Shell curvature as an initial deformation: A geometrically exact finite element approach

An alternative approach for the analysis of arbitrarily curved shells is developed in this paper based on the idea of initial deformations. By `alternative` we mean that neither differential geometry nor the concept of degeneration is invoked here to describe the shell surface. We begin with a flat reference configuration for the shell mid-surface, after which the initial (curved) geometry is mapped as a stress-free deformation from the plane position. The actual motion of the shell takes place only after this initial mapping. In contrast to classical works in the literature, this strategy enables the use of only orthogonal frames within the theory and therefore objects such as Christoffel symbols, the second fundamental form or three-dimensional degenerated solids do not enter the formulation. Furthermore, the issue of physical components of tensors does not appear. Another important aspect (but not exclusive of our scheme) is the possibility to describe exactly the initial geometry. The model is kinematically exact, encompasses finite strains in a totally consistent manner and is here discretized under the light of the finite element method (although implementation via mesh-free techniques is also possible). Assessment is made by means of several numerical simulations. Copyright (C) 2009 John Wiley & Sons, Ltd.

A ductile damage criterion at various stress triaxialities

The paper discusses the effect of stress triaxiality on the onset and evolution of damage in ductile metals. A series of tests including shear tests and experiments oil smooth and pre-notched tension specimens wits carried Out for it wide range of stress triaxialities. The underlying continuum damage model is based oil kinematic definition of damage tensors. The modular structure of the approach is accomplished by the decomposition of strain rates into elastic, plastic and damage parts. Free energy functions with respect to fictitious undamaged configurations as well as damaged ones are introduced separately leading to elastic material laws which are affected by increasing damage. In addition, a macroscopic yield condition and a flow rule are used to adequately describe the plastic behavior. Numerical simulations of the experiments are performed and good correlation of tests and numerical results is achieved. Based oil experimental and numerical data the damage criterion formulated in stress space is quantified. Different branches of this function are taken into account corresponding to different damage modes depending oil stress triaxiality and Lode parameter. In addition, identification of material parameters is discussed ill detail. (C) 2007 Elsevier Ltd. All rights reserved.

Electron paramagnetic resonance and the thermoluminescence emission mechanism of the 280 degrees C peak in natural andalusite crystal

Samples of natural andalusite (Al(2)SiO(5)) crystal have been investigated in terms of thermoluminescence (TL) and electron paramagnetic resonance (EPR) measurements. The TL glow curves of samples previously annealed at 600 degrees C for 30 min and subsequently gamma-irradiated gave rise to four glow peaks at 150, 210, 280 and 350 degrees C. The EPR spectra of natural samples heat-treated at 600 degrees C for 30 min show signals at g = 5.94 and 2.014 that do not change after gamma irradiation and thermal treatments. However, it was observed that the appearance of a paramagnetic center at g=1.882 for the samples annealed at 600 degrees C for 30 min followed gamma irradiation. This line was attributed to Ti(3+) centers. The EPR signals observed at g=5.94 and 2.014 are due to Fe(3+). Correlations between EPR and TL results of these crystals show that the EPR line at g=1.882 and the TL peak at 280 degrees C can be attributed to the same defect center. (C) 2011 Elsevier B.V. All rights reserved.

Emplacement mechanism of the main granite pluton of the Lavras do Sul intrusive complex, South Brazil, determined by magnetic anisotropies

