Some recent applications of non-linear models to the engineering practice

The Department of Structural Analysis of the University of Santander has been for a longtime involved in the solution of the country´s practical engineering problems. Some of these have required the use of non-conventional methods of analysis, in order to achieve adequate engineering answers. As an example of the increasing application of non-linear computer codes in the nowadays engineering practice, some cases will be briefly presented. In each case, only the main features of the problem involved and the solution used to solve it will be shown

Turbulence models of gravitational clustering.

Large-scale structure formation can be modeled as a nonlinear process that transfers energy from the largest scales to successively smaller scales until it is dissipated, in analogy with Kolmogorov’s cascade model of incompressible turbulence. However, cosmic turbulence is very compressible, and vorticity plays a secondary role in it. The simplest model of cosmic turbulence is the adhesion model, which can be studied perturbatively or adapting to it Kolmogorov’s non-perturbative approach to incompressible turbulence. This approach leads to observationally testable predictions, e.g., to the power-law exponent of the matter density two-point correlation function.

Analytical solution to the one-dimensional non-uniform absorption of solar radiation in uncoated and coated single glass panes

The analytical solution to the one-dimensional absorption–conduction heat transfer problem inside a single glass pane is presented, which correctly takes into account all the relevant physical phenomena: the appearance of multiple reflections, the spectral distribution of solar radiation, the spectral dependence of optical properties, the presence of possible coatings, the non-uniform nature of radiation absorption, and the diffusion of heat by conduction across the glass pane. Additionally to the well established and known direct absorptance αe, the derived solution introduces a new spectral quantity called direct absorptance moment βe, that indicates where in the glass pane is the absorption of radiation actually taking place. The theoretical and numerical comparison of the derived solution with existing approximate thermal models for the absorption–conduction problem reveals that the latter ones work best for low-absorbing uncoated single glass panes, something not necessarily fulfilled by modern glazings.

Continuum models of the mechanical behavior of rolled and die-cast magnesium alloys

