Local Displacement Field Research Articles

Optical Response of a Hematite Coating: Ellipsometry Data versus Fourier-Based Computations

The optical properties of a hematite-epoxy coating are predicted numerically and compared with el-lipsometry measurements. The highly-heterogeneous dispersion of nanocubic hematite particles in the epoxy resin is simulated using a previously developed two-scales random model. The local anisotropic permittivity tensor of hematite particles, and that of the epoxy, are estimated by ellipsometry measurements carried out on a macroscopic hematite and epoxy samples. Fourier-based methods using a discrete Green operator are used to treat complex permittivities. They predict the effective and local electric displacement field in the quasi-static approximation. The former is close to two estimates based on the Hashin-Shtrikman bounds and a self-consistent approximation. Good agreement is found between experimental data and FFT computations in the whole range of the visible spectrum.

Multi-scale characterization of topographic anisotropy

We present the every-direction variogram analysis (EVA) method for quantifying orientation and scale dependence of topographic anisotropy to aid in differentiation of the fluvial and tectonic contributions to surface evolution. Using multi-directional variogram statistics to track the spatial persistence of elevation values across a landscape, we calculate anisotropy as a multiscale, direction-sensitive variance in elevation between two points on a surface. Tectonically derived topographic anisotropy is associated with the three-dimensional kinematic field, which contributes (1) differential surface displacement and (2) crustal weakening along fault structures, both of which amplify processes of surface erosion. Based on our analysis, tectonic displacements dominate the topographic field at the orogenic scale, while a combination of the local displacement and strength fields are well represented at the ridge and valley scale. Drainage network patterns tend to reflect the geometry of underlying active or inactive tectonic structures due to the rapid erosion of faults and differential uplift associated with fault motion. Regions that have uniform environmental conditions and have been largely devoid of tectonic strain, such as passive coastal margins, have predominantly isotropic topography with typically dendritic drainage network patterns. Isolated features, such as stratovolcanoes, are nearly isotropic at their peaks but exhibit a concentric pattern of anisotropy along their flanks. The methods we provide can be used to successfully infer the settings of past or present tectonic regimes, and can be particularly useful in predicting the location and orientation of structural features that would otherwise be impossible to elude interpretation in the field. Though we limit the scope of this paper to elevation, EVA can be used to quantify the anisotropy of any spatially variable property.

FEM/BEM Techniques for Modelling of Local Fields in Contact Mechanics

This contribution contains description of modelling technique of contact problems of bodies with curved surfaces when assumption of infinitesimal displacements can be considered to give sufficient accuracy for both displacement and stress analysis. This assumption considers that the local configuration of the bodies in contact will not be influenced during the deformation process and only dimensions and shape of the contact surfaces and contact pressures will change by the load conditions. Such assumptions enable to reduce the contact problem considerably, if the local contact displacement and stress fields are modelled as local fields inside large elements (sub-domains) using superposition of a local Hertz type field and a smooth field modelled in a classical way using large FEM or BEM technique. A technique of obtaining the complex solution of the bodies in contact as a combination of the local contact field defined by the Boussinesq's solution and the smooth field modelled by multi-domain BEM is described and considered to be a basis for the modelling and design of contact problems containing large gradient displacements.

On the Extraction of Elastic–Plastic Constitutive Properties From Three-Dimensional Deformation Measurements

In this article, a coupled experimental and numerical method is utilized for characterizing the elastic–plastic constitutive properties of ductile materials. Three-dimensional digital image correlation (DIC) is used to measure the full field deformation on two mutually orthogonal surfaces of a uniaxial tensile test specimen. The material’s constitutive model, whose parameters are unknown a priori, is determined through an optimization process that compares these experimental measurements with finite element simulations in which the constitutive model is implemented. The optimization procedure utilizes the robust dataset of locally observed deformation measurements from DIC in addition to the standard measurements of boundary load and displacement data. When the difference between the experiment and simulations is reduced sufficiently, a set of parameters is found for the material model that is suitable to large strain levels. This method of material characterization is applied to a tensile specimen fabricated from a sheet of 15-5 PH stainless steel. This method proves to be a powerful tool for calibration of material models. The final parameters produce a simulation that tracks the local experimental displacement field to within a couple percent of error. Simultaneously, the percent error in the simulation for the load carried by the specimen throughout the test is less than 1%. Additionally, half of the parameters for Hill’s yield criterion, describing anisotropy of the normal stresses, are found from a single tensile test. This method will find even greater utility in calibrating more complex material models by greatly reducing the experimental effort required to identify the appropriate model parameters.

