Showing papers on "Displacement field published in 2010"

Three-dimensional imaging of strain in a single ZnO nanorod.

Abstract: Nanoscale structures can be highly strained because of confinement effects and the strong influence of their external boundaries. This results in dramatically different electronic, magnetic and optical material properties of considerable utility. Third-generation synchrotron-based coherent X-ray diffraction has emerged as a non-destructive tool for three-dimensional (3D) imaging of strain and defects in crystals that are smaller than the coherence volume, typically a few cubic micrometres, of the available beams that have sufficient flux to reveal the material's structure(1). Until now, measurements have been possible only at a single Bragg point of a given crystal because of the limited ability to maintain alignment(2); it has therefore been possible to determine only one component of displacement and not the full strain tensor. Here we report key advances in our fabrication and experimental techniques, which have enabled diffraction patterns to be obtained from six Bragg reflections of the same ZnO nanocrystal for the first time. All three Cartesian components of the ion displacement field, and in turn the full nine-component strain tensor, have thereby been imaged in three dimensions.

Electronic transport in dual-gated bilayer graphene at large displacement fields.

Abstract: We study the electronic transport properties of dual-gated bilayer graphene devices. We focus on the regime of low temperatures and high electric displacement fields, where we observe a clear exponential dependence of the resistance as a function of displacement field and density, accompanied by a strong nonlinear behavior in the transport characteristics. The effective transport gap is typically 2 orders of magnitude smaller than the optical band gaps reported by infrared spectroscopy studies. Detailed temperature dependence measurements shed light on the different transport mechanisms in different temperature regimes.

Electronic Transport in Dual-Gated Bilayer Graphene at Large Displacement Fields

Abstract: We study the electronic transport properties of dual-gated bilayer graphene devices. We focus on the regime of low temperatures and high electric displacement fields, where we observe a clear exponential dependence of the resistance as a function of displacement field and density, accompanied by a strong nonlinear behavior in the transport characteristics. The effective transport gap is typically 2 orders of magnitude smaller than the optical band gaps reported by infrared spectroscopy studies. Detailed temperature dependence measurements shed light on the different transport mechanisms in different temperature regimes.

Evolution of force chains in shear bands in sands

Abstract: Precise knowledge of the post-peak constitutive response occurring within shear bands in sands is of keen interest in geomechanics, particularly for accurate modelling of progressive failure phenomena. There is mounting evidence that the displacement field within shear bands in sands is non-uniform and distinguished by distinct meso-scale features: namely, particle force chains. Experimental validation of such features will help elucidate the precise nature of the deformation field within shear bands. This paper presents experimental evidence of the kinematic signatures of force chain activity within shear bands in sands. The meso-scale kinematics are quantified from digital-image-correlation-based, grain-scale displacement analyses performed on digital images of specimens undergoing plane strain compression. As in previous work, the data reveal distinct, systematic patterns in the kinematics along the length of the shear band, which serve as indirect evidence of force chain build-up and collapse. Herein,...

Full Three‐Dimensional Strain Measurements on Wood Exposed to Three‐Point Bending: Analysis by Use of Digital Volume Correlation Applied to Synchrotron Radiation Micro‐Computed Tomography Image Data

Abstract: A microscale three-point bend experiment on wood has been carried out. The full 3D strain field of the microscale wood structure has been determined by use of digital volume correlation, based on reconstructed 3D image data acquired with synchrotron radiation micro-computed tomography. The wood specimen, which measures 1.57 × 3.42 × 0.75 mm3, was scanned in different load states along the three-point bend load cycle, from unloaded state to failure. The correlation algorithm is based on a Chebyshev polynomial description of the displacements, which allows a continuous representation of the 3D deformation fields. The methodology of the correlation algorithm is described thoroughly and its performance is tested for a 3D structure that is exposed to a virtual pre-defined deformation. The performance is tested both for noise free volume data as well as for structures with additive noise content. The performance test shows that the correlation algorithm resolves the applied deformation satisfyingly well. In the real experiment, on wood microstructure, the displacement fields show a structural behaviour that is consistent with what is expected for a specimen exposed to three-point bend. However, there are also anomalous effects present in the displacement fields that can be coupled to characteristic features in the cellular structure of the wood. Furthermore, 3D strain calculations based on the obtained displacement data shows a concentration of tensile strain in the region where the specimen eventually collapses. The experimental results show that the use of X-ray-based tomography with high spatial resolution in combination with digital volume correlation can successfully be used to perform 3D strain measurements on wood, at the microscale.

