Local Displacement Field Research Articles

Quantitative TEM characterizations of La/B 4C and Mo/B 4C ultrathin multilayer gratings by the geometric phase method

Artificially fabricated multilayers that exploit the effect of Bragg diffraction at long wavelengths are used as X-ray optical components. Periodic ultrathin bilayer stacks of, alternatingly, a metallic reflection layer and a non-metallic spacer layer prepared as μm-scaled surface grating promise particularly high performance in applications as X-ray filters for high-resolution spectroscopy. Such gratings can be prepared by multilayer deposition onto Si(0 0 1) gratings or by coating flat Si(0 1 1) substrate surfaces with a multilayer, followed by subsequent etching of a grating structure. The structural quality of ultrathin multilayer gratings of both types has been characterized quantitatively combining TEM bright-field imaging of specimen cross-sections and applying a geometric phase method. The geometric phase method has been originally developed for the analysis of local displacement fields from HREM images and allows to obtain the relevant structure parameters. The application of this method to the characterization of Mo/B 4C and La/B 4C multilayer systems shows that the functionally decisive structure parameters, such as layer perfection, layer periodicity, and layer orientation, can be obtained with high precision from evaluation of TEM bright-field images. The essential role of such data analyses for a quantitative characterization of multilayer systems and for optimising the layer deposition techniques in the fabrication of X-ray optical layer systems will be demonstrated and discussed.

Investigation of the viscoelasticity of human osteosarcoma cells using a shear assay method

This paper presents a shear assay method for the determination of the viscoelastic properties of biological cells. The method was applied to the measurement of the viscoelastic properties of human osteosarcoma (HOS) cells. It involves a combination of shear assay experiments and digital image correlation techniques. Following in situ observations of cell deformation during shear assay experiments, a digital image correlation (DIC) technique was used to determine the local displacement and strain fields. The creep curves were also extracted from multiple digital images that were used to extract the time dependence of local strain under constant stress conditions. The measured creep curves were well described by a generalized viscoelastic Maxwell model. The extracted elastic and viscous parameters were in good agreement with results obtained from prior studies with other techniques. The results also suggested that the nucleus is stiffer than the surrounding cytoplasm of HOS cells.

Spontaneous emission in absorbing dielectrics: an alternative approach

We consider the spontaneous emission in an absorbing medium by calculating the quantum flow of energy from an emitting atom. For this purpose, we extend the analysis by Power and Thirunamachandran of quantized Maxwell fields in the vicinity of an atom in the free space to a situation where the emitter is in a dielectric medium. We represent the quantum flow in terms of the non-equal time commutators involving electric and magnetic fields, as well as the local displacement field. The commutators are calculated applying a previously developed microscopic theory of quantization of radiation in dielectrics. Consequently, we derive from first principles the rate of spontaneous emission in an absorbing medium containing local field factors and other refractive contributions. The results support the previous introduction of the (virtual cavity) local field correction by Barnett et al on a phenomenological basis, as well as our previous approach in which the spontaneous emission is considered as a resonance energy transfer to the far-zone atoms. A distinctive feature of the present formalism is that it deals with the spontaneous emission directly by calculating the quantum flow from the emitting atom. Therefore, the method is free from divergences appearing in other approaches analysing the spontaneous decay in absorbing media.

Determination of Ductile Damage Parameters by Local Deformation Fields: Measurement and Simulation

This work comprises the development, implementation and application of methods for the parameter identification of damage mechanical constitutive laws. Ductile damage is described on a continuum mechanical basis by extension of the von Mises yield condition with the Gurson–Tvergaard–Needleman as well as with the Rousselier model. The classical Rousselier model is complemented by accelerated void growth and void nucleation. The non-linear boundary and initial value problem is solved by the finite element system SPC–PMHP, which was developed in the frame of the special research program SFB393 for parallel computers. The material parameters are identified by locally measured displacement fields and measured force–displacement curves. For the material parameter identification a non-linear optimization algorithm is used, which renders the objective function to a minimum by means of a gradient based method. A useful strategy to identify the material parameters was found by careful numerical studies. Finally, using the object grating method the local displacement fields as well as the force–displacement curves are measured at notched flat bar tension specimens made of StE 690 and the parameters of the material are identified.

