A Multigrid PGD‐based Algorithm for Volumetric Displacement Fields Measurements

The use of a finite elements‐based Digital Volume Correlation (FE‐DVC) leads to lower measurement uncertainties in comparison to subset‐based approaches. However, the associated computing time may become prohibitive when dealing with high‐resolution measurements. To overcome this limitation, a Proper Generalised Decomposition solver was recently applied to 2D digital image correlation. In this paper, this method is extended to measure volumetric displacements from 3D digital images. In addition, a multigrid Proper Generalised Decomposition algorithm is developed, which allows to use different discretisations in each term of the decomposition. Associated to a coarse graining of the digital images, this allows to avoid local minima, especially in presence of large displacements. Synthetic and practical cases are analysed with the present approach, and measurement uncertainties are compared with standard FE‐DVC. Results show that such an approach reduces the computational cost (when compared to FE‐DVC) whilst maintaining lower measurement uncertainties than standard subset‐based DVC.     

Finite element formulation for a digital image correlation method

A finite element formulation for a digital image correlation method is presented that will determine directly the complete, two-dimensional displacement field during the image correlation process on digital images. The entire interested image area is discretized into finite elements that are involved in the common image correlation process by use of our algorithms. This image correlation method with finite element formulation has an advantage over subset-based image correlation methods because it satisfies the requirements of displacement continuity and derivative continuity among elements on images. Numerical studies and a real experiment are used to verify the proposed formulation. Results have shown that the image correlation with the finite element formulation is computationally efficient, accurate, and robust.     

A novel scaled boundary finite element formulation with stabilization and its application to image‐based elastoplastic analysis

Digital images are increasingly being used as input data for computational analyses. This study presents an efficient numerical technique to perform image‐based elastoplastic analysis of materials and structures. The quadtree decomposition algorithm is employed for image‐based mesh generation, which is fully automatic and highly efficient. The quadtree cells are modeled by scaled boundary polytope elements, which eliminate the issue of hanging nodes faced by standard finite elements. A novel, simple, and efficient scaled boundary elastoplastic formulation with stablisation is developed. In this formulation, the return‐mapping calculation is only required to be performed at a single point in a polytope element, which facilitates the computational efficiency of the elastoplastic analysis and simplicity of implementation. Numerical examples are presented to demonstrate the efficiency and accuracy of the proposed technique for performing the elastoplastic analysis of high‐resolution images.     

A domain coupling method for finite element digital image correlation with mechanical regularization: Application to multiscale measurements and parallel computing

A general method is proposed to couple two subregions analyzed with finite element digital image correlation even when using a mechanical regularization (regularized digital image correlation). A Lagrange multiplier is introduced to stitch both displacements fields in order to recover continuity over the full region of interest. Another interface unknown is introduced to ensure, additionally, the equilibrium of the mechanical models used for regularization. As a first application, the method is used to perform a single measurement from images at two different resolutions. Secondly, the method is also extended to parallel computing in regularized digital image correlation. The problem is formulated at the interface and solved with a Krylov‐type algorithm. A dedicated preconditioner is proposed to significantly accelerate convergence. The resulting method is a good candidate for the analysis of large data sets. Copyright © 2016 John Wiley & Sons, Ltd.     

A domain decomposition technique applied to the solution of the coupled electro‐mechanical problem

A domain decomposition approach for the solution of the coupled electro‐mechanical problem in dynamics is proposed. The finite element analysis of a coupled electro‐mechanical system is frequently found, for example, in the modelling and design of microsystems and may lead to a burdensome nonlinear problem solution, particularly in the dynamic case. Two versions of the algorithm are proposed: the first one, called single‐level decomposition, exploits the natural partition of the analysis domain given by the two physics to be solved; the second one, called two‐level decomposition, adds a further subdivision of each physics into subdomains. The multilevel domain decomposition strategy here proposed is shown to accurately predict the response of microsystems subjected to electro‐mechanical coupling and to allow for a significant reduction in the computational burden. Copyright © 2012 John Wiley & Sons, Ltd.     