Influence of thermomechanical interaction effects on the failure behaviour of polymer foam cored sandwich panels

The paper presents an experimentally based and numerically supported investigation of the collapse behaviour of polymer foam cored sandwich beams subjected to combined mechanical and thermal loading. Recent analytical and numerical modelling results available in the literature have ascertained that collapse may be due to loss of stability induced by nonlinear interactions between mechanical loads and thermally induced deformations, when accounting for the reduction of the polymer foam core mechanical properties with increasing temperature. In the paper, experiments are devised whereby a thermal gradient is introduced into a sandwich beam specimen loaded in three-point bending. The experiments cover a range of temperatures where one face sheet is heated from room temperature (25℃) to just below the glass transition temperature of the polymer foam core (70℃) and the other face sheet remains at room temperature. Digital image correlation (DIC) is used to obtain the local displacement field of the sandwich beam and its temperature is monitored using an infrared detector and thermocouples. The experimental results are compared with the predictions of both a generally nonlinear finite element model and an analytical so-called high-order sandwich panel theory (HSAPT) model. It is important to note that the HSAPT model has clear limitations as it takes into account only the geometric nonlinearity and thermal degradation of the foam core elastic properties, and it further assumes that the sandwich constituents are linear elastic with infinite straining capability. The HSAPT model predicts the occurrence of a strongly nonlinear load response leading to loss of stability (limit point behaviour). However, the experiments show that for the investigated sandwich beam configuration, it is necessary to include the nonlinear material properties in the modelling, as the nonlinear beam response leading to failure and collapse is significantly influenced by plastic deformations in the constituent materials. Thus, core indentation and extensive plasticity precede the transition to loss of stability driven by geometric nonlinearity and thermomechanical interaction effects. Finite element analyses that include both geometric and material nonlinearities provide results that correlate closely with the experimental observations. The work presented lays the foundation of a methodology for validating complex thermomechanical behaviour in sandwich structures using non-contact full-field measurement systems, and it demonstrates that analytical or numerical models based on the assumption of linear elastic material behaviour (such as the HSAPT model referenced in the paper) generally cannot adequately describe the thermomechanical behaviour of foam-cored sandwich structures.

A global–local discontinuous Galerkin finite element for finite-deformation analysis of multilayered shells

We present a global–local finite element formulation for the analysis of doubly-curved laminated composite shells. The proposed formulation is applicable to a wide range of problems, including those involving finite strains/rotations, nonlinear constitutive behavior, and static or dynamic structural response. Moreover, in dynamic analysis applications, it can be combined with either explicit or implicit time integration schemes. The global–local framework is based on the superposition of a global displacement field, spanning the thickness of the entire laminate, and local (i.e. layerwise) displacement fields associated with each layer in the laminate. This approach affords highly-resolved representations in regions of critical interest, and allows a smooth transition from higher to lower resolution zones. Discontinuous Galerkin fluxes are used to enforce interlaminar continuity conditions in perfectly-bonded laminates, and the cohesive-zone methodology is used to represent interfacial delamination. Stresses and surface normals are referred to the initial configuration in the proposed total Lagrangian formulation. Assumed natural strain and enhanced assumed strain techniques are employed to alleviate shear locking and other pathologies that are known to afflict bilinear shell elements. The performance of the proposed finite element is examined with the aid of several numerical examples involving thick as well as thin shells.

Crystal Plasticity Finite Element Method Simulations for a Polycrystalline Ni Micro-Specimen Deformed in Tension

A micro-tensile test system equipped with in situ monitoring of the in-plane displacements of a surface and an electron backscattered diffraction-based serial-sectioning technique were used to study the deformation (up to 2.4 pct axial plastic strain in tension) of a polycrystalline nickel micro-specimen. The experimental data include the global engineering stress-engineering strain curve, the local mesoscopic in-plane displacement and strain fields, the three-dimensional microstructure of the micro-specimen reconstructed after the tensile test, and the kernel-average misorientation distribution. The crystal plasticity finite element method using elasto-viscoplastic constitutive formulations was used to simulate the global and local deformation responses of the micro-specimen. Three different boundary conditions (BCs) were applied in simulation in order to study the effects of the lateral displacement (perpendicular to the loading direction) of the top and bottom faces of the specimen gage section. The simulation results were compared to the experimental results. The comparison between experiment and simulation results is discussed, based upon their implications for understanding the deformation of micro-specimens and the causes associated with uncertainties embedded in both experimental and numerical approaches. Also, the sensitivity of BCs to near-field and far-field responses of the micro-specimen was systematically studied. Results show that the experimental methodology used in the present study allows for limited but meaningful comparisons to crystal plasticity finite element simulations of the micro-specimen under the small plastic deformation.

