Meccanismi di formazione dei tubi di lava

Two analytical models are proposed to describe two different mechanisms of lava tubes formation. A first model is introduced to describe the development of a solid crust in the central region of the channel, and the formation of a tube when crust widens until it reaches the leve\'es. The Newtonian assumption is considered and the steady state Navier- Stokes equation in a rectangular conduit is solved. A constant heat flux density assigned at the upper flow surface resumes the combined effects of two thermal processes: radiation and convection into the atmosphere. Advective terms are also included, by the introduction of velocity into the expression of temperature. Velocity is calculated as an average value over the channel width, so that lateral variations of temperature are neglected. As long as the upper flow surface cools, a solid layer develops, described as a plastic body, having a resistance to shear deformation. If the applied shear stress exceeds this resistance, crust breaks, otherwise, solid fragments present at the flow surface can weld together forming a continuous roof, as it happens in the sidewall flow regions. Variations of channel width, ground slope and effusion rate are analyzed, as parameters that strongly affect the shear stress values. Crust growing is favored when the channel widens, and tube formation is possible when the ground slope or the effusion rate reduce. A comparison of results is successfully made with data obtained from the analysis of pictures of actual flows. The second model describes the formation of a stable, well defined crust along both channel sides, their growing towards the center and their welding to form the tube roof. The fluid motion is described as in the model above. Thermal budget takes into account conduction into the atmosphere, and advection is included considering the velocity depending both on depth and channel width. The solidified crust has a non uniform thickness along the channel width. Stresses acting on the crust are calculated using the equations of the elastic thin plate, pinned at its ends. The model allows to calculate the distance where crust thickness is able to resist the drag of the underlying fluid and to sustain its weight by itself, and the level of the fluid can lower below the tube roof. Viscosity and thermal conductivity have been experimentally investigated through the use of a rotational viscosimeter. Analyzing samples coming from Mount Etna (2002) the following results have been obtained: the fluid is Newtonian and the thermal conductivity is constant in a range of temperature above the liquidus. For lower temperature, the fluid becomes non homogeneous, and the used experimental techniques are not able to detect any properties, because measurements are not reproducible.

Static analysis of functionally graded cylindrical and conical shells or panels using the generalized unconstrained third order theory coupled with the stress recovery

A 2D Unconstrained Third Order Shear Deformation Theory (UTSDT) is presented for the evaluation of tangential and normal stresses in moderately thick functionally graded conical and cylindrical shells subjected to mechanical loadings. Several types of graded materials are investigated. The functionally graded material consists of ceramic and metallic constituents. A four parameter power law function is used. The UTSDT allows the presence of a finite transverse shear stress at the top and bottom surfaces of the graded shell. In addition, the initial curvature effect included in the formulation leads to the generalization of the present theory (GUTSDT). The Generalized Differential Quadrature (GDQ) method is used to discretize the derivatives in the governing equations, the external boundary conditions and the compatibility conditions. Transverse and normal stresses are also calculated by integrating the three dimensional equations of equilibrium in the thickness direction. In this way, the six components of the stress tensor at a point of the conical or cylindrical shell or panel can be given. The initial curvature effect and the role of the power law functions are shown for a wide range of functionally conical and cylindrical shells under various loading and boundary conditions. Finally, numerical examples of the available literature are worked out.

Modelling and analysis of thin-walled beams in the context of the Generalized Beam Theory

In this work, the Generalized Beam Theory (GBT) is used as the main tool to analyze the mechanics of thin-walled beams. After an introduction to the subject and a quick review of some of the most well-known approaches to describe the behaviour of thin-walled beams, a novel formulation of the GBT is presented. This formulation contains the classic shear-deformable GBT available in the literature and contributes an additional description of cross-section warping that is variable along the wall thickness besides along the wall midline. Shear deformation is introduced in such a way that the classical shear strain components of the Timoshenko beam theory are recovered exactly. According to the new kinematics proposed, a reviewed form of the cross-section analysis procedure is devised, based on a unique modal decomposition. Later, a procedure for a posteriori reconstruction of all the three-dimensional stress components in the finite element analysis of thin-walled beams using the GBT is presented. The reconstruction is simple and based on the use of three-dimensional equilibrium equations and of the RCP procedure. Finally, once the stress reconstruction procedure is presented, a study of several existing issues on the constitutive relations in the GBT is carried out. Specifically, a constitutive law based on mirroring the kinematic constraints of the GBT model into a specific stress field assumption is proposed. It is shown that this method is equally valid for isotropic and orthotropic beams and coincides with the conventional GBT approach available in the literature. Later on, an analogous procedure is presented for the case of laminated beams. Lastly, as a way to improve an inherently poor description of shear deformability in the GBT, the introduction of shear correction factors is proposed. Throughout this work, numerous examples are provided to determine the validity of all the proposed contributions to the field.