Chondrocyte Deformation Induces Mitochondrial Distortion and Heterogeneous Intracellular Strain Fields

Chondrocyte mechanotransduction is poorly understood but may involve cell deformation and associated distortion of intracellular structures and organelles. This study quantifies the intracellular displacement and strain fields associated with chondrocyte deformation and in particular the distortion of the mitochondria network, which may have a role in mechanotransduction. Isolated articular chondrocytes were compressed in agarose constructs and simultaneously visualised using confocal microscopy. An optimised digital image correlation technique was developed to calculate the local intracellular displacement and strain fields using confocal images of fluorescently labelled mitochondria. The mitochondria formed a dynamic fibrous network or reticulum, which co-localised with microtubules and vimentin intermediate filaments. Cell deformation induced distortion of the mitochondria, which collapsed in the axis of compression with a resulting loss of volume. Compression generated heterogeneous intracellular strain fields indicating mechanical heterogeneity within the cytoplasm. The study provides evidence supporting the potential involvement of mitochondrial deformation in chondrocyte mechanotransduction, possibly involving strain-mediated release of reactive oxygen species. Furthermore the heterogeneous strain fields, which appear to be influenced by intracellular structure and organisation, may generate significant heterogeneity in mechanotransduction behaviour for cells subjected to identical levels of deformation.

Measurement of elastic moduli using spherical indentation and digital speckle pattern interferometry with automated data processing

The Young's modulus and the Poisson's ratio of an isotropic material are measured using digital speckle pattern interferometry. The technique is based on the determination of the permanent local displacement field generated in a specimen after it is plastically deformed with a spherical indenter. Using a phase shifting technique and a phase unwrapping algorithm, the phase distribution coded in the speckle interferograms can be quickly obtained. By adjusting the displacement field generated by the indentation to an empirical model produced by a point force in a semi-infinite elastic medium, the values of both elastic moduli can be determined by applying a least-squares inversion method to the evaluated continuous phase distribution. The performance, accuracy, advantages and limitations of this technique are determined by evaluating the elastic moduli of bronze.

Young's modulus, Poisson's ratio and failure properties of tetrahedral amorphous diamond-like carbon for MEMS devices

The elastic and failure mechanical properties of hydrogen-free tetrahedral amorphous carbon (ta-C) MEMS structures were investigated via in situ direct and local displacement measurements by a method that integrates atomic force microscopy (AFM) with digital image correlation (DIC). On-chip MEMS-scale specimens were tested via a custom-designed apparatus that was integrated with an AFM to conduct in situ uniaxial tension tests. Specimens 10 µm and 50 µm wide and of 1.5 µm average thickness were used to measure the elastic properties while 340 µm wide tension specimens with a central elliptical perforation resulting in a stress concentration factor of 27 were tested to investigate local effects on material strength. The Young's modulus, Poisson's ratio and tensile strength were measured as 759 ± 22 GPa, 0.17 ± 0.03 and 7.3 ± 1.2 GPa, respectively. In an effort to understand the effect of local defects and assess the true material strength, the local failure stress at sharp central elliptical notches with a stress concentration factor of 27 was measured to be 11.4 ± 0.8 GPa. The AFM/DIC method provided for the first time local displacement fields in the vicinity of microscale perforations and these displacement fields were in accordance with those predicted by linear elasticity.

Evaluation of Failure Behaviour of Coated Anisotropic Materials for Dental Implants

This paper presents the results of an experimental procedure where a grid is applied to the edge of a specimen and the local crack-tip displacement fields are calculated using finite element technique. Increasingly, the objective of finite element simulations is to predict the response of the mechanics of material failure are related to microstructural process that occur in the materials as a result of the loading conditions. At the same time, The influences of coating thickness, coating stiffness, and assume crack pattern on the stresses concentration between the neighbouring layers of material are evaluated. Consequently, one approach to simulating the response of structures is to explicity model the mechanisms of damage and failure in the material.

