Analysis of elastic functionally graded materials under large displacements via high-order tetrahedral elements

The purpose of this study is to present a position based tetrahedral finite element method of any order to accurately predict the mechanical behavior of solids constituted by functionally graded elastic materials and subjected to large displacements. The application of high-order elements makes it possible to overcome the volumetric and shear locking that appears in usual homogeneous isotropic situations or even in non-homogeneous cases developing small or large displacements. The use of parallel processing to improve the computational efficiency, allows employing high-order elements instead of low-order ones with reduced integration techniques or strain enhancements. The Green-Lagrange strain is adopted and the constitutive relation is the functionally graded Saint Venant-Kirchhoff law. The equilibrium is achieved by the minimum total potential energy principle. Examples of large displacement problems are presented and results confirm the locking free behavior of high-order elements for non-homogeneous materials. (C) 2011 Elsevier B.V. All rights reserved.

GENERALIZED FINITE ELEMENT METHOD ON NONCONVENTIONAL HYBRID-MIXED FORMULATION

The generalized finite element method (GFEM) is applied to a nonconventional hybrid-mixed stress formulation (HMSF) for plane analysis. In the HMSF, three approximation fields are involved: stresses and displacements in the domain and displacement fields on the static boundary. The GFEM-HMSF shape functions are then generated by the product of a partition of unity associated to each field and the polynomials enrichment functions. In principle, the enrichment can be conducted independently over each of the HMSF approximation fields. However, stability and convergence features of the resulting numerical method can be affected mainly by spurious modes generated when enrichment is arbitrarily applied to the displacement fields. With the aim to efficiently explore the enrichment possibilities, an extension to GFEM-HMSF of the conventional Zienkiewicz-Patch-Test is proposed as a necessary condition to ensure numerical stability. Finally, once the extended Patch-Test is satisfied, some numerical analyses focusing on the selective enrichment over distorted meshes formed by bilinear quadrilateral finite elements are presented, thus showing the performance of the GFEM-HMSF combination.

Finite element methods for the Stokes system based on a Zienkiewicz type N-simplex

Hermite interpolation is increasingly showing to be a powerful numerical solution tool, as applied to different kinds of second order boundary value problems. In this work we present two Hermite finite element methods to solve viscous incompressible flows problems, in both two- and three-dimension space. In the two-dimensional case we use the Zienkiewicz triangle to represent the velocity field, and in the three-dimensional case an extension of this element to tetrahedra, still called a Zienkiewicz element. Taking as a model the Stokes system, the pressure is approximated with continuous functions, either piecewise linear or piecewise quadratic, according to the version of the Zienkiewicz element in use, that is, with either incomplete or complete cubics. The methods employ both the standard Galerkin or the Petrov–Galerkin formulation first proposed in Hughes et al. (1986) [18], based on the addition of a balance of force term. A priori error analyses point to optimal convergence rates for the PG approach, and for the Galerkin formulation too, at least in some particular cases. From the point of view of both accuracy and the global number of degrees of freedom, the new methods are shown to have a favorable cost-benefit ratio, as compared to velocity Lagrange finite elements of the same order, especially if the Galerkin approach is employed.

Numerical assessment of stability of interface discontinuous finite element pressure spaces

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019-1031], which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina [A.H. Coppola-Owen, R. Codina, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, Int. J. Numer. Methods Fluids, 49 (2005) 1287-1304], which can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form. An application of the same numerical assessment tool to the stabilized equal-order P-1/P-1 formulation is then reported. An interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation's stability. An analogous result is also reported for the mini-element P-1(+)/P-1 when the velocity bubbles are removed in an arbitrary band of elements. (C) 2012 Elsevier B.V. All rights reserved.

Contribution to assessing the stiffness reduction of structural elements in the global stability analysis of precast concrete multi-storey buildings

This study deals with the reduction of the stiffness in precast concrete structural elements of multi-storey buildings to analyze global stability. Having reviewed the technical literature, this paper present indications of stiffness reduction in different codes, standards, and recommendations and compare these to the values found in the present study. The structural model analyzed in this study was constructed with finite elements using ANSYS® software. Physical Non-Linearity (PNL) was considered in relation to the diagrams M x N x 1/r, and Geometric Non-Linearity (GNL) was calculated following the Newton-Raphson method. Using a typical precast concrete structure with multiple floors and a semi-rigid beam-to-column connection, expressions for a stiffness reduction coefficient are presented. The main conclusions of the study are as follows: the reduction coefficients obtained from the diagram M x N x 1/r differ from standards that use a simplified consideration of PNL; the stiffness reduction coefficient for columns in the arrangements analyzed were approximately 0.5 to 0.6; and the variation of values found for stiffness reduction coefficient in concrete beams, which were subjected to the effects of creep with linear coefficients from 0 to 3, ranged from 0.45 to 0.2 for positive bending moments and 0.3 to 0.2 for negative bending moments.

