This study numerically investigates the damage process in a granite using an inelastic multiminerallic block model in two‐dimensional Universal Distinct Element Code. In addition to the commonly ...considered calibration targets like uniaxial and triaxial strengths, tensile strength, and Young's modulus, attention was paid to reproduce additional attributes such as postpeak response, residual strengths, and confinement‐dependent dilatancy to minimize the nonuniqueness potential of the models. The fracture pattern transitioned from axial cracking to shear banding as the specimen confinement was increased from 0 to 60 MPa. Most notably, the model could exhibit the cohesion‐weakening‐frictional‐strengthening behavior that is typically associated with brittle rocks. The progressive damage mechanism in the unconfined bonded block model (BBM) was subsequently studied using the 2‐D digital image correlation (2‐D‐DIC) approach. To date, the application of the 2‐D‐DIC approach has been restricted only to real material testing; this study, therefore, is an attempt to extend its applicability to numerical models. It was found that 2‐D‐DIC is capable of imaging the simulated microcracking process very well and the results were similar to those observed from real testing on a different granitic rock. Lastly, the numerical‐based DIC results were analyzed to clarify that even if the point of axial stress‐axial strain nonlinearity does not coincide with the point of volumetric strain reversal in unconfined BBMs, the axial stress‐axial strain nonlinearity approach should always be used for determining the crack damage threshold in BBMs.
Key Points
This study explores the capability of bonded block models to replicate the prepeak and postpeak attributes of a granitic rock
The model exhibited a degradation of specimen‐scale cohesion and mobilization of friction angle with increase in damage
Two‐dimensional digital image correlation analysis was conducted on the model results to evaluate the changes in strain field
We develop a dimension-independent, Delaunay-based anisotropic mesh generation algorithm suitable for integration with adaptive numerical solvers. As such, the mesh produced by our algorithm conforms ...to an anisotropic metric prescribed by the solver as well as the domain geometry, given as a piecewise smooth complex. Motivated by the work of Lévy and Dassi 10-12,20, we use a discrete manifold embedding algorithm to transform the anisotropic problem to a uniform one. This work differs from previous approaches in several ways. First, the embedding algorithm is driven by a Riemannian metric field instead of the Gauss map, lending itself to general anisotropic mesh generation problems. Second we describe our method for computing restricted Voronoi diagrams in a dimension-independent manner which is used to compute constrained centroidal Voronoi tessellations. In particular, we compute restricted Voronoi simplices using exact arithmetic and use data structures based on convex polytope theory. Finally, since adaptive solvers require geometry-conforming meshes, we offer a Steiner vertex insertion algorithm for ensuring the extracted dual Delaunay triangulation is homeomorphic to the input geometries.
The two major contributions of this paper are: a method for isometrically embedding arbitrary mesh-metric pairs in higher dimensional Euclidean spaces and a dimension-independent vertex insertion algorithm for producing geometry-conforming Delaunay meshes. The former is demonstrated on a two-dimensional anisotropic problem whereas the latter is demonstrated on both 3d and 4d problems.
The trend in seismic acquisition is geared toward high geophone densities. Future node densities are expected to be on the order of 1M nodes, leading to a huge aggregate data rate in the geophone ...array and requiring the use of some form of signal compression. This work presents a family of signal compression algorithms based on vector quantization and its transposition to the infinite-dimensional case—functional quantization (FQ). Using FQ, we quantize the entire sample path of the seismic waveform in a target function space, instead of quantizing individual samples. The polynomial design and computational complexity afforded by FQ allow for online training of codebooks where the statistics of the seismic wavefield may be changing. An efficient algorithm for the construction of a functional quantizer is given. It is based on Monte Carlo simulation to circumvent the curse of high dimensionality and avoids explicit construction of Voronoi regions to tessellate the function space of interest. In the sequel, we augment our basic FQ architecture with three different VQ techniques in the literature. The augmentation yields hybridized FQ strategies. These hybrid quantization algorithms are: (1) FQ-classified VQ, (2) FQ-residual/multistage VQ and (3) FQ-recursive VQ. The joint quantizers are obtained by replacing regular VQ codebooks in these hybrid quantizers by their FQ equivalents. Simulation results show that the FQ combined with these different VQ techniques performs better in the rate–distortion sense than either FQ alone or the aforementioned VQ techniques in isolation.
Self-assembly of shapes from spheres to nonsmooth and possibly nonconvex shapes is pervasive throughout the sciences. These arrangements arise in biology for animal flocking and herding, in condensed ...matter physics with molecular and nano self-assembly, and in control theory for coordinated motion problems. While idealizing these often nonconvex objects as points or spheres aids in analysis, the effects of shape curvature and convexity are often dramatic, especially for shortrange interactions. In this paper, we develop a general-purpose model for arranging rigid shapes in Euclidean domains and on flat tori. The shapes are arranged optimally with respect to minimization of a geometric Voronoi-based cost function which generalizes the notion of a centroidal Voronoi tessellation from point sources to general rigid shapes. Building upon our previous work in L. J. Larsson, R. Choksi, and J.-C. Nave, SIAM J. Sci. Comput., 36 (2014), pp. A792-A827, we present an efficient and fast algorithm for the minimization of this nonlocal, albeit finite-dimensional variational problem. The algorithm applies in any space dimension and can be used to generate self-assemblies of any collection of nonconvex, piecewise smooth shapes. We also provide a result which supports the intuition that self-assembled shapes should be centered in and aligned with their Voronoi regions.