Second‐order computational homogenization of heterogeneous materials with periodic microstructure

Abstract: A procedure for second-order computational homogenization of heterogeneous materials is derived from the unit cell homogenization, in which an appropriate representation of the micro-displacement field is assumed as the superposition of a local macroscopic displacement field, expressed in a polynomial form related to the macro-displacement field, and an unknown micro-fluctuation field accounting for the effects of the heterogeneities. This second contribution is represented as the superposition of two unknown functions each of which related to the first-order and to the second-order strain, respectively. This kinematical micro-macro framework guarantees that the micro-displacement field is continuous across the interfaces between adjacent unit cells and implies a computationally efficient procedure that applies in two steps. The first step corresponds to the standard homogenization, while the second step is based on the results of the first step and completes the second-order homogenization. Two multi-phase composites, a three-phase and a laminated composite, are analysed in the examples to assess the reliability of the homogenization techniques. The computational homogenization is carried out by a FE analysis of the unit cell; the overall elastic moduli and the characteristic lengths of the second-order equivalent continuum model are obtained. Finally, the simple shear of a constrained heterogeneous two-dimensional strip made up of the composites considered is analysed by considering a heterogeneous continuum and a homogenized second-order continuum; the corresponding results are compared and discussed in order to identify the validity limits of the proposed technique.

Extended multiscale finite element method for elasto-plastic analysis of 2D periodic lattice truss materials

Abstract: An extended multiscale finite element method is developed for small-deformation elasto-plastic analysis of periodic truss materials. The base functions constructed numerically are employed to establish the relationship between the macroscopic displacement and the microscopic stress and strain. The unbalanced nodal forces in the micro-scale of unit cells are treated as the combined effects of macroscopic equivalent forces and microscopic perturbed forces, in which macroscopic equivalent forces are used to solve the macroscopic displacement field and microscopic perturbed forces are used to obtain the stress and strain in the micro-scale to make sure the correctness of the results obtained by the downscale computation in the elastic-plastic problems. Numerical examples are carried out and the results verify the validity and efficiency of the developed method by comparing it with the conventional finite element method.

Fundamental-solution-based finite element model for plane orthotropic elastic bodies

Abstract: A new hybrid finite element formulation is presented for solving two-dimensional orthotropic elasticity problems. A linear combination of fundamental solutions is used to approximate the intra-element displacement fields and conventional shape functions are employed to construct elementary boundary fields, which are independent of the intra-element fields. To establish a linkage between the two independent fields and produce the final displacement-force equations, a hybrid variational functional containing integrals along the elemental boundary only is developed. Results are presented for four numerical examples including a cantilever plate, a square plate under uniform tension, a plate with a circular hole, and a plate with a central crack, respectively, and are assessed by comparing them with solutions from ABAQUS and other available results.

On the Use of NURBS Functions for Displacement Derivatives Measurement by Digital Image Correlation

Abstract: In this paper, we propose to investigate the potential improvement of using Non-Uniform Rational B-Spline (NURBS) functions for displacement measurements by digital image correlation (DIC). The aim is at improving the performance of DIC to capture with low uncertainty and low noise levels not only the displacement field but also its derivatives. Indeed, when the displacement field is used to feed constitutive law identification procedures, displacement derivatives are required and thus may be measured with robustness. Two examples illustrate the potential of NURBS for DIC: a compressive test on a wood sample and a bending test on a steel beam. For the latter, beam kinematics are adopted and NURBS are used in order to capture the variation of the curvature (second derivative of the displacement) along the beam axis. For these two examples, an error study based on a decomposition of the error into the correlation error and the interpolation error, is carried out and shows the great potential of NURBS functions for DIC.