Extended digital image correlation with crack shape optimization

The methodology of eXtended finite element method is applied to the measurement of displacements through digital image correlation. An algorithm, initially based on a finite element decomposition of displacement fields, is extended to benefit from discontinuity and singular enrichments over a suited subset of elements. This allows one to measure irregular displacements encountered, say, in cracked solids, as demonstrated both in artificial examples and experimental case studies. Moreover, an optimization strategy for the support of the discontinuity enables one to adjust the crack path configuration to reduce the residual mismatch, and hence to be tailored automatically to a wavy or irregular crack path. Copyright © 2007 John Wiley & Sons, Ltd.     

Automatic image‐based stress analysis by the scaled boundary finite element method

Digital imaging technologies such as X‐ray scans and ultrasound provide a convenient and non‐invasive way to capture high‐resolution images. The colour intensity of digital images provides information on the geometrical features and material distribution which can be utilised for stress analysis. The proposed approach employs an automatic and robust algorithm to generate quadtree (2D) or octree (3D) meshes from digital images. The use of polygonal elements (2D) or polyhedral elements (3D) constructed by the scaled boundary finite element method avoids the issue of hanging nodes (mesh incompatibility) commonly encountered by finite elements on quadtree or octree meshes. The computational effort is reduced by considering the small number of cell patterns occurring in a quadtree or an octree mesh. Examples with analytical solutions in 2D and 3D are provided to show the validity of the approach. Other examples including the analysis of 2D and 3D microstructures of concrete specimens as well as of a domain containing multiple spherical holes are presented to demonstrate the versatility and the simplicity of the proposed technique. Copyright © 2016 John Wiley & Sons, Ltd.     

An X‐FEM and level set computational approach for image‐based modelling: Application to homogenization

The advances in material characterization by means of imaging techniques require powerful computational methods for numerical analysis. The present contribution focuses on highlighting the advantages of coupling the extended finite elements method and the level sets method, applied to solve microstructures with complex geometries. The process of obtaining the level set data starting from a digital image of a material structure and its input into an extended finite element framework is presented. The coupled method is validated using reference examples and applied to obtain homogenized properties for heterogeneous structures. Although the computational applications presented here are mainly two‐dimensional, the method is equally applicable for three‐dimensional problems. Copyright © 2010 John Wiley & Sons, Ltd.     

A scalable Lagrange multiplier based domain decomposition method for time-dependent problems

We present a new efficient and scalable domain decomposition method for solving implicitly linear and non-linear time-dependent problems in computational mechanics. The method is derived by adding a coarse problem to the recently proposed transient FETI substructuring algorithm in order to propagate the error globally and accelerate convergence. It is proved that in the limit for large time steps, the new method converges toward the FETI algorithm for time-independent problems. Computational results confirm that the optimal convergence properties of the time-independent FETI method are preserved in the time-dependent case. We employ an iterative scheme for solving efficiently the coarse problem on massively parallel processors, and demonstrate the effective scalability of the new transient FETI method with the large-scale finite element dynamic analysis on the Paragon XP/S and IBM SP2 systems of several diffraction grating finite element structural models. We also show that this new domain decomposition method outperforms the popular direct skyline solver. The coarse problem presented herein is applicable and beneficial to a large class of Lagrange multiplier based substructuring algorithms for time-dependent problems, including the fictitious domain decomposition method.     

Cross‐Correlation and Differential Technique Combination to Determine Displacement Fields

Abstract: This study presents a method to measure the displacement fields on the surface of planar objects with sub‐pixel resolution, by combining image correlation with a differential technique. First, a coarse approximation of the pixel level displacement is obtained by cross‐correlation (CC). Two consecutive images, taken before and after the application of a given deformation, are recursively split in sub‐images, and the CC coefficient is used as the similarity measure. Secondly, a fine approximation is performed to assess the sub‐pixel displacements by means of an optical flow method based on a differential technique. To validate the effectiveness and robustness of the proposed method, several numerical tests were carried out on computer‐generated images. Moreover, real images from a static test were also processed for estimating the displacement resolution. The results were compared with those obtained by a commercial digital image correlation code. Both methods showed similar and reliable results according to the proposed tests.     