A generalized, multilength scale framework for thermo-diffusional-mechanically coupled, nonlinear, laminated plate theories with delaminations

A new type of plate theory based on a general, unified, theoretical framework for the response of (von Karman) nonlinear, delaminated plate theories in the presence of thermo-diffusional-mechanical coupling is presented. The theory is based on the unique use of two length scale expansions obtained from a superposition of global and local effects for the displacement, temperature, and solute concentration fields. The orders and forms of these local and global displacement, temperature, and solute fields are arbitrary. The theory incorporates delamination and/or nonlinear elastic or inelastic interfacial behavior for the mechanical, thermal, and concentration effects in a unified fashion through the use of generalized interfacial constitutive (cohesive) relations. The mathematical framework introduces new types of coupling effects between the different length scale effects of all three fields. The resulting unified theoretical framework can be used to consider the general thermo-diffusionally-mechanically coupled response of laminated (or homogeneous) plates in the presence of delaminations, buckling, and/or nonlinear material behavior. The author is unaware of any previous attempts to develop plate theory formulations capable of considering the multitude of effects incorporated into the proposed framework. It is shown that existing displacement-based plate theories for both the mechanical as well as thermo-mechanical behavior of laminated plates can be obtained via suitable specializations of the proposed framework. New types of plate theories can be obtained through various specializations of the proposed general theory.

Realization of high sensitivity displacement field from moiré interferometer with rough phase shifting mechanism and pattern matching technique

In this study, phase shifting method is used to modify moiré system into micro moiré interferometer which can measure displacement field with highly improved sensitivity. Apart from existing micro moiré technique, a low cost and less precise translation stage with rough resolution (10 μm resolution) is adapted for the phase shifter. Least square algorithm is applied to estimate the arbitrary phase shifted amount and to minimize the errors induced by lowering the cost. Moreover, specimen grating is phase shifted instead of reference grating which enables simple construction from given moiré system. To compensate for rigid body in-plane translation of specimen that may occur during phase shifting, pattern matching algorithm is put into practice to ensure pixel correspondence for each phase shifted images. To verify the newly constructed micro moiré technique, local displacement fields of Fine pitch Ball Grid Array package and Wafer Level Chip Size Package with elevated sensitivity up to 26 nm per fringe was acquired.

An experimental-computational investigation of fracture in brittle materials

A combined experimental-computational study of a double edge-notched stone specimen subjected to tensile loading is presented. In the experimental part, the load-deformation response and the displacement field around the crack tip are recorded. An Electronic Speckle Pattern Interferometer (ESPI) is used to obtain the local displacement field. The experimental results are used to validate a numerical model for the description of fracture using finite elements. The numerical model uses displacement discontinuities to model cracks. At the discontinuity, a plasticity-based cohesive zone model is applied for monotonic loading and a combined damage-plasticity cohesive zone model is used for cyclic loading. Both local and global results from the numerical simulations are compared with experimental data. It is shown that local measurements add important information for the validation of the numerical model. Consequently, the numerical models are enhanced in order to correctly capture the experimentally observed behaviour.

A layered agarose approach to fabricate depth-dependent inhomogeneity in chondrocyte-seeded constructs

