Advanced solid elements for sheet metal forming simulation

The solid-shells are an attractive kind of element for the simulation of forming processes, due to the fact that any kind of generic 3D constitutive law can be employed without any additional hypothesis. The present work consists in the improvement of a triangular prism solid-shell originally developed by Flores [2, 3]. The solid-shell can be used in the analysis of thin/thick shell, undergoing large deformations. The element is formulated in total Lagrangian formulation, and employs the neighbour (adjacent) elements to perform a local patch to enrich the displacement field. In the original formulation a modified right Cauchy-Green deformation tensor (C¯) is obtained; in the present work a modified deformation gradient (F¯) is obtained, which allows to generalise the methodology and allows to employ the Pull-Back and Push-Forwards operations. The element is based in three modifications: (a) a classical assumed strain approach for transverse shear strains (b) an assumed strain approach for the in-plane components using information from neighbour elements and (c) an averaging of the volumetric strain over the element. The objective is to use this type of elements for the simulation of shells avoiding transverse shear locking, improving the membrane behaviour of the in-plane triangle and to handle quasi-incompressible materials or materials with isochoric plastic flow.Postprint (published version

Classical Tensors and Quantum Entanglement II: Mixed States

Invariant operator-valued tensor fields on Lie groups are considered. These define classical tensor fields on Lie groups by evaluating them on a quantum state. This particular construction, applied on the local unitary group U(n)xU(n), may establish a method for the identification of entanglement monotone candidates by deriving invariant functions from tensors being by construction invariant under local unitary transformations. In particular, for n=2, we recover the purity and a concurrence related function (Wootters 1998) as a sum of inner products of symmetric and anti-symmetric parts of the considered tensor fields. Moreover, we identify a distinguished entanglement monotone candidate by using a non-linear realization of the Lie algebra of SU(2)xSU(2). The functional dependence between the latter quantity and the concurrence is illustrated for a subclass of mixed states parametrized by two variables.Comment: 23 pages, 4 figure

Strain quantification related to the Berzosa/fault (Spanish Central System)

[Resumen] En relación con la zona de cizalla dúctil de Berzosa Honrubia que actúa durante la segunda fase de deformación Hercínica, se han calculado los elipsoides de deformación finita asociados a la misma. Para el cálculo se usan los métodos de Ramsay (1967), Dunnet (1969), y Fry (1979). Los resultados muestran una variación en el tipo de elipsoide a lo largo de la traza de la zona de cizalla. En los extremos tienen valores K>t, y en la parte central de Kl en la región donde son paralelos.[Abstract] In the ductil shear zone of Berzosa Honrubia, active during the Hercynic second phase, finite strain ellipsoids have been calculated. Methods of Ramsay, Dunnet, and Fry have been used for this calculation. The results show a variation in the strain elipsoid shape through the shear zone trace. The central part h(!s strain ellipsoids with K1. Interpretation of those values is based on the variation in the orientation of the fault cartographic trace and tectonic transport direction. Ellipsoids with K1 are located where the trace and tectonic transport direction are parallel

Paleoseismological analysis of late Miocene lacustrine successions in the Prebetic Zone, SE Spain

A paleoseismological study of late Miocene lacustrine sediments was carried out in the Neogene basins of the Prebetic Zone in Albacete (Spain). We developed a multidisciplinary methodology which could be used to extrapolate the paleoseismic data to the present day. This multidisciplinary approach includes different disciplines, i.e. stratigraphy, structural analysis, seismological analysis and paleoseismology. Paleoseismological analysis was focussed on both shallow and deep lake deposits given that these sediments behave differently in different deformation fields. The seismites formed in shallow sediments were generated by liquefaction and include: sand dikes, pillow structures and intruded and fractured gr avels. The deep lake deposits show varied structures, such as loop bedding, disturbed varved lamination, mixed layers and pseudonodules. Seismites indicate paleoearthquake magnitude intervals. The trends of the seismites are usually oriented ve ry close to the stress field trends (from the late Miocene to the Present): NW-SE and NE-SW trends. This constitutes a link between tectonics and seismites. The va rved annual sedimentation evidenced by the deep lake facies was used as a relative dating method. Mixed layers were employed as paleoseismic indicators to calculate the earthquake recurrence interval. The mean recurrence interval is close to 130 years (9446 years of total record with 73 dated events), one maximum interval of 454 years and one minimum interval of 23 years and the mean estimated magnitude value is 5.1. The Gutenberg-Richter relationship shows similar "b" values close to 0.86 from paleoseismological and seismological data. This suggests that the seismic conditions have been similar since the late Miocene

Monitoring of agricultural land use in São Paulo State - Brazil using geotechnology approach.