Magnetic fabric and rock magnetism studies were performed on apparently isotropic granite facies from the main intrusion of the Lavras do Sul Intrusive Complex pluton (LSIC, Rio Grande do Sul, South Brazil). This intrusion is roughly circular (similar to 12 x 13.5 km), composed of alkali-calcic and alkaline granitoids, with the latter occupying the margin of the pluton. Magnetic fabrics were determined by applying both anisotropy of low-field magnetic susceptibility (AMS) and anisotropy of anhysteretic remanent magnetization (AARM). The two fabrics are coaxial. The parallelism between AMS and AARM tensors excludes the presence of a single domain (SD) effect on the AMS fabric of the granites. Several rock-magnetism experiments performed in one specimen from each sampled site show that for all sites the magnetic susceptibility is dominantly carried by ferromagnetic minerals, while mainly magnetite carries the magnetic fabrics. Lineations and foliations in the granite facies were successful determined by applying magnetic methods. Magnetic lineations are gently plunging and roughly parallel to the boundaries of the pluton facies, except at the few sites in the central facies which have a radial orientation pattern. In contrast, the magnetic foliations tend to follow the contacts between the different granite facies. They are gently outerward-dipping inside the pluton, and become either steeply southwesterly dipping or vertical towards its margin. The lack of solid-state and subsolidus deformations at outcrop scale and in thin sections precludes deformation after full crystallization of the pluton. This evidence allows us to interpret the observed magnetic fabrics as primary in origin (magmatic) acquired when the rocks were solidified as a result of processes reflecting magma flow. The foliation pattern displays a dome-shaped form for the main LSIC-pluton. However, the alkaline granites which outcrop in the southern part of the studied area have an inward-dipping foliation, and the steeply plunging magnetic lineation suggests that this area could be part of a feeder zone. The magma ascent probably occurred due to ring-diking. (C) 2008 Elsevier B.V. All rights reserved.

Tectonic fabric revealed by AARM of the proterozoic mafic dike swarm in the Salvador city (Bahia state): Sao Francisco Craton, NE Brazil

Magnetic fabric and rock magnetism studies were performed on 25 unmetamorphosed mafic dikes of the Meso-Late Proterozoic (similar to 1.02 Ga) dike swarm from Salvador (Bahia State, NE Brazil). This area lies in the north-eastern part of the Sao Francisco Craton, which was dominantly formed/reworked during the Transamazonian orogeny (2.14-1.94 Ga). The dikes crop out along the beaches and in quarries around Salvador city, and cut across both amphibolite dikes and granulites. Their widths range from a few centimeters up to 30 m with an average of similar to 4 m, and show two main trends N 140-190 and N 100-120 with vertical dips. Magnetic fabrics were determined using both anisotropy of low-field magnetic susceptibility (AMS) and anisotropy of anhysteretic remanent magnetization (AARM). The magnetic mineralogy was investigated by many experiments including remanent magnetization measurements at variable low temperatures (10-300 K), Mossbauer spectroscopy, high temperature magnetization curves (25-700 degrees C) and scanning electron microscopy (SEM). The rock magnetism study suggests pseudo-single-domain magnetite grains carrying the bulk magnetic susceptibility and AARM fabrics. The magnetite grains found in these dikes are large and we discard the presence of single-domain grains. Its composition is close to stoichiometric with low Ti substitution, and its Verwey transition occurs around 120 K. The main AMS fabric recognized in the swarm is so-called normal, in which the K(max)-K(int) plane is parallel to the dike plane and the magnetic foliation pole K(min)) is perpendicular to it. This fabric is interpreted as due to magma flow, and analysis of the K m inclination permitted to infer that approximately 80% of the dikes were fed by horizontal or sub-horizontal flows (K(max) < 30 degrees). This interpretation is supported by structural field evidence found in five dikes. In addition, based on the plunge of K(max), two mantle sources could be inferred; one of them which fed about 80% of the swarm would be located in the southern part of the region, and the other underlied the Valeria quarry. However, for all dikes the AARM tensors are not coaxial with AMS fabrics and show a magnetic lineation (AARM(max)) oriented to N30-60E, suggesting that magnetite grains were rotated clockwise from dike plane. The orientation of AARM lineation is similar to the orientation of a system of faults in which the Salvador normal fault is the most important. These faults were formed during Cretaceous rifting in the Reconcavo-Tucano-jatoba assemblage that corresponds to an aborted intra-continental rift formed during the opening of the South Atlantic. Therefore, the AARM fabric found for the Salvador dikes is probably tectonic in origin and suggests that the dike swarm was affected by the important tectonic event responsible for the break-up of the Gondwanaland. (C) 2008 Elsevier B.V. All rights reserved.

Maslov index in semi-Riemannian submersions

We study focal points and Maslov index of a horizontal geodesic gamma : I -> M in the total space of a semi-Riemannian submersion pi : M -> B by determining an explicit relation with the corresponding objects along the projected geodesic pi omicron gamma : I -> B in the base space. We use this result to calculate the focal Maslov index of a (spacelike) geodesic in a stationary spacetime which is orthogonal to a timelike Killing vector field.