(Table 1) Magnetic susceptibility readings in the western part of the Sør Rondane Montains

The Sør Rondane Mountains (SRM) in eastern Dronning Maud Land (DML) are located in an area, where two apparent Pan-African (650-520 Ma) orogenic mobile belts appear to intersect, the East African-Antarctic Orogen and the Kuunga Orogen. Hence, a better understanding of the tectonic structure of the Sør Rondane region is an important key for unravelling the complex geodynamic evolution of the eastern DML and adjacent regions of East Antarctica during the Late Neoproterozoic/Early Palaeozoic amalgamation of Gondwana. The SRM were recently (2011-2012) aerogeophysically investigated with a 5 km flight line spacing, covering a total area of ~140,000 km². The aeromagnetic data are correlated with ground-based magnetic susceptibility measurements and geological field data and allow to project tectonic terranes and individual structures into ice-covered areas. Magnetic anomalies and basement foliation trends are collinear in areas dominated by simple shear deformation, whereas an area of large-scale refolding correlates with a subdued small-scale broken magnetic anomaly pattern. The latter area can be regarded as a distinct tectonic domain, the central Sør Rondane corridor. It magnetically separates the SRM into an eastern, a central, and a western portion. This subdivision is presumably related to late Pan-African extensional tectonics and suggests that such a tectonic regime may play a larger role than previously assumed. Voluminous late Pan-African granitoids, which are mainly undeformed, correlate with positive magnetic anomalies between +30 and +80 nT, while a strong magnetic high (+680 nT) near the granitic intrusion at Dufekfjellet is caused by a highly magnetised enigmatic body. The recently discovered prominent magnetic anomaly province of southeastern DML continues into the southern part of the Sør Rondane region, where only a few outcrops are exposed. Findings at these westernmost nunataks of the SRM indicate that the subdued magnetic anomaly pattern of this southeastern DML province is most likely caused by the predominance of metasedimentary rocks of yet unknown age.