Analysis, manufacture and characterization of Ni/Cu functionally graded structures

In this work, an experimental and numerical analysis and characterization of functionally graded structures (FGSs) is developed. Nickel (Ni) and copper (Cu) materials are used as basic materials in the numerical modeling and experimental characterization. For modeling, a MATLAB finite element code is developed, which allows simulation of harmonic and modal analysis considering the graded finite element formulation. For experimental characterization, Ni-Cu FGSs are manufactured by using spark plasma sintering technique. Hardness and Young's modulus are found by using microindentation and ultrasonic measurements, respectively. The effective gradation of Ni/Cu FGS is addressed by means of optical microscopy, energy dispersive spectrometry, scanning electron microscopy and hardness testing. For the purpose of comparing modeling and experimental results, the hardness curve, along the gradation direction, is used for identifying the gradation profile; accordingly, the experimental hardness curve is used for approximating the Young's modulus variation and the graded finite element modeling is used for verification. For the first two resonance frequency values, a difference smaller than 1% between simulated and experimental results is obtained. (C) 2012 Elsevier Ltd. All rights reserved.

Spin-glass behaviour on random lattices

The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction w of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an analysis of stability of the replica-symmetric solution, it is shown that w = 1/2, corresponding to an unbiased spin glass, is a singular point in the phase diagram, separating a region with a spin-glass phase (w < 1/2) from a region with spin-glass, ferromagnetic, mixed and paramagnetic phases (w > 1/2).

Atomically resolved study of the morphology change of InAs/GaAs quantum dot layers induced by rapid thermal annealing

The optoelectronic properties of InAs/GaAs quantum dots can be tuned by rapid thermal annealing. In this study, the morphology change of InAs/GaAs quantum dots layers induced by rapid thermal annealing was investigated at the atomic-scale by cross-sectional scanning tunneling microscopy. Finite elements calculations that model the outward relaxation of the cleaved surface were used to determine the indium composition profile of the wetting layer and the quantum dots prior and post rapid thermal annealing. The results show that the wetting layer is broadened upon annealing. This broadening could be modeled by assuming a random walk of indium atoms. Furthermore, we show that the stronger strain gradient at the location of the quantum dots enhances the intermixing. Photoluminescence measurements show a blueshift and narrowing of the photoluminescence peak. Temperature dependent photoluminescence measurements show a lower activation energy for the annealed sample. These results are in agreement with the observed change in morphology. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4770371]

Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation

We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly predict a nonequilibrium phase transition which is not allowed in the model. We propose an excitable-wave mean-field approximation which shows good agreement with previously published simulation results [Gollo et al., PLoS Comput. Biol. 5, e1000402 (2009)] and accounts for finite-size effects. We also discuss the relevance of our results to experiments in neuroscience, emphasizing the role of active dendrites in the enhancement of dynamic range and in gain control modulation.

On Equilibrium Distribution of a Reversible Growth Model

We study a probabilistic model of interacting spins indexed by elements of a finite subset of the d-dimensional integer lattice, da parts per thousand yen1. Conditions of time reversibility are examined. It is shown that the model equilibrium distribution converges to a limit distribution as the indexing set expands to the whole lattice. The occupied site percolation problem is solved for the limit distribution. Two models with similar dynamics are also discussed.

Towards the stabilization of the low density elements in topology optimization with large deformation

This work addresses the treatment of lower density regions of structures undergoing large deformations during the design process by the topology optimization method (TOM) based on the finite element method. During the design process the nonlinear elastic behavior of the structure is based on exact kinematics. The material model applied in the TOM is based on the solid isotropic microstructure with penalization approach. No void elements are deleted and all internal forces of the nodes surrounding the void elements are considered during the nonlinear equilibrium solution. The distribution of design variables is solved through the method of moving asymptotes, in which the sensitivity of the objective function is obtained directly. In addition, a continuation function and a nonlinear projection function are invoked to obtain a checkerboard free and mesh independent design. 2D examples with both plane strain and plane stress conditions hypothesis are presented and compared. The problem of instability is overcome by adopting a polyconvex constitutive model in conjunction with a suggested relaxation function to stabilize the excessive distorted elements. The exact tangent stiffness matrix is used. The optimal topology results are compared to the results obtained by using the classical Saint Venant–Kirchhoff constitutive law, and strong differences are found.