Investigation of Displacement Fields in Contact Problems with Friction by Means of a Moiré-Technique

For a number of relevant engineering problems, the stress field in elastic bodies under contact loads must be known. Studies on their failure have emphasized the effect of localised contact with friction that produces small zones undergoing high tensile stresses on the surface near the contact. The failure probability is related to global variables obtained by integrating spatial functions of the stresses on the domain of interest. An experimental analysis is necessary in order to validate the results obtained in numerical works or to extend the half space solution when considering the problem of the local stresses in a bar under contact loads between disks of the same material. This paper describes how the moire-interferometry technique can be applied in order to obtain the local displacement fields in contact problems with friction. KeywordsFriction; Moire; Displacement Fields

A computational tool for estimating stress fields along a surface crack front

AbstractA combined experimental and computational method for determination of the singular and non‐singular stress terms along the front of the 3D surface crack is proposed. It is suggested to evaluate the terms by means of comprehensive comparison between deformation responses on the structure surface in the vicinity of the crack obtained experimentally and from numerical solutions of the corresponding boundary problem of solid mechanics. As the deformation response, a local displacement field caused by the formation of a small hole at the tip of the crack recorded by digital speckle pattern interferometry may be considered. The proposed approach allows defining such real parameters of the structure as the active load conditions in the crack region and crack sizes. These parameters are used to solve the direct problem and to determine the stress intensity factor KI and Txx‐, Tzz‐stresses along the surface crack front by means of an improved technique of their calculation.The approach accuracy and stability at different conditions have been proved by means of numerical simulation that examined half‐space with planar semi‐elliptical surface crack under biaxial loading. So, the potential applicability of the proposed method is demonstrated. The biaxiality effect on KI and Txx, Tzz is discussed.

Localized strain field measurement on laminography data with mechanical regularization

For an in-depth understanding of the failure of structural materials the study of deformation mechanisms in the material bulk is fundamental. In situ synchrotron computed laminography provides 3D images of sheet samples and digital volume correlation yields the displacement and strain fields between each step of experimental loading by using the natural contrast of the material. Difficulties arise from the lack of data, which is intrinsic to laminography and leads to several artifacts, and the little absorption contrast in the 3D image texture of the studied aluminum alloy. To lower the uncertainty level and to have a better mechanical admissibility of the measured displacement field, a regularized digital volume correlation procedure is introduced and applied to measure localized displacement and strain fields.

A global–local discontinuous Galerkin shell finite element for small-deformation analysis of multi-layered composites

This paper focuses on the development of a global–local doubly-curved shell element, suitable for small-deformation implicit and/or explicit dynamic analysis of laminated composite structures. The global–local framework is based on the superposition of a global displacement field, spanning the thickness of the entire laminate, and local (layerwise) displacement fields associated with each layer of the laminate. This approach affords highly-resolved representations in regions of critical interest, and allows a smooth transition from higher to lower resolution zones. Continuity between adjacent layers is enforced by means of discontinuous Galerkin fluxes. Parasitic phenomena characteristic of bilinear shell elements, such as shear locking, are alleviated with the aid of assumed natural strain techniques. Performance characteristics of the proposed finite element are examined with the aid of several numerical examples involving static and dynamic analysis of thick as well as thin shells.

Experimental measurement of surface strains and local lattice rotations combined with 3D microstructure reconstruction from deformed polycrystalline ensembles at the micro-scale

AbstractThis article describes a new approach to characterize the deformation response of polycrystalline metals using a combination of novel micro-scale experimental methodologies. An in-situ scanning electron microscope (SEM)-based tension testing system was used to deform micro-scale polycrystalline samples to modest and moderate plastic strains. These tests included measurement of the local displacement field with nm-scale resolution at the sample surface. After testing, focused ion beam serial sectioning experiments that incorporated electron backscatter diffraction mapping were performed to characterize both the internal 3D grain structure and local lattice rotations that developed within the deformed micro-scale test samples. This combination of experiments enables the local surface displacements and internal lattice rotations to be directly correlated with the underlying 3D polycrystalline microstructure, and such information can be used to validate and guide further development of modeling and simulation methods that predict the local plastic deformation response of polycrystalline ensembles.