En los últimos años ha habido una fuerte tendencia a disminuir las emisiones de CO2 y su negativo impacto medioambiental. En la industria del transporte, reducir el peso de los vehículos aparece como la mejor opción para alcanzar este objetivo. Las aleaciones de Mg constituyen un material con gran potencial para el ahorro de peso. Durante la última década se han realizado muchos esfuerzos encaminados a entender los mecanismos de deformación que gobiernan la plasticidad de estos materiales y así, las aleaciones de Mg de colada inyectadas a alta presión y forjadas son todavía objeto de intensas campañas de investigación. Es ahora necesario desarrollar modelos que contemplen la complejidad inherente de los procesos de deformación de éstos. Esta tesis doctoral constituye un intento de entender mejor la relación entre la microestructura y el comportamiento mecánico de aleaciones de Mg, y dará como resultado modelos de policristales capaces de predecir propiedades macro- y microscópicas. La deformación plástica de las aleaciones de Mg está gobernada por una combinación de mecanismos de deformación característicos de la estructura cristalina hexagonal, que incluye el deslizamiento cristalográfico en planos basales, prismáticos y piramidales, así como el maclado. Las aleaciones de Mg de forja presentan texturas fuertes y por tanto los mecanismos de deformación activos dependen de la orientación de la carga aplicada. En este trabajo se ha desarrollado un modelo de plasticidad cristalina por elementos finitos con el objetivo de entender el comportamiento macro- y micromecánico de la aleación de Mg laminada AZ31 (Mg-3wt.%Al-1wt.%Zn). Este modelo, que incorpora el maclado y tiene en cuenta el endurecimiento por deformación debido a las interacciones dislocación-dislocación, dislocación-macla y macla-macla, predice exitosamente las actividades de los distintos mecanismos de deformación y la evolución de la textura con la deformación. Además, se ha llevado a cabo un estudio que combina difracción de electrones retrodispersados en tres dimensiones y modelización para investigar el efecto de los límites de grano en la propagación del maclado en el mismo material. Ambos, experimentos y simulaciones, confirman que el ángulo de desorientación tiene una influencia decisiva en la propagación del maclado. Se ha observado que los efectos no-Schmid, esto es, eventos de deformación plástica que no cumplen la ley de Schmid con respecto a la carga aplicada, no tienen lugar en la vecindad de los límites de baja desorientación y se hacen más frecuentes a medida que la desorientación aumenta. Esta investigación también prueba que la morfología de las maclas está altamente influenciada por su factor de Schmid. Es conocido que los procesos de colada suelen dar lugar a la formación de microestructuras con una microporosidad elevada, lo cuál afecta negativamente a sus propiedades mecánicas. La aplicación de presión hidrostática después de la colada puede reducir la porosidad y mejorar las propiedades aunque es poco conocido su efecto en el tamaño y morfología de los poros. En este trabajo se ha utilizado un enfoque mixto experimentalcomputacional, basado en tomografía de rayos X, análisis de imagen y análisis por elementos finitos, para la determinación de la distribución tridimensional (3D) de la porosidad y de la evolución de ésta con la presión hidrostática en la aleación de Mg AZ91 (Mg- 9wt.%Al-1wt.%Zn) colada por inyección a alta presión. La distribución real de los poros en 3D obtenida por tomografía se utilizó como input para las simulaciones por elementos finitos. Los resultados revelan que la aplicación de presión tiene una influencia significativa tanto en el cambio de volumen como en el cambio de forma de los poros que han sido cuantificados con precisión. Se ha observado que la reducción del tamaño de éstos está íntimamente ligada con su volumen inicial. En conclusión, el modelo de plasticidad cristalina propuesto en este trabajo describe con éxito los mecanismos intrínsecos de la deformación de las aleaciones de Mg a escalas meso- y microscópica. Más especificamente, es capaz de capturar las activadades del deslizamiento cristalográfico y maclado, sus interacciones, así como los efectos en la porosidad derivados de los procesos de colada. ---ABSTRACT--- The last few years have seen a growing effort to reduce CO2 emissions and their negative environmental impact. In the transport industry more specifically, vehicle weight reduction appears as the most straightforward option to achieve this objective. To this end, Mg alloys constitute a significant weight saving material alternative. Many efforts have been devoted over the last decade to understand the main mechanisms governing the plasticity of these materials and, despite being already widely used, high pressure die-casting and wrought Mg alloys are still the subject of intense research campaigns. Developing models that can contemplate the complexity inherent to the deformation of Mg alloys is now timely. This PhD thesis constitutes an attempt to better understand the relationship between the microstructure and the mechanical behavior of Mg alloys, as it will result in the design of polycrystalline models that successfully predict macro- and microscopic properties. Plastic deformation of Mg alloys is driven by a combination of deformation mechanisms specific to their hexagonal crystal structure, namely, basal, prismatic and pyramidal dislocation slip as well as twinning. Wrought Mg alloys present strong textures and thus specific deformation mechanisms are preferentially activated depending on the orientation of the applied load. In this work a crystal plasticity finite element model has been developed in order to understand the macro- and micromechanical behavior of a rolled Mg AZ31 alloy (Mg-3wt.%Al-1wt.%Zn). The model includes twinning and accounts for slip-slip, slip-twin and twin-twin hardening interactions. Upon calibration and validation against experiments, the model successfully predicts the activity of the various deformation mechanisms and the evolution of the texture at different deformation stages. Furthermore, a combined three-dimensional electron backscatter diffraction and modeling approach has been adopted to investigate the effect of grain boundaries on twin propagation in the same material. Both experiments and simulations confirm that the misorientation angle has a critical influence on twin propagation. Non-Schmid effects, i.e. plastic deformation events that do not comply with the Schmid law with respect to the applied stress, are absent in the vicinity of low misorientation boundaries and become more abundant as misorientation angle increases. This research also proves that twin morphology is highly influenced by the Schmid factor. Finally, casting processes usually lead to the formation of significant amounts of gas and shrinkage microporosity, which adversely affect the mechanical properties. The application of hydrostatic pressure after casting can reduce the porosity and improve the properties but little is known about the effects on the casting’s pores size and morphology. In this work, an experimental-computational approach based on X-ray computed tomography, image analysis and finite element analysis is utilized for the determination of the 3D porosity distribution and its evolution with hydrostatic pressure in a high pressure diecast Mg AZ91 alloy (Mg-9wt.%Al-1wt.%Zn). The real 3D pore distribution obtained by tomography is used as input for the finite element simulations using an isotropic hardening law. The model is calibrated and validated against experimental stress-strain curves. The results reveal that the pressure treatment has a significant influence both on the volume and shape changes of individuals pores, which have been precisely quantified, and which are found to be related to the initial pore volume. In conclusion, the crystal plasticity model proposed in this work successfully describes the intrinsic deformation mechanisms of Mg alloys both at the mesoscale and the microscale. More specifically, it can capture slip and twin activities, their interactions, as well as the potential porosity effects arising from casting processes.

