Discontinuous solutions and boundary value problems for non-linearly elastic fibre-reinforced materials

En este trabajo se han analizado varios problemas en el contexto de la elasticidad no lineal basándose en modelos constitutivos representativos. En particular, se han analizado problemas relacionados con el fenómeno de perdida de estabilidad asociada con condiciones de contorno en el caso de material reforzados con fibras. Cada problema se ha formulado y se ha analizado por separado en diferentes capítulos. En primer lugar se ha mostrado el análisis del gradiente de deformación discontinuo para un material transversalmente isótropo, en particular, el modelo del material considerado consiste de una base neo-Hookeana isótropa incrustada con fibras de refuerzo direccional caracterizadas con un solo parámetro. La solución de este problema se vincula con instabilidades que dan lugar al mecanismo de fallo conocido como banda de cortante. La perdida de elipticidad de las ecuaciones diferenciales de equilibrio es una condición necesaria para que aparezca este tipo de soluciones y por tanto las inestabilidades asociadas. En segundo lugar se ha analizado una deformación combinada de extensión, inación y torsión de un tubo cilíndrico grueso donde se ha encontrado que la deformación citada anteriormente puede ser controlada solo para determinadas direcciones de las fibras refuerzo. Para entender el comportamiento elástico del tubo considerado se ha ilustrado numéricamente los resultados obtenidos para las direcciones admisibles de las fibras de refuerzo bajo la deformación considerada. En tercer lugar se ha estudiado el caso de un tubo cilíndrico grueso reforzado con dos familias de fibras sometido a cortante en la dirección azimutal para un modelo de refuerzo especial. En este problema se ha encontrado que las inestabilidades que aparecen en el material considerado están asociadas con lo que se llama soluciones múltiples de la ecuación diferencial de equilibrio. Se ha encontrado que el fenómeno de instabilidad ocurre en un estado de deformación previo al estado de deformación donde se pierde la elipticidad de la ecuación diferencial de equilibrio. También se ha demostrado que la condición de perdida de elipticidad y ^W=2 = 0 (la segunda derivada de la función de energía con respecto a la deformación) son dos condiciones necesarias para la existencia de soluciones múltiples. Finalmente, se ha analizado detalladamente en el contexto de elipticidad un problema de un tubo cilíndrico grueso sometido a una deformación combinada en las direcciones helicoidal, axial y radial para distintas geotermias de las fibras de refuerzo . In the present work four main problems have been addressed within the framework of non-linear elasticity based on representative constitutive models. Namely, problems related to the loss of stability phenomena associated with boundary value problems for fibre-reinforced materials. Each of the considered problems is formulated and analysed separately in different chapters. We first start with the analysis of discontinuous deformation gradients for a transversely isotropic material under plane deformation. In particular, the material model is an augmented neo-Hookean base with a simple unidirectional reinforcement characterised by a single parameter. The solution of this problem is related to material instabilities and it is associated with a shear band-type failure mode. The loss of ellipticity of the governing differential equations is a necessary condition for the existence of these material instabilities. The second problem involves a detailed analysis of the combined non-linear extension, inflation and torsion of a thick-walled circular cylindrical tube where it has been found that the aforementioned deformation is controllable only for certain preferred directions of transverse isotropy. Numerical results have been illustrated to understand the elastic behaviour of the tube for the admissible preferred directions under the considered deformation. The third problem deals with the analysis of a doubly fibre-reinforced thickwalled circular cylindrical tube undergoing pure azimuthal shear for a special class of the reinforcing model where multiple non-smooth solutions emerge. The associated instability phenomena are found to occur prior to the point where the nominal stress tensor changes monotonicity in a particular direction. It has been also shown that the loss of ellipticity condition that arises from the equilibrium equation and ^W=2 = 0 (the second derivative of the strain-energy function with respect to the deformation) are equivalent necessary conditions for the emergence of multiple solutions for the considered material. Finally, a detailed analysis in the basis of the loss of ellipticity of the governing differential equations for a combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube is carried out.

Railway Rapid Transit timetables with variable and elastic demand.

This paper focuses on the design of railway timetables considering a variable elastic demand profile along a whole design day. Timetabling is the third stage in the classical hierarchical railway planning process. Most of previous works on this topic consider a uniform demand behavior for short planning intervals. In this paper, we propose a MINLP model for designing non-periodic timetables on a railway corridor where demand is dependent on waiting times. In the elastic demand case, long waiting times lead to a loss of passengers, who may select an alternative transportation mode. The mode choice is modeled using two alternative methods. The first one is based on a sigmoid function and can be used in case of absence of information for competitor modes. In the second one, the mode choice probability is obtained using a Logit model that explicitly considers the existence of a main alternative mode. With the purpose of obtaining optimal departure times, in both cases, a minimization of the loss of passengers is used as objective function. Finally, as illustration, the timetabling MINLP model with both mode choice methods is applied to a real case and computational results are shown.