FE2 multiscale in linear elasticity based on parametrized microscale models using proper generalized decomposition

In recent years, a tremendous growth of activity in multiscale modelling has been produced to get the mechanical response of highly heterogenous materials, where the complexity of solving numerically all microscale details is not feasible. In this paper we present a multiscale framework based on the decomposition of the displacement field into coarse (macro) and fine (micro) scales, earlier proposed in the Variational Multiscale approach or the hp-d method. The novelty of this work lies in solving the microscale step, where a multidimensional parametrized model of a generic RVE is solved, by means of the multidimensional model reduction technique, named as proper generalized decomposition (PGD). As result of this previous and off-line step, the displacement field over the RVE is obtained by simple algebraic operations for any combination of parameters (boundary condition, material properties, loads, etc.), allowing a significant reduction in computational cost when solving the macro scale problem. For problems where the detailed structure of the localized displacement, strain and stress fields are of interest, recovery of the fine scale components can be performed immediately. The basic concepts and several 1-D and 2-D linear elastic problems are presented to demonstrate the robustness of the formulation and computer time saving.

Micromechanical modelling of damage evolution in highly filled particulate composites – Induced effects at different scales

An unconventional multi-scale approach is investigated to model interfacial damage and subsequent effects in highly filled particulate composites such as solid propellants. The basic framework by Nadot et al. (2006 Damage modelling framework for viscoelastic particulate composites via a scale transition approach, Journal of Theoretical and Applied Mechanics 44:553–583) is enhanced to deal with damage state and configuration evolution under any loading. Three criteria are formulated at the microscale. The first one concerns the nucleation of new defects, while the other two (for closure and re-opening) monitor the respective proportions of open and closed defects. The formulation exploits the explicit microstructure representation and the knowledge of the local displacement field as a function of local morphology around the interfaces. The multi-scale model is finally implemented through a numerical solving procedure able to deal with successive and/or simultaneous discrete damage events (nucleation/closure/re-opening of defects) depending on the loading path. Numerical illustrations are given for a three-dimensional microstructure containing 351 particles submitted to complex loading sequence involving extension, shear and contraction stages. The results show the ability of the model to estimate damage characteristics (position, orientation within the material) in addition to induced effects at both microscale and macroscale (induced anisotropy, unilateral effects and influence on local fields).

The standardized Brazilian disc test as a contact problem

The standardized Brazilian disc test is revisited considering the disc-jaw complex as a system of two elastic bodies in contact. The aim of the study is to shed light on the conditions at the disc-jaw interface in an effort to quantify the length of the common contact rim developed as the jaw and the disc are compressed against each other. The problem is approached both analytically and experimentally. The analytic solution is based on the complex potentials method introduced by Muskhelishvili and leads to a Mixed Fundamental plane problem of the classic linear elasticity theory. The local displacement field is determined and then the contact length is obtained in closed form in terms of geometrical and material parameters of both the specimen and the loading jaws and also of the externally applied load. Moreover interesting conclusions are drawn concerning the exact variation of the radial pressure along the contact rim. The experimental approach is carried out using the 3D Digital Image Correlation technique which provides a full field representation of the displacement- and strain-fields developed. Taking advantage of the experimental data it was possible to estimate the contact length experimentally. Comparison between analytic and experimental results for the specific quantity is satisfactory.

Landslide stabilizing piles: Experimental evidences and numerical interpretation

A well instrumented field trial consisting of five piles was installed in an active mudslide in the Basento Valley, Southern Italy, and monitored for 3years. The large amount of experimental data (slide movements, ground water levels, rainfall heights, pile displacements and strains) was processed to highlight the influence of the row of piles on the local and overall mudslide displacement field, as well as to quantify the shear forces and bending moments within the piles. The experimental evidences have been back analysed by a 3D numerical analysis (code FLAC3D) to gain a deeper insight on piles' structural behaviour and stabilizing effectiveness. In particular, the 3D analysis has given an indication on the length of mudslide on the uphill side of the piles whose displacements are clearly influenced by the piles. Furthermore, the predicted lateral loads on piles are in good agreement with those deduced by processing the experimental data, indicating the capability of 3D numerical analysis as a research tool to integrate the information obtained by field data.