Quantitative chemical imaging of element diffusion into heterogeneous media using laser ablation inductively coupled plasma mass spectrometry, synchrotron micro-X-ray fluorescence, and extended X-ray absorption fine structure spectroscopy

Quantitative chemical imaging of trace elements in heterogeneous media is important for the fundamental understanding of a broad range of chemical and physical processes. The primary aim of this study was to develop an analytical methodology for quantitative high spatial resolution chemical imaging based on the complementary use of independent microanalytical techniques. The selected scientific case study is focused on high spatially resolved quantitative imaging of major elements, minor elements, and a trace element (Cs) in Opalinus clay, which has been proposed as the host rock for high-level radioactive waste repositories. Laser ablation inductively coupled plasma mass spectrometry (LA-ICPMS), providing quantitative chemical information, and synchrotron radiation based micro-X-ray fluorescence (SR-microXRF), providing high spatial resolution images, were applied to study Cs migration into Opalinus clay rock. The results indicate that combining the outputs achievable by the two independent techniques enhances the imaging capabilities significantly. The qualitative high resolution image of SR-microXRF is in good agreement with the quantitative image recorded with lower spatial resolution by LA-ICPMS. Combining both techniques, it was possible to determine that the Opalinus clay sample contains two distinct domains: (i) a clay mineral rich domain and (ii) a calcium carbonate dominated domain. The two domains are separated by sharp boundaries. The spatial Cs distribution is highly correlated to the distribution of the clay. Furthermore, extended X-ray absorption fine structure analysis indicates that the trace element Cs preferentially migrates into clay interlayers rather than into the calcite domain, which complements the results acquired by LA-ICPMS and SR-microXRF. By using complementary techniques, the quantification robustness was improved to quantitative micrometer spatial resolution. Such quantitative, microscale chemical images allow a more detailed understanding of the chemical reactive transport process into and within heterogeneous media to be gained.     

Hyperelastic Behaviour Identification by a Forward Problem Resolution: Application to a Tear Test of a Silicone-Rubber

Abstract:  The mechanical behaviour of synthetic rubbers shows very high deformability, compressibility, time-dependent effect and strain softening. The present study is devoted to the analysis of local mechanical behaviour of silica-filled silicone rubber. New testing and identification are proposed in this paper by using standardised tear test, kinematic field measurements and a numerical inverse problem resolution to investigate localisation strain phenomena. The experimental procedure described hereafter, is based on strain field measurements using digital image processing. In-plane kinematic measurements by the digital image correlation are suitable to analyse non-homogeneous mechanical tests performed especially on thin sheets: indeed, rubber-like materials are characterised by a very high deformability and a non-linear behaviour leading to important gradients of deformation. The identification procedure is conducted in two steps. First, parameters of the viscosity and stress softening (Mullins effect) are evaluated analytically by using axial and biaxial tensile tests. Then, hyperelastic parameters are identified by an inverse resolution based on standardised tear tests. The mechanical model is implemented into the finite element code Zebulon (Transvalor/ENSMP). The numerical model is built up by using informations on geometry and boundary conditions extracted from image sequence that were acquired during the test. Usage of different functions evaluating the distance between computed and experimental quantities (cost functions) in a minimisation process is discussed.     

Online variational learning of finite inverted Beta-Liouville mixture model for biomedical analysis

Image segmentation is widely applied for biomedical image analysis. However, segmentation of medical images is challenging due to many image modalities, such as, CT, X-ray, MRI, microscopy among others. An additional challenge to this is the high variability, inconsistent regions with missing edges, absence of texture contrast, and high noise in the background of biomedical images. Thus, many segmentation approaches have been investigated to address these issues and to transform medical images into meaningful information. During the past decade, finite mixture models have been revealed to be one of the most flexible and popular approaches in data clustering. In this article, we propose a statistical framework for online variational learning of finite inverted Beta-Liouville mixture model for clustering medical images. The online variational learning framework is used to estimate the parameters and the number of mixture components simultaneously, thus decreasing the computational complexity of the model. To this end, we evaluated our proposed algorithm on five different biomedical image data sets including optic disc detection and localization in diabetic retinopathy, digital imaging in melanoma lesion detection and segmentation, brain tumor detection, colon cancer detection and computer aid detection (CAD) of Malaria. Furthermore, we compared the proposed algorithm with three other popular algorithms. In our results, we analyze that the proposed online variational learning of finite IBL mixture model algorithm performs accurately on multiple modalities of medical images. It detects the disease patterns with high confidence. Computational and statistical approaches like the one presented in this article hold a significant impact on medical image analysis and interpretation in both clinical applications and scientific research. We believe that the proposed algorithm has the capacity to address multi modal biomedical image data sets and can be further applied by researchers to analyze correct disease patterns.     