High fidelity simulations of failure in fiber-reinforced composites

Los ensayos virtuales de materiales compuestos han aparecido como un nuevo concepto dentro de la industria aeroespacial, y disponen de un vasto potencial para reducir los enormes costes de certificación y desarrollo asociados con las tediosas campañas experimentales, que incluyen un gran número de paneles, subcomponentes y componentes. El objetivo de los ensayos virtuales es sustituir algunos ensayos por simulaciones computacionales con alta fidelidad. Esta tesis es una contribución a la aproximación multiescala desarrollada en el Instituto IMDEA Materiales para predecir el comportamiento mecánico de un laminado de material compuesto dadas las propiedades de la lámina y la intercara. La mecánica de daño continuo (CDM) formula el daño intralaminar a nivel constitutivo de material. El modelo de daño intralaminar se combina con elementos cohesivos para representar daño interlaminar. Se desarrolló e implementó un modelo de daño continuo, y se aplicó a configuraciones simples de ensayos en laminados: impactos de baja y alta velocidad, ensayos de tracción, tests a cortadura. El análisis del método y la correlación con experimentos sugiere que los métodos son razonablemente adecuados para los test de impacto, pero insuficientes para el resto de ensayos. Para superar estas limitaciones de CDM, se ha mejorado la aproximación discreta de elementos finitos enriqueciendo la cinemática para incluir discontinuidades embebidas: el método extendido de los elementos finitos (X-FEM). Se adaptó X-FEM para un esquema explícito de integración temporal. El método es capaz de representar cualitativamente los mecanismos de fallo detallados en laminados. Sin embargo, los resultados muestran inconsistencias en la formulación que producen resultados cuantitativos erróneos. Por último, se ha revisado el método tradicional de X-FEM, y se ha desarrollado un nuevo método para superar sus limitaciones: el método cohesivo X-FEM estable. Las propiedades del nuevo método se estudiaron en detalle, y se concluyó que el método es robusto para implementación en códigos explícitos dinámicos escalables, resultando una nueva herramienta útil para la simulación de daño en composites. Virtual testing of composite materials has emerged as a new concept within the aerospace industry. It presents a very large potential to reduce the large certification costs and the long development times associated with the experimental campaigns, involving the testing of a large number of panels, sub-components and components. The aim of virtual testing is to replace some experimental tests by high-fidelity numerical simulations. This work is a contribution to the multiscale approach developed in Institute IMDEA Materials to predict the mechanical behavior of a composite laminate from the properties of the ply and the interply. Continuum Damage Mechanics (CDM) formulates intraply damage at the the material constitutive level. Intraply CDM is combined with cohesive elements to model interply damage. A CDM model was developed, implemented, and applied to simple mechanical tests of laminates: low and high velocity impact, tension of coupons, and shear deformation. The analysis of the results and the comparison with experiments indicated that the performance was reasonably good for the impact tests, but insuficient in the other cases. To overcome the limitations of CDM, the kinematics of the discrete finite element approximation was enhanced to include mesh embedded discontinuities, the eXtended Finite Element Method (X-FEM). The X-FEM was adapted to an explicit time integration scheme and was able to reproduce qualitatively the physical failure mechanisms in a composite laminate. However, the results revealed an inconsistency in the formulation that leads to erroneous quantitative results. Finally, the traditional X-FEM was reviewed, and a new method was developed to overcome its limitations, the stable cohesive X-FEM. The properties of the new method were studied in detail, and it was demonstrated that the new method was robust and can be implemented in a explicit finite element formulation, providing a new tool for damage simulation in composite materials.

Análisis de elementos viga-columna en régimen no lineal con deformación por cortante