Finite element based coupled mode initial post-buckling analysis of a composite cylindrical shell ☆

Abstract: In this paper a multi-mode finite element implementation of Koiter’s initial post-buckling theory with the inclusion of the pre-buckling nonlinearity is presented. Using this implementation a multi-mode initial post-buckling analysis of an axially loaded composite cylindrical shell has been carried out with a small number of representative modes. The implementation has been done in a general purpose finite element code. Results are compared with results from semi-analytical perturbation analysis and from finite element based fully nonlinear analysis. I. Introduction Thin-walled cylindrical and conical shells are the main structural components in space industry for spacecraft and launch vehicles. Buckling is the key design criterion for these thin-walled structures. Moreover, this type of structures exhibits unstable post-buckling behavior which makes them highly sensitive to small geometric or load imperfections. Standard finite element based incremental-iterative analysis approach of such structures is computationally expensive and not suitable for repeated runs necessary for a design and optimization process, and often it is difficult to interpret the result and guarantee its correctness. Hence there is a strong need for intermediate tools that address these shortcomings. A modified form of Koiter’s perturbation approach proposed by Byskov and Hutchinson 1 can be used as the foundation of such intermediate tools. In this approach a perturbation expansion of the initial post-buckling displacement field is made in terms of buckling modes and corresponding second order modes. Often a limited number of modes is sufficient and consequently the initial post-buckling behaviour can be described by a reduced set of nonlinear algebraic equations (the number of equations is the same as the number of buckling modes chosen). In the present work a finite element implementation of such perturbation approach has been done that serves as the basis of a reduction method. Along with the computation of buckling and second order modes the post-buckling slopes (a coefficients) and curvatures ( coefficients) are also computed. These postbuckling coefficients give a measure of the stability and imperfection sensitivity of the structure. For instance in the case of conical and cylindrical shells we have zero a coefficients and typically negativeb coefficients indicating unstable post-buckling behavior with high imperfection sensitivity. The buckling and second order modes and the corresponding post-buckling coefficients are c of the perfect structure. They are computed only once and the effect of various geometric imperfections can be obtained a posteriori with very little additional computational cost for each imperfection pattern. Finite element implementation of this type of approach was done in the past by several researchers. 2–5 In those works basically a linear pre-buckling state was assumed and isotropic material was considered. In the present work we analyse cylindrical shells under axial compression. For such problems often it is not possible to determine the buckling modes correctly if the pre-buckling nonlinearity is ignored. The effect of pre-buckling nonlinearity was included in the recent work done by the authors 6,7 in a single-mode context. In the present work that implementation has been extended for multi-mode analysis and composite material has been considered. The implementation has been done in the development environment of the general purpose finite element software DIANA. 8 The implementation makes use of DIANA’s original implementation and does the necessary extension for the inclusion of the effect of pre-buckling nonlinearity.

Finite Element Model for Hybrid Active-Passive Damping Analysis of Anisotropic Laminated Sandwich Structures

Abstract: In this article, we present a new finite element model for the analyzis of active sandwich laminated plates with a viscoelastic core and laminated anisotropic face layers, as well as piezoelectric sensor and actuator layers. The model is formulated using a mixed layerwise approach, by considering a higher order shear deformation theory to represent the displacement field of the viscoelastic core and a first-order shear deformation theory for the displacement field of the adjacent laminated anisotropic face layers and exterior piezoelectric layers. Control laws are implemented and the model is validated using reference solutions from the literature, and a benchmark application is proposed.

FEM for Directly Coupled Magneto-Mechanical Phenomena in Electrical Machines

Abstract: A directly coupled magneto-mechanical model is proposed for simulating the effect of the magnetostriction and electromagnetic stress in iron. The model is based on the general balance laws of electromagnetism, mechanics, and continuum thermodynamics. It is implemented in 2-D by using a conforming finite element method for the magnetic vector potential and the displacement field. The method is applied to two different types of induction machines.

Hypoelastic, hyperelastic, discrete and semi-discrete approaches for textile composite reinforcement forming

Abstract: The clear multi-scale structure of composite textile reinforcements leads to develop continuous and discrete approaches for their forming simulations. In this paper two continuous modelling respectively based on a hypoelastic and hyperelastic constitutive model are presented. A discrete approach is also considered in which each yarn is modelled by shell finite elements and where the contact with friction and possible sliding between the yarns are taken into account. Finally the semi-discrete approach is presented in which the shell finite element interpolation involves continuity of the displacement field but where the internal virtual work is obtained as the sum of tension, in-plane shear and bending ones of all the woven unit cells within the element. The advantages and drawbacks of the different approaches are discussed.

