns. Different finite element approaches have been implemented to predict the residual stress field left by the laser treatment, mostly by means of the commercial software Abaqus/Explicit. The Afgrow software has been used to predict the crack growth behavior of the component following the laser peening treatment and to detect the improvement in fatigue life comparing to the specimen baseline. Furthermore, an analytical model has been implemented on the Matlab software to make more accurate predictions on fatigue life of the treated components. An educational internship at the Research and Technologies Germany- Hamburg department of Airbus helped to achieve knowledge and experience to write this thesis. The main tasks of the thesis are the following: -To up to date Literature Survey related to laser shock peening in metallic structures -To validate the FE models developed against experimental measurements at coupon level -To develop design of crack growth slow down in centered and edge cracked tension specimens based on residual stress engineering approach using laser peened patterns transversal to the crack path -To predict crack growth behavior of thin aluminum panels -To validate numerical and analytical results by means of experimental tests.

Fatigue Crack Propagation in Pressurized metallic Fuselages

On the basis of well-known literature, an analytical tool named LEAF (Linear Elastic Analysis of Fracture) was developed to predict the Damage Tolerance (DT) proprieties of aeronautical stiffened panels. The tool is based on the linear elastic fracture mechanics and the displacement compatibility method. By means of LEAF, an extensive parametric analysis of stiffened panels, representative of typical aeronautical constructions, was performed to provide meaningful design guidelines. The effects of riveted, integral and adhesively bonded stringers on the fatigue crack propagation performances of stiffened panels were investigated, as well as the crack retarder contribution using metallic straps (named doublers) bonded in the middle of the stringers bays. The effect of both perfectly bonded and partially debonded doublers was investigated as well. Adhesively bonded stiffeners showed the best DT properties in comparison with riveted and integral ones. A great reduction of the skin crack growth propagation rate can be achieved with the adoption of additional doublers bonded between the stringers.

Bonded structures for enhanced damage tolerant pressurized fuselages

Adhesive bonding provides solutions to realize cost effective and low weight aircraft fuselage structures, in particular where the Damage Tolerance (DT) is the design criterion. Bonded structures that combine Metal Laminates (MLs) and eventually Selective Reinforcements can guarantee slow crack propagation, crack arrest and large damage capability. To optimize the design exploiting the benefit of bonded structures incorporating selective reinforcement requires reliable analysis tools. The effect of bonded doublers / selective reinforcements is very difficult to be predicted numerically or analytically due to the complexity of the underlying mechanisms and failures modes acting. Reliable predictions of crack growth and residual strength can only be based on sound empirical and phenomenological considerations strictly related to the specific structural concept. Large flat stiffened panels that combine MLs and selective reinforcements have been tested with the purpose of investigating solutions applicable to pressurized fuselages. The large test campaign (for a total of 35 stiffened panels) has quantitatively investigated the role of the different metallic skin concepts (monolithic vs. MLs) of the aluminum, titanium and glass-fiber reinforcements, of the stringers material and cross sections and of the geometry and location of doublers / selective reinforcements. Bonded doublers and selective reinforcements confirmed to be outstanding tools to improve the DT properties of structural elements with a minor weight increase. However the choice of proper materials for the skin and the stringers must be not underestimated since they play an important role as well. A fuselage structural concept has been developed to exploit the benefit of a metal laminate design concept in terms of high Fatigue and Damage Tolerance (F&DT) performances. The structure used laminated skin (0.8mm thick), bonded stringers, two different splicing solutions and selective reinforcements (glass prepreg embedded in the laminate) under the circumferential frames. To validate the design concept a curved panel was manufactured and tested under loading conditions representative of a single aisle fuselage: cyclic internal pressurization plus longitudinal loads. The geometry of the panel, design and loading conditions were tailored for the requirements of the upper front fuselage. The curved panel has been fatigue tested for 60 000 cycles before the introduction of artificial damages (cracks in longitudinal and circumferential directions). The crack growth of the artificial damages has been investigated for about 85 000 cycles. At the end a residual strength test has been performed with a “2 bay over broken frame” longitudinal crack. The reparability of this innovative concept has been taken into account during design and demonstrated with the use of an external riveted repair. The F&DT curved panel test has confirmed that a long fatigue life and high damage tolerance can be achieved with a hybrid metal laminate low weight configuration. The superior fatigue life from metal laminates and the high damage tolerance characteristics provided by integrated selective reinforcements are the key concepts that provided the excellent performances. The weight comparison between the innovative bonded concept and a conventional monolithic riveted design solution showed a significant potential weight saving but the weight advantages shall be traded off with the additional costs.