Inspired by the depth-dependent inhomogeneity of articular cartilage, it was hypothesized that a novel layered agarose technique, using a 2% (wt/vol) top and a 3% (wt/vol) bottom layer, would create an inhomogenous tissue construct with distinct material properties in conjoined regions. The biochemical and mechanical development of these constructs was observed alongside uniform 2% and 3% constructs. Initially, uniform 3% agarose disks had the highest bulk Young's modulus ( E Y∼28 kPa) of all groups. After 28 days of culture in 20% FBS-containing media, however, uniform 2% chondrocyte-seeded constructs achieved the highest Young's modulus compared to bilayered and 3% agarose disks. Though all three groups contained similar GAG content (∼1.5% ww), uniform 2% agarose disks on day 28 possessed the highest collagen content (∼1% ww). Unlike in either homogeneous construct type, microscopic analysis of axial strain fields in bilayered constructs in response to applied static compression revealed two mechanically disparate regions on day 0: a softer 2% layer and a stiffer 3% layer. With time in culture, this inhomogeneity became less distinct, as indicated by increased continuity in both the local displacement field and local E Y, and depended on the level of FBS supplementation of the feed media, with lower FBS concentrations (10%) more closely maintaining the original distinction of material properties. These results shed positive light on a layered agarose technique for the production of inhomogeneous bilayered chondrocyte-seeded agarose constructs with applications for investigations of chondrocyte mechanotransduction and for possible use in the tissue engineering of inhomogeneous articular cartilage constructs.

Quantitative evaluation of plastic strain gradients generated during orthogonal cutting of an aluminum alloy

Deformation microstructures developed in the material ahead of tool tip in the 6061 Al alloy samples subjected to an orthogonal cutting process were investigated. Samples of hot extruded 6061 Al that contained inherent microstructural markers in the form of extrusion lines were cut at a low speed. Metallographic sections were examined to measure local displacement fields in the deformed material. This information was used to estimate local variations in shear angles. A method to determine the plastic strain gradients in the material ahead of the tool tip has been established and the distribution of equivalent strains has been summarized in a diagram constructed from the measured deformation angles.

Automatic detection and segmentation of evolving processes in 3D medical images: Application to multiple sclerosis

The study of temporal series of medical images can be helpful for physicians to perform pertinent diagnoses and to help them in the follow-up of a patient: in some diseases, lesions, tumors or anatomical structures vary over time in size, position, composition, etc., either because of a natural pathological process or under the effect of a drug or a therapy. It is a laborious and subjective task to visually and manually analyze such images. Thus the objective of this work was to automatically detect regions with apparent local volume variation with a vector field operator applied to the local displacement field obtained after a non-rigid registration between two successive temporal images. On the other hand, quantitative measurements, such as the volume variation of lesions or segmentation of evolving lesions, are important. By studying the information of apparent shrinking areas in the direct and reverse displacement fields between images, we are able to segment evolving lesions. Then we propose a method to segment lesions in a whole temporal series of images. In this article we apply this approach to automatically detect and segment multiple sclerosis lesions that evolve in time series of MRI scans of the brain. At this stage, we have only applied the approach to a few experimental cases to demonstrate its potential. A clinical validation remains to be done, which will require important additional work.

Higher-order theory for periodic multiphase materials with inelastic phases

An extension of a recently-developed linear thermoelastic theory for multiphase periodic materials is presented which admits inelastic behavior of the constituent phases. The extended theory is capable of accurately estimating both the effective inelastic response of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material's periodic microstructure. The model's analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite-element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading. The model's predictive accuracy in generating both the effective inelastic stress-strain response and the local stress and inelastic strain fields is demonstrated by comparison with the results of an analytical inelastic solution for the axisymmetric and axial shear response of a unidirectional composite based on the concentric cylinder model and with finite-element results for transverse loading.

Effect of tangential interface motion on the viscous instability in fluid flow past flexible surfaces

