3D FEA modelling of laminated composites in bending and their failure mechanisms

keywords: 3D keywords: 3D keywords: 3D keywords: 3D keywords: 3DAbstract This paper developed three-dimensional (3D) Finite Element Analysis (FEA) to investigate the effect of fibre lay-up on the initiation of failure of laminated composites in bending. Tsai-Hill failure criterion was applied to identify the critical areas of failure in composite laminates. In accordance with the 3D FEA, unidirectional ([0]16), cross-ply ([0/90]4s) and angle-ply ([±45]4s) laminates made up of pre-preg Carbon Fibre Reinforced Plastics (CFRP) composites were manufactured and tested under three-point bending. The basic principles of Classical Laminate Theory (CLT) were extended to three-dimension, and the analytical solution was critically compared with the FEA results. The 3D FEA results revealed significant transverse normal stresses in the cross-ply laminate and in-plane shear stress in the angle-ply laminate near free edge regions which are overlooked by conventional laminate model. The microscopic images showed that these free edge effects were the main reason for stiffness reduction observed in the bending tests. The study illustrated the significant effects of fibre lay-up on the flexural failure mechanisms in composite laminates which lead to some suggestions to improve the design of composite laminates

Deformation-enhanced recrystallization of titanite drives decoupling between U-Pb and trace elements

Titanite is a common accessory mineral that is useful in determining both age (U-Pb isotopes) and pressure-temperature (P–T) conditions (trace-element composition: Zr, rare earth elements (REE)). However, titanite has a propensity to recrystallize during metamorphism, fluid flow, and deformation, which can result in modifications to its isotopic and trace-element compositions. This modification has implications for the interpretation of titanite dates and the evaluation of pressure–temperature–time paths. The impact of deformation and recrystallization on trace-element mobility in titanite is investigated through microstructural and compositional mapping of titanite crystals from a sheared orthogneiss within an ultrahigh-pressure domain of the Western Gneiss Region (WGR), Norway. Results show that optically coherent titanite single crystals deformed in the dislocation creep regime and recrystallized by the process of grain-boundary migration, forming aggregates of titanite grains. Some of the aggregate grains record Caledonian-exhumation dates, whereas others have an inherited isotopic composition. Individual grains within the aggregate, regardless of their U-Pb isotopic composition, contain patchy zoning that formed during syn- to post-recrystallization fluid alteration and that is characterized by generally decreasing Ca and Ti and increasing Al and Fe from cores to rims. However, Zr and Sr concentrations are broadly zoned with respect to the long axis of the host crystal, without regard for the aggregate grain boundaries. REE do not show any obvious correlation with microstructure or age. These results indicate that many trace elements in titanite are unaffected by multi-stage, deformation-driven recrystallization; in contrast, Pb is variably mobile in these deformed titanite crystals. The combination of microstructural and high-spatial resolution geochemical and isotopic data reveals the potential extent of decoupling between the U-Pb isotopic system and the behavior of trace elements as pressure–temperature conditions change through time

Anisotropic smoothness classes : from finite element approximation to image models

We propose and study quantitative measures of smoothness which are adapted to anisotropic features such as edges in images or shocks in PDE's. These quantities govern the rate of approximation by adaptive finite elements, when no constraint is imposed on the aspect ratio of the triangles, the simplest examples of such quantities are based on the determinant of the hessian of the function to be approximated. Since they are not semi-norms, these quantities cannot be used to define linear function spaces. We show that they can be well defined by mollification when the function to be approximated has jump discontinuities along piecewise smooth curves. This motivates for using them in image processing as an alternative to the frequently used record variation semi-norm which does not account for the geometric smoothness of the edges.Comment: 24 pages, 2 figure

Quantum Tomography under Prior Information

We provide a detailed analysis of the question: how many measurement settings or outcomes are needed in order to identify a quantum system which is constrained by prior information? We show that if the prior information restricts the system to a set of lower dimensionality, then topological obstructions can increase the required number of outcomes by a factor of two over the number of real parameters needed to characterize the system. Conversely, we show that almost every measurement becomes informationally complete with respect to the constrained set if the number of outcomes exceeds twice the Minkowski dimension of the set. We apply the obtained results to determine the minimal number of outcomes of measurements which are informationally complete with respect to states with rank constraints. In particular, we show that 4d-4 measurement outcomes (POVM elements) is enough in order to identify all pure states in a d-dimensional Hilbert space, and that the minimal number is at most 2 log_2(d) smaller than this upper bound.Comment: v3: There was a mistake in the derived finer upper bound in Theorem 3. The corrected upper bound is +1 to the earlier versio

Horizontal Branch Stars: The Interplay between Observations and Theory, and Insights into the Formation of the Galaxy

We review HB stars in a broad astrophysical context, including both variable and non-variable stars. A reassessment of the Oosterhoff dichotomy is presented, which provides unprecedented detail regarding its origin and systematics. We show that the Oosterhoff dichotomy and the distribution of globular clusters (GCs) in the HB morphology-metallicity plane both exclude, with high statistical significance, the possibility that the Galactic halo may have formed from the accretion of dwarf galaxies resembling present-day Milky Way satellites such as Fornax, Sagittarius, and the LMC. A rediscussion of the second-parameter problem is presented. A technique is proposed to estimate the HB types of extragalactic GCs on the basis of integrated far-UV photometry. The relationship between the absolute V magnitude of the HB at the RR Lyrae level and metallicity, as obtained on the basis of trigonometric parallax measurements for the star RR Lyrae, is also revisited, giving a distance modulus to the LMC of (m-M)_0 = 18.44+/-0.11. RR Lyrae period change rates are studied. Finally, the conductive opacities used in evolutionary calculations of low-mass stars are investigated. [ABRIDGED]Comment: 56 pages, 22 figures. Invited review, to appear in Astrophysics and Space Scienc

BSD2 is a Rubisco-specific assembly chaperone, forms intermediary hetero-oligomeric complexes, and is nonlimiting to growth in tobacco

The folding and assembly of Rubisco large and small subunits into L 8 S 8 holoenzyme in chloroplasts involves many auxiliary factors, including the chaperone BSD2. Here we identify apparent intermediary Rubisco-BSD2 assembly complexes in the model C 3 plant tobacco. We show BSD2 and Rubisco content decrease in tandem with leaf age with approximately half of the BSD2 in young leaves (~70 nmol BSD2 protomer.m 2 ) stably integrated in putative intermediary Rubisco complexes that account for <0.2% of the L 8 S 8 pool. RNAi-silencing BSD2 production in transplastomic tobacco producing bacterial L 2 Rubisco had no effect on leaf photosynthesis, cell ultrastructure, or plant growth. Genetic crossing the same RNAi-bsd2 alleles into wild-type tobacco however impaired L 8 S 8 Rubisco production and plant growth, indicating the only critical function of BSD2 is in Rubisco biogenesis. Agrobacterium mediated transient expression of tobacco, Arabidopsis, or maize BSD2 reinstated Rubisco biogenesis in BSD2-silenced tobacco. Overexpressing BSD2 in tobacco chloroplasts however did not alter Rubisco content, activation status, leaf photosynthesis rate, or plant growth in the field or in the glasshouse at 20°C or 35°C. Our findings indicate BSD2 functions exclusively in Rubisco biogenesis, can efficiently facilitate heterologous plant Rubisco assembly, and is produced in amounts nonlimiting to tobacco growth