An introduction to flow and transport in fractal models of porous media: Part I

This special issue gathers together a number of recent papers on fractal geometry and its applications to the modeling of flow and transport in porous media. The aim is to provide a systematic approach for analyzing the statics and dynamics of fluids in fractal porous media by means of theory, modeling and experimentation. The topics covered include lacunarity analyses of multifractal and natural grayscale patterns, random packing's of self-similar pore/particle size distributions, Darcian and non-Darcian hydraulic flows, diffusion within fractals, models for the permeability and thermal conductivity of fractal porous media and hydrophobicity and surface erosion properties of fractal structures.

Non-linear Control of an Autonomous Ground Vehicle

In this paper, in order to select a speed controller for a specific non-linear autonomous ground vehicle, proportional-integral-derivative (PID), Fuzzy, and linear quadratic regulator (LQR) controllers were designed. Here, in order to carry out the tuning of the above controllers, a multicomputer genetic algorithm (MGA) was designed. Then, the results of the MGA were used to parameterize the PID, Fuzzy and LQR controllers and to test them under laboratory conditions. Finally, a comparative analysis of the performance of the three controllers was conducted.

Assembling models of embryo development: Image analysis and the construction of digital atlases

Digital atlases of animal development provide a quantitative description of morphogenesis, opening the path toward processes modeling. Prototypic atlases offer a data integration framework where to gather information from cohorts of individuals with phenotypic variability. Relevant information for further theoretical reconstruction includes measurements in time and space for cell behaviors and gene expression. The latter as well as data integration in a prototypic model, rely on image processing strategies. Developing the tools to integrate and analyze biological multidimensional data are highly relevant for assessing chemical toxicity or performing drugs preclinical testing. This article surveys some of the most prominent efforts to assemble these prototypes, categorizes them according to salient criteria and discusses the key questions in the field and the future challenges toward the reconstruction of multiscale dynamics in model organisms.

Non-destructive measurements of the optical properties of apples by means of time-resolved reflectance

Time-resolved reflectance is proposed and effectively used for the nondestructive measurement of the optical properties in apples. The technique is based on the detection of the temporal dispersion of a short laser pulse injected into the probed medium. The time-distribution of re-emitted photons interpreted with a solution of the Diffusion equation yields the mean values of the absorption and reduced scattering coefficients of the medium. The proposed technique proved valuable for the measurement of the absorption and scattering spectra of different varieties of apples. No major variations were observed in the experimental data when the fruit was peeled, proving that the measured optical properties are referred to the pulp. The depth of probed volume was determined to be about 2 cm. Finally, the technique proved capable to follow the change in chlorophyll absorption during storage.

Non-destructive measurements of the optical properties of apples by means of time-resolved reflectance

Time-resolved reflectance is proposed and effectively used for the nondestructive measurement of the optical properties in apples. The technique is based on the detection of the temporal dispersion of a short laser pulse injected into the probed medium. The time-distribution of re-emitted photons interpreted with a solution of the Diffusion equation yields the mean values of the absorption and reduced scattering coefficients of the medium. The proposed technique proved valuable for the measurement of the absorption and scattering spectra of different varieties of apples. No major variations were observed in the experimental data when the fruit was peeled, proving that the measured optical properties are referred to the pulp. The depth of probed volume was determined to be about 2 cm. Finally, the technique proved capable to follow the change in chlorophyll absorption during storage.

Evaluation and improvement of empirical models of global solar irradiation: Case study northern Spain

This paper presents a new methodology to build parametric models to estimate global solar irradiation adjusted to specific on-site characteristics based on the evaluation of variable im- portance. Thus, those variables higly correlated to solar irradiation on a site are implemented in the model and therefore, different models might be proposed under different climates. This methodology is applied in a study case in La Rioja region (northern Spain). A new model is proposed and evaluated on stability and accuracy against a review of twenty-two already exist- ing parametric models based on temperatures and rainfall in seventeen meteorological stations in La Rioja. The methodology of model evaluation is based on bootstrapping, which leads to achieve a high level of confidence in model calibration and validation from short time series (in this case five years, from 2007 to 2011). The model proposed improves the estimates of the other twenty-two models with average mean absolute error (MAE) of 2.195 MJ/m2 day and average confidence interval width (95% C.I., n=100) of 0.261 MJ/m2 day. 41.65% of the daily residuals in the case of SIAR and 20.12% in that of SOS Rioja fall within the uncertainty tolerance of the pyranometers of the two networks (10% and 5%, respectively). Relative differences between measured and estimated irradiation on an annual cumulative basis are below 4.82%. Thus, the proposed model might be useful to estimate annual sums of global solar irradiation, reaching insignificant differences between measurements from pyranometers.