Abnormal photoresponses and light-induced apoptosis in rods lacking rhodopsin kinase

Phosphorylation is thought to be an essential first step in the prompt deactivation of photoexcited rhodopsin. In vitro, the phosphorylation can be catalyzed either by rhodopsin kinase (RK) or by protein kinase C (PKC). To investigate the specific role of RK, we inactivated both alleles of the RK gene in mice. This eliminated the light-dependent phosphorylation of rhodopsin and caused the single-photon response to become larger and longer lasting than normal. These results demonstrate that RK is required for normal rhodopsin deactivation. When the photon responses of RK−/− rods did finally turn off, they did so abruptly and stochastically, revealing a first-order backup mechanism for rhodopsin deactivation. The rod outer segments of RK−/− mice raised in 12-hr cyclic illumination were 50% shorter than those of normal (RK+/+) rods or rods from RK−/− mice raised in constant darkness. One day of constant light caused the rods in the RK−/− mouse retina to undergo apoptotic degeneration. Mice lacking RK provide a valuable model for the study of Oguchi disease, a human RK deficiency that causes congenital stationary night blindness.

Integral elastic, electronic-state, ionization, and total cross sections for electron scattering with furfural

We report absolute experimental integral cross sections (ICSs) for electron impact excitation of bands of electronic-states in furfural, for incident electron energies in the range 20-250 eV. Wherever possible, those results are compared to corresponding excitation cross sections in the structurally similar species furan, as previously reported by da Costa et al. [Phys. Rev. A 85, 062706 (2012)] and Regeta and Allan [Phys. Rev. A 91, 012707 (2015)]. Generally, very good agreement is found. In addition, ICSs calculated with our independent atom model (IAM) with screening corrected additivity rule (SCAR) formalism, extended to account for interference (I) terms that arise due to the multi-centre nature of the scattering problem, are also reported. The sum of those ICSs gives the IAM-SCAR+I total cross section for electron-furfural scattering. Where possible, those calculated IAM-SCAR+I ICS results are compared against corresponding results from the present measurements with an acceptable level of accord being obtained. Similarly, but only for the band I and band II excited electronic states, we also present results from our Schwinger multichannel method with pseudopotentials calculations. Those results are found to be in good qualitative accord with the present experimental ICSs. Finally, with a view to assembling a complete cross section data base for furfural, some binary-encounter-Bethe-level total ionization cross sections for this collision system are presented. (C) 2016 AIP Publishing LLC.

Relationship between static and dynamic elastic modulus of calcarenite heated at different temperatures: the San Julián's stone

The San Julián’s stone is the main material used to build the most important historical buildings in Alicante city (Spain). This paper describes the analysis developed to obtain the relationship between the static and the dynamic modulus of this sedimentary rock heated at different temperatures. The rock specimens have been subjected to heating processes at different temperatures to produce different levels of weathering on 24 specimens. The static and dynamic modulus has been measured for every specimen by means of the ISRM standard and ultrasonic tests, respectively. Finally, two analytic formulas are proposed for the relationship between the static and the dynamic modulus for this stone. The results have been compared with some relationships proposed by different researchers for other types of rock. The expressions presented in this paper can be useful for the analysis, using non-destructive techniques, of the integrity level of historical constructions built with San Julián’s stone affected by fires.

A practical treatise on caoutchouc and gutta percha, comprising the properties of the raw materials and the manner of mixing and working them; with the fabrication of vulcanized and hard rubbers, caoutchouc and gutta percha compositions, waterproof substances, elastic tissues, the utilization of waste, etc.

Mode of access: Internet.

Partial wave analysis of elastic and inelastic scattering of Dirac particles,

Vita.

Determination of the causes of weld-metal cracking in high-strength steels and the development of heat-treatable low-alloy-steel filler wires for use with the inert-gas-shielded arc-welding process

"Materials Central, Contract no. AF 33(616)-5878, Project no. 7351."

Damping of flexural vibrations by alternate visco-elastic and elastic layers

"Materials Laboratory, Contract no. AF 33(616)-5426, Project no. 7360."

Electrical wires and cables; catalogue and handbook, systems of wiring.

cover-title

Thrusts, moments, and shears in elastic arches,

Mode of access: Internet.

Account of the ule-tree, Castilla elastica, and of other trees producing the elastic gum.

The notes are signed "T."

The angler; poem, in ten cantos: with proper instructions in the art, rules to choose fishing rods, lines, hooks, floats, baits, and to make artificial flies; receipts for pastes, &c., and, in short, every article relating to the sport.

"Copied almost ̲̲in ̲̲̲̲toto from 'The anglers, Eight dialogues in verse,' London, 1758 ... (reprinted in Ruddiman's 'Scarce, curious, and valuable pieces,' Edinburgh, 1773), by 'Dr. Thomas Scott of Ispwich.'"--Dict. Nat. Biog.

The angler; : a poem, in ten cantos. Comprising proper instructions in the art, with rules to choose fishing rods, lines, hooks, floats, baits, and to make artificial flies; receipts for pastes, &c. &c. Embellished with upwards of twenty beautiful wood-cuts. /

References: Westwood, T. Bibliotheca piscatoria, p. 131.