Inferring three-dimensional surface displacement field by combining SAR interferometric phase and amplitude information of ascending and descending orbits

Abstract: Conventional Interferometric Synthetic Aperture Radar (InSAR) technology can only measure one-dimensional surface displacement (along the radar line-of-sight (LOS) direction). Here we presents a method to infer three-dimensional surface displacement field by combining SAR interferometric phase and amplitude information of ascending and descending orbits. The method is realized in three steps: (1) measuring surface displacements along the LOS directions of both ascending and descending orbits based on interferometric phases; (2) measuring surface displacements along the azimuth directions of both the ascending and descending orbits based on the SAR amplitude data; and (3) estimating the three-dimensional (3D) surface displacement field by combining the above four independent one-dimensional displacements using the method of least squares and Helmert variance component estimation. We apply the method to infer the 3D surface displacement field caused by the 2003 Bam, Iran, earthquake. The results reveal that in the northern part of Bam the ground surface experienced both subsidence and southwestward horizontal movement, while in the southern part uplift and southeastward horizontal movement occurred. The displacement field thus determined matches the location of the fault very well with the maximal displacements reaching 22, 40, and 30 cm, respectively in the up, northing and easting directions. Finally, we compare the 3D displacement field with that simulated from the Okada model. The results demonstrate that the method presented here can be used to generate reliable and highly accurate 3D surface displacement fields.

Spatial deformation measurement using transparent soil

Abstract: This paper addresses the need for nonintrusively measuring spatial deformation pattern inside soils. In this study, transparent soil surrogates are used in model tests instead of natural soils. Transparent soil with macrogeotechnical properties similar to those of natural soils was made of either transparent amorphous silica gels or powders and a pore fluid with a matching refractive index. An optical system consisting of a laser light, a line-generator lens, a charge-coupled device (CCD) camera, a frame grabber, and a computer was developed to optically slice a transparent soil model. A distinctive speckle pattern is generated by the interaction of the laser light and transparent soil. The laser speckle images before and after deformation were used to nonintrusively measure the relative displacement field using digital image cross-correlation. Spatial displacement fields under a model footing were obtained by combining several cross-sections in MATLAB®. Test results showed that the developed optical system and transparent soil are suitable for studying soil-structural interaction problems.

A mesh-free method for analysis of the thermal and mechanical buckling of functionally graded cylindrical shell panels

Abstract: The buckling response of functionally graded ceramic-metal cylindrical shell panels under axial compression and thermal load is presented here. The formulation is based on the first-order shear deformation shell theory and element-free kp-Ritz method. The material properties of shell panels are assumed to vary through their thickness direction according to a power-law distribution of the volume fraction of constituents. Approximations of the displacement field are expressed in terms of a set of mesh-free kernel particle functions. A stabilized conforming nodal integration approach is employed to estimate the bending stiffness, and the shear and membrane terms are evaluated using a direct nodal integration technique to eliminate membrane and shear locking for very thin shells. The mechanical and thermal buckling responses of functionally graded shell panels are investigated, and the influences of the volume fraction exponent, boundary conditions, and temperature distribution on their buckling strengths are also examined.

Hybrid analytical and extended finite element method (HAX‐FEM): A new enrichment procedure for cracked solids

Abstract: A new numerical method is proposed to estimate directly stress intensity factors at the tip of a crack in an elastic body. In the same spirit as for the extended finite element method, the approximation of the displacement field is enriched in the vicinity of the crack tip. Yet the method proposed herein differs by the way the enrichment is introduced. Instead of using partition of unity concepts, a two-description formulation is implemented. The first one uses standard finite elements while the second one, in the vicinity of the crack tip, resorts to a few purely analytical expressions. These two descriptions are then coupled by partitioning the energy with an overlapping zone. The performance of this new enrichment technique is illustrated and compared with existing techniques by means of two examples.

A static flexure of thick isotropic plates using trigonometric shear deformation theory

Abstract: A Trigonometric Shear Deformation Theory (TSDT) for the analysis of isotropic plate, taking into account transverse shear deformation effect as well as transverse normal strain effect, is presented. The theory presented herein is built upon the classical plate theory. In this displacement-based, trigonometric shear deformation theory, the in-plane displacement field uses sinusoidal function in terms of thickness coordinate to include the shear deformation effect. The cosine function in terms of thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. It accounts for realistic variation of the transverse shear stress through the thickness and satisfies the shear stress free surface conditions at the top and bottom surfaces of the plate. The theory obviates the need of shear correction factor like other higher order or equivalent shear deformation theories. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. Results obtained for static flexural analysis of simply supported thick isotropic plates for various loading cases are compared with those of other refined theories and exact solution from theory of elasticity. © 2010 IAU, Arak Branch. All rights reserved.