The stability of linear shear flow of a Newtonian fluid past a flexible membrane is analysed in the limit of low Reynolds number as well as in the intermediate Reynolds number regime for two different membrane models. The objective of this paper is to demonstrate the importance of tangential motion in the membrane on the stability characteristics of the shear flow. The first model assumes the wall to be a spring-backed plate membrane, and the displacement of the wall is phenomenologically related in a linear manner to the change in the fluid stresses at the wall. In the second model, the membrane is assumed to be a two-dimensional compressible viscoelastic sheet of infinitesimal thickness, in which the constitutive relation for the shear stress contains an elastic part that depends on the local displacement field and a viscous component that depends on the local velocity in the membrane. The stability characteristics of the laminar flow in the limit of low Re are crucially dependent on the tangential motion in the membrane wall. In both cases, the flow is stable in the low Reynolds number limit in the absence of tangential motion in the membrane. However, the presence of tangential motion in the membrane destabilises the shear flow even in the absence of fluid inertia. In this case, the non-dimensional velocity (At) required for unstable fluctuations is proportional to the wavenumber k (At~k) in the plate membrane type of wall while it scales as k2 in the viscoelastic membrane type of wall (At~k2) in the limit k-0. The results of the low Reynolds number analysis are extended numerically to the intermediate Reynolds number regime for the case of a viscoelastic membrane. The numerical results show that for a given set of wall parameters, the flow is unstable only in a finite range of Reynolds number, and it is stable in the limit of large Reynolds number.

The quintic finite element and finite strip with generalized degrees of freedom in structural analysis

This paper presents the method of quintic finite element and quintic finite strip with generalized degrees of freedom (DOF) based on the philosophy that the local displacement fields of an element or strip should be compatible with the global displacement field. At first, the global displacement field of a structure is developed using the quintic B-spline functions. Then, the local displacement field of element/strip is constructed employing the multi-term interpolation functions of degree 5. At last, the displacement field of finite element/strip with generalized DOF is generated when the local and global displacement fields are equally matched in their deformation. This kind of high order finite element/strip can not only effectively widen the scope of application of the conventional quintic element/strip and the spline function method, but also greatly reduce the amount of DOF with the same degrees of accuracy as compared to the conventional finite element method. Several numerical examples demonstrate the accuracy, simplicity and versatility of the present methods for analysis of thin-walled structures.

Nonlinear local response of foam-filled sandwich plates with laminated faces under combined transverse and in-plane loads

This paper deals with the nonlinear local response of foam-filled sandwich plates with composite laminated faces subjected to transverse patch load combined with in-plane compressive edge loads. The analysis is carried out by modeling loaded faces as thin laminated plates resting on a two-parameter (Vlasov-type) elastic foundation, from which the shearing interaction between the loaded face and the supporting core-layer are included. An analytical–numerical approach is developed to determine the local bending or postbuckling responses of foam-filled sandwich plates with different sets of boundary conditions. Both local displacement and stress fields are examined. A detailed numerical investigation of the influence played by a number of laminate parameters (fiber orientation, geometric dimensions) and foundation parameters (elastic modular ratio and thickness ratio between face and core layers) as well as the load parameters is performed and pertinent conclusions are outlined.

The quadratic finite element/strip with generalized degrees of freedom and their application

This paper presents a quadratic finite element with generalized degrees of freedom (GDOF) and a quadratic finite strip with GDOF based on the principle that the local displacement fields of elements should be compatible with the global displacement field of the corresponding systems. Firstly, a global displacement field is developed using quadratic B-spline functions. Secondly, local displacement fields of elements and strips are constructed, employing multi-term interpolation polynomials of second degree. Making the local displacement fields of elements and strips be compatible with their corresponding global displacement fields, respectively, models of the finite element with GDOF and the finite strip with GDOF are accordingly generated. On the other hand, the quadratic B-spline function is convenient to derive the explicit form of characteristic equations for computing model because of its lower order, and accordingly simplifies the computation, compared with cubic and quintic spline functions. Several numerical examples demonstrate the accuracy, simplicity and versatility of the present element and strip in the analysis of thin-walled structures.

Linear Thermoelastic Higher-Order Theory for Periodic Multiphase Materials

A new micromechanics model is presented which is capable of accurately estimating both the effective elastic constants of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material’s periodic microstructure. The model’s analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading which, in turn, can be incorporated into a structural analysis computer code. The model’s predictive accuracy is demonstrated by comparison with reported results of detailed finite element analyses of periodic composites as well as with the classical elasticity solution for an inclusion in an infinite matrix.