El hormigón estructural sigue siendo sin duda uno de los materiales más utilizados en construcción debido a su resistencia, rigidez y flexibilidad para diseñar estructuras. El cálculo de estructuras de hormigón, utilizando vigas y vigas-columna, es complejo debido a los fenómenos de acoplamiento entre esfuerzos y al comportamiento no lineal del material. Los modelos más empleados para su análisis son el de Bernoulli-Euler y el de Timoshenko, indicándose en la literatura la conveniencia de usar el segundo cuando la relación canto/luz no es pequeña o los elementos están fuertemente armados. El objetivo fundamental de esta tesis es el análisis de elementos viga y viga-columna en régimen no lineal con deformación por cortante, aplicando el concepto de Pieza Lineal Equivalente (PLE). Concepto éste que consiste básicamente en resolver el problema de una pieza en régimen no lineal, transformándolo en uno lineal equivalente, de modo que ambas piezas tengan la misma deformada y los mismos esfuerzos. Para ello, se hizo en primer lugar un estudio comparado de: las distintas propuestas que aplican la deformación por cortante, de los distintos modelos constitutivos y seccionales del hormigón estructural y de los métodos de cálculo no lineal aplicando el método de elementos finitos (MEF). Teniendo en cuenta que la resolución del problema no lineal se basa en la resolución de sucesivos problemas lineales empleando un proceso de homotopía, los problemas lineales de la viga y viga-columna de Timoshenko, se resuelven mediante MEF, utilizando soluciones nodalmente exactas (SNE) y acción repartida equivalente de cualquier orden. Se obtiene así, con muy pocos elementos finitos, una excelente aproximación de la solución, no sólo en los nodos sino en el interior de los elementos. Se introduce el concepto PLE para el análisis de una barra, de material no lineal, sometida a acciones axiales, y se extiende el mismo para el análisis no lineal de vigas y vigas-columna con deformación por cortante. Cabe señalar que para estos últimos, la solución de una pieza en régimen no lineal es igual a la de una en régimen lineal, cuyas rigideces son constantes a trozos, y donde además hay que añadir momentos y cargas puntuales ficticias en los nodos, así como, un momento distribuido ficticio en toda la pieza. Se han desarrollado dos métodos para el análisis: uno para problemas isostáticos y otro general, aplicable tanto a problemas isostáticos como hiperestáticos. El primero determina de entrada la PLE, realizándose a continuación el cálculo por MEF-SNE de dicha pieza, que ahora está en régimen lineal. El general utiliza una homotopía que transforma de manera iterativa, unas leyes constitutivas lineales en las leyes no lineales del material. Cuando se combina con el MEF, la pieza lineal equivalente y la solución del problema original quedan determinadas al final de todo el proceso. Si bien el método general es un procedimiento próximo al de Newton- Raphson, presenta sobre éste la ventaja de permitir visualizar las deformaciones de la pieza en régimen no lineal, de manera tanto cualitativa como cuantitativa, ya que es posible observar en cada paso del proceso la modificación de rigideces (a flexión y cortante) y asimismo la evolución de las acciones ficticias. Por otra parte, los resultados obtenidos comparados con los publicados en la literatura, indican que el concepto PLE ofrece una forma directa y eficiente para analizar con muy buena precisión los problemas asociados a vigas y vigas-columna en las que por su tipología los efectos del cortante no pueden ser despreciados. ABSTRACT The structural concrete clearly remains the most used material in construction due to its strength, rigidity and structural design flexibility. The calculation of concrete structures using beams and beam-column is complex as consequence of the coupling phenomena between stresses and of its nonlinear behaviour. The models most commonly used for analysis are the Bernoulli-Euler and Timoshenko. The second model is strongly recommended when the relationship thickness/span is not small or in case the elements are heavily reinforced. The main objective of this thesis is to analyse the beam and beam-column elements with shear deformation in nonlinear regime, applying the concept of Equivalent Linear Structural Element (ELSE). This concept is basically to solve the problem of a structural element in nonlinear regime, transforming it into an equivalent linear structural element, so that both elements have the same deformations and the same stresses. Firstly, a comparative study of the various proposals of applying shear deformation, of various constitutive and sectional models of structural concrete, and of the nonlinear calculation methods (using finite element methods) was carried out. Considering that the resolution of nonlinear problem is based on solving the successive linear problem, using homotopy process, the linear problem of Timoshenko beam and beam-columns is resolved by FEM, using the exact nodal solutions (ENS) and equivalent distributed load of any order. Thus, the accurate solution approximation can be obtained with very few finite elements for not only nodes, but also for inside of elements. The concept ELSE is introduced to analyse a bar of nonlinear material, subjected to axial forces. The same bar is then used for other nonlinear beam and beam-column analysis with shear deformation. It is noted that, for the last analyses, the solution of a structural element in nonlinear regime is equal to that of linear regime, in which the piecewise-stiffness is constant, the moments and fictitious point loads need to be added at nodes of each element, as well as the fictitious distributed moment on element. Two methods have been developed for analysis: one for isostatic problem and other more general, applicable for both isostatic and hiperstatic problem. The first method determines the ELSE, and then the calculation of this piece is performed by FEM-ENS that now is in linear regime. The general method uses the homotopy that transforms iteratively linear constitutive laws into nonlinear laws of material. When combined with FEM, the ELSE and the solution of the original problem are determined at the end of the whole process. The general method is well known as a procedure closed to Newton-Raphson procedure but presents an advantage that allows displaying deformations of the piece in nonlinear regime, in both qualitative and quantitative way. Since it is possible to observe the modification of stiffness (flexural and shear) in each step of process and also the evolution of the fictitious actions. Moreover, the results compared with those published in the literature indicate that the ELSE concept offers a direct and efficient way to analyze with very good accuracy the problems associated with beams and beams columns in which, by typology, the effects of shear cannot be neglected.

Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections

This paper investigates the nonlinear vibration of imperfect shear deformable laminated rectangular plates comprising a homogeneous substrate and two layers of functionally graded materials (FGMs). A theoretical formulation based on Reddy's higher-order shear deformation plate theory is presented in terms of deflection, mid-plane rotations, and the stress function. A semi-analytical method, which makes use of the one-dimensional differential quadrature method, the Galerkin technique, and an iteration process, is used to obtain the vibration frequencies for plates with various boundary conditions. Material properties are assumed to be temperature-dependent. Special attention is given to the effects of sine type imperfection, localized imperfection, and global imperfection on linear and nonlinear vibration behavior. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with graded silicon nitride/stainless steel layers. It is shown that the vibration frequencies are very much dependent on the vibration amplitude and the imperfection mode and its magnitude. While most of the imperfect laminated plates show the well-known hard-spring vibration, those with free edges can display soft-spring vibration behavior at certain imperfection levels. The influences of material composition, temperature-dependence of material properties and side-to-thickness ratio are also discussed. (C) 2004 Elsevier Ltd. All rights reserved.

On the possibility of elastic strain localisation in a fault

The phenomenon of strain localisation is often observed in shear deformation of particulate materials, e.g., fault gouge. This phenomenon is usually attributed to special types of plastic behaviour of the material (e.g., strain softening or mismatch between dilatancy and pressure sensitivity or both). Observations of strain localisation in situ or in experiments are usually based on displacement measurements and subsequent computation of the displacement gradient. While in conventional continua the symmetric part of the displacement gradient is equal to the strain, it is no longer the case in the more realistic descriptions within the framework of generalised continua. In such models the rotations of the gouge particles are considered as independent degrees of freedom the values of which usually differ from the rotation of an infinitesimal volume element of the continuum, the latter being described for infinitesimal deformations by the non-symmetric part of the displacement gradient. As a model for gouge material we propose a continuum description for an assembly of spherical particles of equal radius in which the particle rotation is treated as an independent degree of freedom. Based on this model we consider simple shear deformations of the fault gouge. We show that there exist values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-layers of the fault, even in the absence of inelasticity. Inelastic effects are neglected in order to highlight the role of the independent rotations and the associated additional parameters. The localisation-like behaviour occurs if (a) the particle rotations on the boundary of the shear layer are constrained (this type of boundary condition does not exist in a standard continuum) and (b) the contact moment-or bending stiffness is much smaller than the product of the effective shear modulus of the granulate and the square of the width of the gouge layer. It should be noted however that the virtual work functional is positive definite over the range of physically meaningful parameters (here: contact stiffnesses, solid volume fraction and coordination number) so that strictly speaking we are not dealing with a material instability.

Random vibration of the functionally graded laminates in thermal environments

This work deals with the random free vibration of functionally graded laminates with general boundary conditions and subjected to a temperature change, taking into account the randomness in a number of independent input variables such as Young's modulus, Poisson's ratio and thermal expansion coefficient of each constituent material. Based on third-order shear deformation theory, the mixed-type formulation and a semi-analytical approach are employed to derive the standard eigenvalue problem in terms of deflection, mid-plane rotations and stress function. A mean-centered first-order perturbation technique is adopted to obtain the second-order statistics of vibration frequencies. A detailed parametric study is conducted, and extensive numerical results are presented in both tabular and graphical forms for laminated plates that contain functionally graded material which is made of aluminum and zirconia, showing the effects of scattering in thermo-clastic material constants, temperature change, edge support condition, side-to-thickness ratio, and plate aspect ratio on the stochastic characteristics of natural frequencies. (c) 2005 Elsevier B.V. All rights reserved.

Effect of rolling on dissipation in fault gouges

Sliding and rolling are two outstanding deformation modes in granular media. The first one induces frictional dissipation whereas the latter one involves deformation with negligible resistance. Using numerical simulations on two-dimensional shear cells, we investigate the effect of the grain rotation on the energy dissipation and the strength of granular materials under quasistatic shear deformation. Rolling and sliding are quantified in terms of the so-called Cosserat rotations. The observed spontaneous formation of vorticity cells and clusters of rotating bearings may provide an explanation for the long standing heat flow paradox of earthquake dynamics.