Direct Mean Strain Estimation for Elastography Using Nearest-Neighbor Weighted Least-Squares Approach in the Frequency Domain

Ultrasound elastography is emerging with enormous potential as a medical imaging modality for effective discrimination of pathological changes in soft tissue. It maps the tissue elasticity or strain due to a mechanical deformation applied to it. The strain image most often calculated from the derivative of the local displacement field is highly noisy because of the de-correlation effect mainly due to unstable free-hand scanning and/or irregular tissue motion; consequently, improving the SNR of the strain image is still a challenging problem in this area. In this paper, a novel approach using the nearest-neighbor weighted least-squares is presented for direct estimation of the ‘mean’ axial strain for high quality strain imaging. Like other time/frequency domain reported schemes, the proposed method exploits the fact that the post-compression rf echo signal is a time-scaled and shifted replica of the pre-compression rf echo signal. However, the elegance of our technique is that it directly computes the mean strain without explicitly using any post filter and/or previous local displacement/strain estimates as is usually done in the conventional approaches. It is implemented in the short-time Fourier transform domain through a nearest-neighbor weighted least-squares-based Fourier spectrum equalization technique. As the local tissue strain is expected to maintain continuity with its neighbors, we show here that the mean strain at the interrogative window can be directly computed from the common stretching factor that minimizes a cost function derived from the exponentially weighted windowed pre- and post-compression rf echo segments in both the lateral and axial directions. The performance of our algorithm is verified for up to 8% applied strain using simulation and experimental phantom data and the results reveal that the SNR of the strain image can be significantly improved compared to other reported algorithms in the literature. The efficacy of the algorithm is also tested with in vivo breast data known to have malignant or benign masses from histology.

COMBINING LOCAL FEATURES AND PROGRESSIVE SUPPORT VECTOR MACHINE FOR URBAN CHANGE DETECTION OF VHR IMAGES

Abstract. The difficulties about change detection of VHR images are analyzed from different perspectives. Motivated by perception and cognition mechanism of human vision, visual change detection principles are discussed, and a unified change detection framework is proposed. To address the difficulties in change detection of VHR images, a novel approach is presented within the framework, which exploits the combination of local features and change vector displacement field to represent the complex changes of VHR images and utilizes transductive SVM (Support Vector Machine) to classify change features progressively. Experiments demonstrate the effectiveness of the proposed approach.

Fracture behaviour of adhesively bonded single lap joint with 45° ply oriented four layered symmetric and antisymmetric adherends

In aerospace and many types of civil infrastructure applications, the use of adhesive-bonded composite joints have been constantly increasing. In this study, fracture behaviour of adhesively bonded single lap joint (SLJ) with pre-existing damage at the interface of free edge of the top adherend and adhesive along the width of the joint is studied by strain energy release rate (SERR) approach using virtual crack closure technique (VCCT). Adherends are four layered laminated fiber reinforced plastic (FRP) composite plates and each lamina of adherend having either +45° or -45° fiber angle. The distributions of strain energy release rates along the delamination front are predicted by evaluating 3D local displacement fields and reaction forces required to close them, along the delamination length and width. The present investigation reveals that strain energy release rates are not constant along the delamination front, insisting on three dimensional modeling of problem. It is observed that location of damage propagation and mode of failure responsible for damage propagation varies with lay-up sequence of +45° or -45° ply oriented laminas within the top and bottom adherends. Total strain energy release rate (G) values are very high in the SLJs having (+45/-45)s FRP laminated adherends and in the SLJ with (-45/+45)s FRP laminated adherends, when compared with SLJs having (+45/-45)asand/or (-45/+45)as FRP laminated adherends. Key words: Delamination length, strain energy release rate (SERR), virtual crack closure technique (VCCT), suffix s and as, fiber angle.

Precise bending stress analysis of corrugated-core, honeycomb-core and X-core sandwich panels

A semi-analytical method for bending analysis of corrugated-core, honeycomb-core and X-core sandwich panels is presented. The real displacement of sandwich panels is divided into the global displacement field and local displacement field. The discrete geometric nature of the core is taken into account by treating the core sheets as beams and the sandwich panel as composite structure of plates and beams with proper displacement compatibility. In the global displacement field, the governing equations of these sandwich panels are derived using energy variation principle and solved by employing Fourier series and the Galerkin approach. In the local displacement field, the face sheets under external loads are taken as a multi-span thin plate and the local bending response are then computed. Then the real bending responses are obtained by superposing these bending responses calculated in the two displacement fields and the structural stress fluctuation can be captured. Results from the proposed method agree well with available results in the literature and those from detailed finite element analysis. Furthermore, the mechanical properties of the three kinds of sandwich panels have been compared.