Non-periodic driving of coupled oscillators:a spherical swing

Nonlinearly coupled, damped oscillators at 1:1 frequency ratio, one oscillator being driven coherently for efficient excitation, are exemplified by a spherical swing with some phase-mismatch between drive and response. For certain damping range, excitation is found to succeed if it lags behind, but to produce a chaotic attractor if it leads the response. Although a period-doubhng sequence, for damping increasing, leads to the attractor, this is actually born as a hard (as regards amplitude) bifurcation at a zero growth-rate parametric line; as damping decreases, an unstable fixed point crosses an invariant plane to enter as saddle-focus a phase-space domain of physical solutions. A second hard bifurcation occurs at the zero mismatch line, the saddle-focus leaving that domain. Times on the attractor diverge when approaching either fine, leading to exactly one-dimensional and noninvertible limit maps, which are analytically determined.

Influence of temperature and moisture content in Non-destructive values of Scots pine (Pinus sylvestris L.)

Good results evaluating material properties using non-destructive testing (NDT) techniques have been achieved for decades. Several studies to understand the influence of temperature and moisture content on NDT have concluded different effects. In this study, NDT parameters were measured on the principal structural Spanish sawn timber species, Scots pine (Pinus sylvestris L.). NDT were conducted on 216 specimens of nominal dimensions 20 by 20 by 400 mm. Specimens were divided into several groups and studied at six different temperatures and four different moisture contents. Commercial equipment and techniques applied were Sylvatest Duo (ultrasonic wave technique), Steinkamp BPV (ultrasonic wave technique), and Grindo Sonic Mk5 "Industrial" (vibration analysis technique). Differences in NDT values within specimens at different temperatures and moisture contents were obtained. Main results of this study and relationships that describe changes in NDT values by effect of temperature and moisture content are presented.

Non-Destructive Identification of Woolly Peaches combining Mechanical Impact Response and NIR Spectroscopy.

Woolliness (mealiness in other fruits) is a negative attribute of peach sensory texture that is a physiological disorder associated with inadequate cold storage. It is characterised by lack of crispness and juiciness without variation in the tissue water content (Harker and Hallet, 1992). Many attempts have been made to develop destructive instrumental procedures to detect mealiness and woolliness. Non-destructive procedures attempted include using nuclear magnetic resonance (Sonego et al., 1995). However, this technique has economical limitations and is not practical at present. Non-destructive impact tests and NIR are non-destructive techniques which have been used to assess internal characteristics of fruits (Chen and Sun, 1991). The objective of this study was to develop a novel non-destructive procedure to identify woolly peaches by combining impact and NIR approaches.

Characterization of ICT-based business models of social enterprises

In recent years new models for organizations working on overty alleviation have emerged. One of them, the social enterprise, has attracted the attention of both academics and practitioners all over the world. Even if defined in different ways depending on the context, social enterprise has an enormous potential to generate social benefits and to promote local agency and private initiative in poverty alleviation. In this sense, it is fitting to highlight the importance of identifying the main standards that permit the characterization of diverse social enterprises, in order to understand their main specificities and guarantee value generation for low-income populations. Another crucial factor is understanding innovation as a critical factor in promoting social enterprises. A powerful tool to enhance the impact and application of this model is Information and Communication Technologies. In the 21st century,these tools allow users to find new ways of collaboration, new sustainable business models and a cost-effective way of scaling-up initiatives. This paper, a product of the collaborative research between the Universidad Politécnica de Madrid and the Universidade Federal Fluminense, examines different business models for social enterprises and the role that ICT can play in scale and impact of these initiatives

Brain injury MRI simulator based on theoretical models of neuroanatomic damage

In order to improve the body of knowledge about brain injury impairment is essential to develop image database with different types of injuries. This paper proposes a new methodology to model three types of brain injury: stroke, tumor and traumatic brain injury; and implements a system to navigate among simulated MRI studies. These studies can be used on research studies, to validate new processing methods and as an educational tool, to show different types of brain injury and how they affect to neuroanatomic structures.