Vibration of symmetrically laminated thick super elliptical plates

This paper reports a free vibration analysis of thick plates with rounded corners subject to a free, simply-supported or clamped boundary condition. The plate perimeter is defined by a super elliptic function with a power defining the shape ranging from an ellipse to a rectangle. To incorporate transverse shear deformation, the Reddy third-order plate theory is employed. The energy integrals incorporating shear deformation and rotary inertia are formulated and the p-Ritz procedures are used to derive the governing eigenvalue equation. Numerical examples for plates with different shapes and boundary conditions are solved and their frequency parameters, where possible, are compared with known results. Parametric studies are carried out to show the sensitivities of frequency parameters by varying the geometry, fibre stacking sequence, and boundary condition. (C) 1999 Academic Press.

First principles calculation of electron-phonon and alloy scattering in strained SiGe

First-principles electronic structure methods are used to predict the mobility of n-type carrier scattering in strained SiGe. We consider the effects of strain on the electron-phonon deformation potentials and the alloy scattering parameters. We calculate the electron-phonon matrix elements and fit them up to second order in strain. We find, as expected, that the main effect of strain on mobility comes from the breaking of the degeneracy of the six Δ and L valleys, and the choice of transport direction. The non-linear effects on the electron-phonon coupling of the Δ valley due to shear strain are found to reduce the mobility of Si-like SiGe by 50% per % strain. We find increases in mobility between 2 and 11 times that of unstrained SiGe for certain fixed Ge compositions, which should enhance the thermoelectric figure of merit in the same order, and could be important for piezoresistive applications.

Strain hardening during constrained deformation of metal foams - Effect of shear displacement

The crush bands that form during plastic deformation of closed-cell metal foams are often inclined at 11-20 degrees to the loading axis, allowing for shear displacement of one part of the foam with respect to the other. Such displacement is prevented by the presence of a lateral constraint. This was analysed in this study, which shows that resistance against shear by the constraint leads to the strain-hardening effect in the foam that has been reported in a recent experimental study. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Ductile deformation of single inclusions in simple shear with a finite-strain hyperelastoviscoplastic rheology

We examine the 2D plane-­strain deformation of initially round, matrix-­bonded, deformable single inclusions in isothermal simple shear using a recently introduced hyperelastoviscoplastic rheology. The broad parameter space spanned by the wide range of effective viscosities, yield stresses, relaxation times, and strain rates encountered in the ductile lithosphere is explored systematically for weak and strong inclusions, the effective viscosity of which varies with respect to the matrix. Most inclusion studies to date focused on elastic or purely viscous rheologies. Comparing our results with linear-­viscous inclusions in a linear-­viscous matrix, we observe significantly different shape evolution of weak and strong inclusions over most of the relevant parameter space. The evolution of inclusion inclination relative to the shear plane is more strongly affected by elastic and plastic contributions to rheology in the case of strong inclusions. In addition, we found that strong inclusions deform in the transient viscoelastic stress regime at high Weissenberg numbers (≥0.01) up to bulk shear strains larger than 3. Studies using the shapes of deformed objects for finite-­strain analysis or viscosity-­ratio estimation should establish carefully which rheology and loading conditions reflect material and deformation properties. We suggest that relatively strong, deformable clasts in shear zones retain stored energy up to fairly high shear strains. Hence, purely viscous models of clast deformation may overlook an important contribution to the energy budget, which may drive dissipation processes within and around natural inclusions.

Image-Segmentation Technique to Analyze Deformation Profiles in Different Direct Shear Tests

Results from interface shear tests on sand-geosynthetic interfaces are examined in light of surface roughness of the interacting geosynthetic material. Three different types of interface shear tests carried out in the frame of direct shear-test setup are compared to understand the effect of parameters like box fixity and symmetry on the interface shear characteristics. Formation of shear bands close to the interface is visualized in the tests and the bands are analyzed using image-segmentation techniques in MATLAB. A woven geotextile with moderate roughness and a geomembrane with minimal roughness are used in the tests. The effect of surface roughness of the geosynthetic material on the formation of shear bands, movement of sand particles, and interface shear parameters are studied and compared through visual observations, image analyses, and image-segmentation techniques.