A finite element strategy coupling a gradient-enhanced damage model and cohesive cracks for quasi-brittle materials

A new combined strategy to describe failure of quasi-brittle materials is presented thus allowing the complete description of the process, from initiation of damage to crack propagation. For the early stages of the process, and in order to overcome the well-known problems characterising local descriptions of damage (e.g. mesh-dependence), a gradient-enhanced model based on smoothed displacements is employed. In order to deal with material separation, this continuous description is coupled to a cohesive crack when damage parameter exceeds a critical value. Some difficulties may arise when dealing with the transition from regularised damage models to evolving cracks: crack initiation, crack-path direction, energetic equivalence... In this work, a discrete cohesive crack is introduced when the damage parameter exceeds a critical value. On the one hand, and to determine the crack-path direction, the medial axis of the already damaged profile is computed. That is, a geometric tool widely used in the computer graphics field is used here to track the crack surface. Since this technique is exclusively based on the shape of the regularised damage profile, no mesh sensitivity is observed when determining the crack direction. On the other hand, and to define the cohesive law, an energy balance is imposed thus ensuring that the fracture energy not yet dissipated in the damage zone is transferred to the crack

Rol de la musculatura isquiosural en el dolor bajo de la espalda : aumento de su extensibilidad como factor protector

El dolor bajo de la espalda es un problema común en nuestra sociedad, suponiendo un alto número de bajas en el ámbito laboral y un elevado gasto público a nivel mundial. Las causas que producen este dolor no están claras, pero existen hallazgos frecuentes en pacientes con dolor lumbar no específico con una reducción de la extensibilidad isquiosural. Al no conocerse con certeza cuál es el papel de esta musculatura sobre el dolor lumbar, el propósito de esta revisión bibliográfica fue determinar si el acortamiento isquiosural podía provocar dolor no específico en la zona baja de la espalda y, en caso de existir una relación evidente, comprobar si un tratamiento basado en esta musculatura acortada disminuiría la sensación de dolor. Sin embargo, existe una gran controversia en la literatura al respecto, siendo complicado establecer si el rol de la musculatura isquiosural influye positiva o negativamente sobre el dolor bajo de la espalda. Por tanto, deberían realizarse futuras investigaciones para aclarar dicha hipótesis y, de esta manera, reducir el dolor lumbar y disminuir el alto coste que supone esta lesión

Meanings of fractions as demonstrated by future primary teachers in the initial phase of teacher education

Fractions are a fundamental content of primary-level education and must therefore be included in the training courses for primary school teachers. Experts argue that deep understanding is required to improve primary school teachers’ knowledge of this mathematical concept (Ball, 1990; Cramer, Post & del Mas, 2002; Newton, 2008). Our study focuses on the part-whole relationship as a crucial foundation in working with fractions. This paper characterizes some of the meanings of this relationship for a group of future primary school teachers

Meaning of the part-whole relation and the concept of fraction for primary teachers

The part-whole relation is complex and raises questions that affect different disciplines. Researchers have proposed different interpretations of the notions of fraction and rational number (e.g., Behr, Lesh, Post & Silver, 1983; Kieren, 1976). We highlight three kinds of relations in the study of rational numbers—the part whole-relation, the part-part relation, and the functional relation—through which we organize the different subconstructs of rational number. We claim that the meaning of fractions should be understood through three components: their mathematical structure, their representations and their senses

Surface modification after ethanol wet milling: A comparison between pristine glasses produced from natural minerals and analytical grade raw materials

Four glass compositions were produced taking into account different theoretical Leucite (KAlSi2O6)/Bioglass 45S5 (45% SiO2, 24.5% Na2O, 24.5% CaO, 6% P2O5) ratios using analytical grade reagents only; and replacing some of the reagents by natural minerals, all that were found to be bioactive when they were transformed to glass ceramics. Glasses of particle size below 174 μm were wet milled using ethanol in a high energy planetary ball mill. After wet milling, samples with 25 and 30% of theoretical Leucite content using reagents grade raw materials showed a higher dissolution rate in comparison to the same glasses made from natural mineral, while no differences were found on glasses with 40 and 50% of Leucite theoretical content. Samples with higher dissolution showed a crystalline carbonate phase named Pirssonite on its surface, while on the rest of samples amorphous carbonates were present.Fil: Stábile, Franco Matías. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Tecnología de Recursos Minerales y Cerámica. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Tecnología de Recursos Minerales y Cerámica; ArgentinaFil: Rodríguez Aguado, Elena. Universidad de Málaga; EspañaFil: Rodríguez Castellón, Enrique. Universidad de Málaga; EspañaFil: Volzone, Cristina. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Tecnología de Recursos Minerales y Cerámica. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Tecnología de Recursos Minerales y Cerámica; Argentin

Integrating descriptions of knowledge management learning activities into large ontological structures: A case study

Ontologies have been recognized as a fundamental infrastructure for advanced approaches to Knowledge Management (KM) automation, and the conceptual foundations for them have been discussed in some previous reports. Nonetheless, such conceptual structures should be properly integrated into existing ontological bases, for the practical purpose of providing the required support for the development of intelligent applications. Such applications should ideally integrate KM concepts into a framework of commonsense knowledge with clear computational semantics. In this paper, such an integration work is illustrated through a concrete case study, using the large OpenCyc knowledge base. Concretely, the main elements of the Holsapple & Joshi KM ontology and some existing work on e-learning ontologies are explicitly linked to OpenCyc definitions, providing a framework for the development of functionalities that use the built-in reasoning services of OpenCyc in KM ctivities. The integration can be used as the point of departure for the engineering of KM-oriented systems that account for a shared understanding of the discipline and rely on public semantics provided by one of the largest open knowledge bases available

Approximation theory for weighted Sobolev spaces on curves

17 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR1882649 (2003c:42002)In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete. We also prove the density of the polynomials in these spaces for non-closed compact curves and, finally, we find conditions under which the multiplication operator is bounded on the completion of polynomials. These results have applications to the study of zeroes and asymptotics of Sobolev orthogonal polynomials.Research of V. Álvarez, D. Pestana and J.M. Rodríguez partially supported by a grant from DGI, BFM2000-0206-C04-01, Spain.Publicad

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, I

36 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.-- Part II of this paper published in: Approx. Theory Appl. 18(2): 1-32 (2002), available at: http://e-archivo.uc3m.es/handle/10016/6483MR#: MR2047389 (2005k:42062)Zbl#: Zbl 1081.42024In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measure and find general conditions under which these spaces are complete. These results have important consequences in approximation theory. We also find conditions under which the evaluation operator is bounded.Research by first (J.M.R.), third (E.R.) and fourth (D.P.) authors was partially supported by a grant from DGI (BFM 2000-0206-C04-01), Spain.Publicad