Numeric reconstruction of cytoskeleton with finite element method and topology optimization method

The importance of mechanical aspects related to cell activity and its environment is becoming more evident due to their influence in stem cell differentiation and in the development of diseases such as atherosclerosis. The mechanical tension homeostasis is related to normal tissue behavior and its lack may be related to the formation of cancer, which shows a higher mechanical tension. Due to the complexity of cellular activity, the application of simplified models may elucidate which factors are really essential and which have a marginal effect. The development of a systematic method to reconstruct the elements involved in the perception of mechanical aspects by the cell may accelerate substantially the validation of these models. This work proposes the development of a routine capable of reconstructing the topology of focal adhesions and the actomyosin portion of the cytoskeleton from the displacement field generated by the cell on a flexible substrate. Another way to think of this problem is to develop an algorithm to reconstruct the forces applied by the cell from the measurements of the substrate displacement, which would be characterized as an inverse problem. For these kind of problems, the Topology Optimization Method (TOM) is suitable to find a solution. TOM is consisted of an iterative application of an optimization method and an analysis method to obtain an optimal distribution of material in a fixed domain. One way to experimentally obtain the substrate displacement is through Traction Force Microscopy (TFM), which also provides the forces applied by the cell. Along with systematically generating the distributions of focal adhesion and actin-myosin for the validation of simplified models, the algorithm also represents a complementary and more phenomenological approach to TFM. As a first approximation, actin fibers and flexible substrate are represented through two-dimensional linear Finite Element Method. Actin contraction is modeled as an initial stress of the FEM elements. Focal adhesions connecting actin and substrate are represented by springs. The algorithm was applied to data obtained from experiments regarding cytoskeletal prestress and micropatterning, comparing the numerical results to the experimental ones

New historical archeointensity data from Brazil: Evidence for a large regional non-dipole field contribution over the past few centuries

We report new archeointensity data obtained from the analyses of baked clay elements (architectural and kiln brick fragments) sampled in Southeast Brazil and historically and/or archeologically dated between the end of the XVIth century and the beginning of the XXth century AD. The results were determined using the classical Thellier and Thellier protocol as modified by Coe, including partial thermoremanent magnetization (pTRM) and pTRM-tail checks, and the Triaxe protocol, which involves continuous high-temperature magnetization measurements. In both protocols, TRM anisotropy and cooling rate TRM dependence effects were taken into account for intensity determinations which were successfully performed for 150 specimens from 43 fragments, with a good agreement between intensity results obtained from the two procedures. Nine site-mean intensity values were derived from three to eight fragments and defined with standard deviations of less than 8%. The site-mean values vary from similar to 25 mu T to similar to 42 mu T and describe in Southeast Brazil a continuous decreasing trend by similar to 5 mu T per century between similar to 1600 AD and similar to 1900 AD. Their comparison with recent archeointensity results obtained from Northeast Brazil and reduced at a same latitude shows that: (1) the geocentric axial dipole approximation is not valid between these southeastern and northeastern regions of Brazil, whose latitudes differ by similar to 10 degrees, and (2) the available global geomagnetic field models (gufm1 models, their recalibrated versions and the CALSK3 models) are not sufficiently precise to reliably reproduce the non-dipole field effects which prevailed in Brazil for at least the 1600-1750 period. The large non-dipole contribution thus highlighted is most probably linked to the evolution of the South Atlantic Magnetic Anomaly (SAMA) during that period. Furthermore, although our dataset is limited, the Brazilian archeointensity data appear to support the view of a rather oscillatory behavior of the axial dipole moment during the past three centuries that would have been marked in particular by a moderate increase between the end of the XVIIIth century and the middle of the XIXth century followed by the well-known decrease from 1840 AD attested by direct measurements. (C) 2011 Elsevier B.V. All rights reserved.

Optical Excitations and Field Enhancement in Short Graphene Nanoribbons

The optical excitations of elongated graphene nanoflakes of finite length are investigated theoretically through quantum chemistry semiempirical approaches. The spectra and the resulting dipole fields are analyzed, accounting in full atomistic details for quantum confinement effects, which are crucial in the nanoscale regime. We find that the optical spectra of these nanostructures are dominated at low energy by excitations with strong intensity, comprised of characteristic coherent combinations of a few single-particle transitions with comparable weight. They give rise to stationary collective oscillations of the photoexcited carrier density extending throughout the flake and to a strong dipole and field enhancement. This behavior is robust with respect to width and length variations, thus ensuring tunability in a large frequency range. The implications for nanoantennas and other nanoplasmonic applications are discussed for realistic geometries.

Local symmetries in gauge theories in a finite-dimensional setting

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge theories, but is already true even for global symmetries when one allows for fields that are sections of bundles with (possibly) non-trivial topology or, even when these are topologically trivial, in the absence of a preferred trivialization. (C) 2012 Elsevier B.V. All rights reserved.