Experimental characterization of meso‐scale deformation mechanisms and the RVE size in plastically deformed carbon steel

The local deformation response of low carbon steel subjected to uniaxial tensile loading is investigated, and the local strain field at sub‐grain scale is obtained using high‐spatial‐resolution digital image correlation. The implemented digital image correlation method enables the observation and study of inhomogeneous deformation response at microstructural levels. Detailed local deformation mechanisms including mesoscopic slip bands are captured. Furthermore, the local information is used for the determination of representative volume element size in polycrystalline low carbon steel. To obtain the representative volume element size, we proposed and successfully implemented a strain variation method. Further, the influence of global strain on the local deformation mechanisms and representative volume element size is discussed. The challenges associated with the local strain measurement using digital image correlation are also discussed.     

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.     

Recycling of solution spaces in multipreconditioned FETI methods applied to structural dynamics

This article presents a new method to recycle the solution space of an adaptive multipreconditioned finite element tearing and interconnecting algorithm in the case where the same operator is solved for multiple right‐hand sides like in linear structural dynamics. It accelerates the computation from the second time step on by applying a coarse space that is generated from Ritz approximations of local eigenproblems, using the solution space of the first time step. These eigenproblems are known to provide very efficient coarse spaces but must usually be solved a priori at high computational cost. Their Ritz approximations are much smaller and less expensive to solve. Recycling methods based on Ritz approximations of global eigenproblems have been published for classical finite element tearing and interconnecting algorithms, but their efficient application to multipreconditioned variants is not possible. This article also presents the application of a simpler recycling procedure, which reuses plain solution spaces, to adaptive multipreconditioned finite element tearing and interconnecting. Numerical results of the application of the presented methods to four test cases are shown. The new Ritz approximation method leads to coarse spaces, which turn out to be as efficient as those obtained from solving the unreduced eigenproblems. It is the most efficient recycling method currently available for multipreconditioned dual domain decomposition techniques.     

Parallel computational strategies for structural optimization

The objective of this paper is to investigate the efficiency of various computational algorithms implemented in the framework of structural optimization methods based on evolutionary algorithms. In particular, the efficiency of parallel computational strategies is examined with reference to evolution strategies (ES) and genetic algorithms (GA). Parallel strategies are implemented both at the level of the optimization algorithm, by exploiting the natural parallelization features of the evolutionary algorithms, as well as at the level of the repeated structural analysis problems that are required by ES and GA. In the latter case the finite element solutions are performed by the FETI domain decomposition method specially tailored to the particular type of problems at hand. The proposed methodology is generic and can be applied to all types of optimization problems as long as they involve large‐scale finite element simulations. The numerical tests of the present study are performed on sizing optimization of skeletal structures. The numerical tests demonstrate the computational advantages of the proposed parallel strategies, which become more pronounced in large‐scale optimization problems. Copyright © 2003 John Wiley & Sons, Ltd.     

A multiscale mass scaling approach for explicit time integration using proper orthogonal decomposition

One of the main computational issues with explicit dynamics simulations is the significant reduction of the critical time step as the spatial resolution of the finite element mesh increases. In this work, a selective mass scaling approach is presented that can significantly reduce the computational cost in explicit dynamic simulations, while maintaining accuracy. The proposed method is based on a multiscale decomposition approach that separates the dynamics of the system into low (coarse scales) and high frequencies (fine scales). Here, the critical time step is increased by selectively applying mass scaling on the fine scale component only. In problems where the response is dominated by the coarse (low frequency) scales, significant increases in the stable time step can be realized. In this work, we use the proper orthogonal decomposition (POD) method to build the coarse scale space. The main idea behind POD is to obtain an optimal low‐dimensional orthogonal basis for representing an ensemble of high‐dimensional data. In our proposed method, the POD space is generated with snapshots of the solution obtained from early times of the full‐scale simulation. The example problems addressed in this work show significant improvements in computational time, without heavily compromising the accuracy of the results. Copyright © 2013 John Wiley & Sons, Ltd.