Fracture Toughening and Self-Healing of Composite Laminates by Nanofibrous Mats Interleaving

Composite laminates present important advantages compared to conventional monolithic materials, mainly because for equal stiffness and strength they have a weight up to four times lower. However, due to their ply-by-ply nature, they are susceptible to delamination, whose propagation can bring the structure to a rapid catastrophic failure. In this thesis, in order to increase the service life of composite materials, two different approaches were explored: increase the intrinsic resistance of the material or confer to them the capability of self-repair. The delamination has been hindered through interleaving the composite laminates with polymeric nanofibers, which completed the hierarchical reinforcement scale of the composite. The manufacturing process for the integration of the nanofibrous mat in the laminate was optimized, resulting in an enhancement of mode I fracture toughness up to 250%. The effect of the geometrical dimensions of the nano-reinforcement on the architecture of the micro one (UD and woven laminates) was studied on mode I and II. Moreover, different polymeric materials were employed as nanofibrous reinforcement (Nylon 66 and polyvinylidene fluoride). The nano toughening mechanism was studied by micrograph analysis of the crack path and SEM analysis of the fracture surface. The fatigue behavior to the onset of the delamination and the crack growth rate for woven laminates interleaved with Nylon 66 nanofibers was investigated. Furthermore, the impact behavior of GLARE aluminum-glass epoxy laminates, toughened with Nylon 66 nanofibers was investigated. Finally, the possibility of confer to the composite material the capability of self-repair was explored. An extrinsic self-healing-system, based on core-shell nanofibers filled with a two-component epoxy system, was developed by co-electrospinning technique. The healing potential of the nano vascular system has been proved by microscope electron observation of the healing agent release as result of the vessels rupture and the crosslinking reaction was verified by thermal analysis.

Essays on asset pricing

The first chapter provides evidence that aggregate Research and Development (R&D) investment drives a persistent component in productivity growth and that this embodies a risk priced in financial markets. In a semi-endogenous growth model, this component is identified by the R&D in excess of equilibrium levels and can be approximated by the Error Correction Term in the cointegration between R&D and Total Factor Productivity. Empirically, the component results being well defined and it satisfies all key theoretical predictions: it exhibits appropriate persistency, it forecasts productivity growth, and it is associated with a cross-sectional risk premium. CAPM is the most foundational model in financial economics, but is known to empirically underestimate expected returns of low-risk assets and overestimate those with high risk. The second chapter studies how risks omission and funding tightness jointly contribute to explaining this anomaly, with the former affecting the definition of assets’ riskiness and the latter affecting how risk is remunerated. Theoretically, the two effects are shown to counteract each other. Empirically, the spread related to binding leverage constraints is found to be significant at 2% yearly. Nonetheless, average returns of portfolios that exploit this anomaly are found to mostly reflect omitted risks, in contrast to their employment in previous literature. The third chapter studies how ‘sustainability’ of assets affect discount rates, which is intrinsically mediated by the risk profile of the assets themselves. This has implications for the assessment of the sustainability-related spread and for hedging changes in the sustainability concern. This mechanism is tested on the ESG-score dimension for US data, with inconclusive evidence regarding the existence of an ESG-related premium in the first place. Also, the risk profile of the long-short ESG portfolio is not likely to impact the sign of its average returns with respect to the sustainability-spread, for the time being.

Physical model of PD behavior and relevant damage growth from micro-cavities in polyethylene-based material under AC voltage

In the framework of developing defect-based life models, in which breakdown is explicitly associated with partial discharge (PD)-induced damage growth from a defect, ageing tests and PD measurements were carried out in the lab on polyethylene (PE) layered specimens containing artificial cavities. PD activity was monitored continuously during aging. A quasi-deterministic series of stages can be observed in the behavior of the main PD parameters (i.e. discharge repetition rate and amplitude). Phase-resolved PD patterns at various ageing stages were reproduced by numerical simulation which is based on a physical discharge model devoid of adaptive parameters. The evolution of the simulation parameters provides insight into the physical-chemical changes taking place at the dielectric/cavity interface during the aging process. PD activity shows similar time behavior under constant cavity gas volume and constant cavity gas pressure conditions, suggesting that the variation of PD parameters may not be attributed to the variation of the gas pressure. Brownish PD byproducts, consisting of oxygen containing moieties, and degradation pits were found at the dielectric/cavity interface. It is speculated that the change of PD activity is related to the composition of the cavity gas, as well as to the properties of dielectric/cavity interface.