This study evaluated changes in agricultural land use on São Paulo state, Brazil, mapping and qualifying sugarcane expansion. The Percentage Change Index (PCi), calculated using official municipal census data was used to identify areas where sugarcane caused the main land use changes. The PCi provided the sugarcane percentage changes over 20 years of data. Detailed land cover maps for four municipalities with high PCi were created for two time periods (1990 and 2005), using satellite images. Results showed that sugarcane expansion over the 15 year period occurred mainly over pasture lands however, for one municipality, a high substitution of forest plantation areas was observed. Also, only one municipality showed a strong increase in short cycle crop agriculture, which also occurred over pasture areas. Results revealed that sugarcane expansion has a relationship with local economic aspects and the method used provided an important tool to define public policies and management decisions

Classical Tensors and Quantum Entanglement I: Pure States

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a flat Riemannian metric tensor while the imaginary part represents a symplectic two-form. The immersion of classical manifolds in the complex projective space associated with the Hilbert space allows to pull-back tensor fields related to previous ones, via the immersion map. This makes available, on these selected manifolds of states, methods of usual Riemannian and symplectic geometry. Here we consider these pulled-back tensor fields when the immersed submanifold contains separable states or entangled states. Geometrical tensors are shown to encode some properties of these states. These results are not unrelated with criteria already available in the literature. We explicitly deal with some of these relations.Comment: 16 pages, 1 figure, to appear in Int. J. Geom. Meth. Mod. Phy

Population analysis of the late hercynian faulting in the Spanish Central System

[Resumen] En la región comprendida entre Cercedilla, El Espinar y Robleao de Chavela (Sistema Central), se han observado una serie de zonas de cizalla ductiles que cortan a las estructuras Hercínicas anteriores; son de dirección N80-NIIOE y poseen movimientos de tipo normal. Este tipo de régimen distensivo concuerda con tipos deformacionales descritos por otros autores en el Sistema Central Español. En la misma zona están también presentes una serie de diques y fallas frágiles que corresponden a un régimen deformacional inicialmente de tipo distensión uniaxial, según NS-NIOE. Las principales direcciones de fraturación se concretan en dos familias muy próximas (N80E y NIOOE), o en una única familia según N90E. A favor de esta última dirección, yen régimen de tipo extensión uniaxial se emplazan una serie de porfidos graníticos, muy característicos del área estudiada. Debido al temprano emplazamiento de estos diques ya los planos de movimiento deducibles para unos y otros tipos de fallas, pensamos que ambos eventos han de tener una cierta relación temporal. La distensión uniaxial pasa en el tiempo, mediante aumento de las compresiones de dirección N9S-NIOO E, a tectónica de tipo de desgarre. A toda esta evolución deformacional se le denomina «Etapa Malagon». Estos desgarres afectan de una manera dúctil, si bien sin recristalizaciones posteriores, a los diques de porfido granítico, que aun se están emplazando. Posteriormente, y ya dentro de la tectónica netamente de tipo frágil, se produce un régimen deformacional de tipo desgarre, con dirección de compresión NSOE que termina en distensión radial, que hemos denominado «Etapa Hiendelaencina ». En esta fase se emplazan diques de cuarzo y baritina de direcciones N20E' y N80E.[Abstract] In the region between Cercedilla, El Espinar and Robledo de Chavela (Middle Occidental Sector of the Central System) a series of ductile shear zones have been observed that cut to the former Hercynian structures with Nao-NIOO trends and having normal movement. This extensive regime agrees with other previous works. There are, in the same area, a series of dykes and brittle faults that correspond .to a deformational regime with uniaxial extension (initially from N5 to NIO). The main fault trends are Nao and NIOO (or only one with N90 trend). Following this last direction a series of granitic dykes are emplaced. This dyke emplacement and the movement scheme make us think in a certain temporal relation between them. The uniaxial extension changes, with an increase of the compresive axis (N95-NIOO), to a strike-slip fault tectonics. We will call this deformational evolution, «Malagon Phase». Subsequently, and in a clear brittle tectonics, it is produced a deformational regime of strike slip type with a direction of compression of N50E, ending in a radial extension named «Hiendelaencina Phase», with emplacement of quartz and baryte dykes with N20 and Nao trends

Geometrical Description of Quantum Mechanics - Transformations and Dynamics

In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the study of separability and entanglement for states of composite quantum systems.Comment: 22 pages, to be published in Physica Script

Tensorial analisis of the superposed deformation in the easthern border of the Madrid basin

An analysis of Neogene brittle deformation using fault populatíon analysis methods has been carried out between the SW border of the Iberian Range and Altomira Range. Two main paleostress fields have been established: 1) N70E - N120E compression (Altomira paleostress field) ofLate Oligocene - Early Miocene age that induced the formation of the SW border of Iberian Range and Altomira - Pareja thrust belts with reverse and strike-slip faults. 2) N140-N160E compression (Guadarrama paleostress field) of Middle Aragonian - early Pleistocene age that reactivated previous faults with strikeslip movement along the Iberian Range. A superposition of two regional stress fields (Iberian and Guadarrama) is proposed to explain E-W compression that formed Altomira Range. Stress tensorial additions have been realized to check this hypothesis