Finite element method (FEM) is commonly used for deformable image registration. However, there is no existing literature studying how the superimposed mesh structure would influence the image ...registration process. We study this problem in this paper, and propose a dynamic meshing strategy to generate mesh structure for image registration. To construct such a dynamic mesh during image registration, three steps are performed. Firstly, a density field that measures the importance of a pixel/voxel’s displacement to the registration process is computed. Secondly, an efficient contraction–optimization scheme is applied to compute a discrete Centroidal Voronoi Tessellation of the density field. Thirdly, the final mesh structure is constructed by its dual triangulation, with some post-processing to preserve the image boundary. In each iteration of the deformable image registration, the mesh structure is efficiently updated with GPU-based parallel implementation. We conduct experiments of the new dynamic mesh-guided registration framework on both synthetic and real medical images, and compare our results with the other state-of-the-art FEM-based image registration methods.
•We study how the superimposed mesh structure would influence the Finite Element Method (FEM)-based image registration process.•We propose a mesh generation algorithm based on how the mesh will influence the registration process, using the discrete Centroidal Voronoi Tessellation idea.•We present a parallel algorithm to compute and update the mesh structure efficiently during image registration.
In recent years, porous shape memory alloys have found several industrial applications. Thanks to biocompatibility, corrosion resistance, and superior mechanical properties, porous NiTi has been ...introduced as a promising candidate for being used as bone scaffolds. Since the mechanical response of a scaffold is of importance in order to prevent stress-shielding phenomena and trigger ossteointegration, predicting the mechanical response of these scaffolds before fabrication is inevitable. In this paper, a new mesoscale model based on Voronoi tessellation of three-dimensional space is presented for the simulation of porous shape memory alloys. To do so, after tessellating the space, some cells are selected randomly to be assigned as pores and a suitable constitutive model of dense SMA is attributed to the other cells. The model is validated against experimental findings reported in the literature demonstrating good agreement. In addition, the effects of number of cells, level of randomness, and the type of boundary conditions on the stress–strain response is assessed. The results show that in order to achieve desirable results, the number of cells and the value of randomness must be chosen greater than minimum corresponding values. As another result, the geometrically periodic model is more computationally efficient than the mechanically periodic one.
The ab-initio molecular dynamics simulations were conducted to etude the microscopic atomic and electronic structures of Co54Ta11B35 bulk metallic glasses in the surface composition. The structure ...properties such as partial pair correlation function, bond pairs and Voronoi tessellation analysis were analyzed. Then the atomic charge and the density of states are also characterized. The degree of local ordering for B is illustrated to decrease in the surface. A liquid-phase B-center cluster was found to increase during annealing. The Co-center distorted icosahedron cluster transformed to the perfect one which could be a signature of surface crystallization. But this crystallization did not change the electronic structure of Co54Ta11B35 alloy obviously.
•We simulated the surface structure of a new bulk metallic glass.•The two main elements Co and B showed different tendency during the anneal.•The distorted icosahedron cluster transformed to the perfect one which could be a signature of surface crystallization.•A liquid-phase B-centre cluster was found to increase during the anneal.•This variation of atomic structure do not change the electronic structure of this material.
are not the usual dyadic meshes but random Voronoi tessellations generated by Poisson point processes. This approach leads us to a continuous function whose random graph is shown to be fractal with ...explicit and equal box and Hausdorff dimensions. The proof of this main result is based on several new distributional properties of the Poisson-Voronoi tessellation on the one hand, and an estimate of the oscillations of the function coupled with an application of a Frostman-type lemma on the other hand. Finally, we introduce two related models and provide in particular a box-dimension calculation for a derived deterministic Takagi-Knopp series with hexagonal bases.>
A Centroidal Voronoi tessellation (CVT) is a Voronoi tessellation in which the generators are the centroids for each Voronoi region. CVTs have many applications to computer graphics, image ...processing, data compression, mesh generation, and optimal quantization. Lloyd’s method, the most widely method used to generate CVTs, converges very slowly for larger scale problems. Recently quasi-Newton methods using the Hessian of the associated energy as a preconditioner are developed to speed up the rate of convergence. In this work a graph Laplacian preconditioner and a two-grid method are used to speed up quasi-Newton schemes. The proposed graph Laplacian is always symmetric, positive definite and easy to assemble, while the Hessian, in general, may not be positive definite nor easy to assemble. The two-grid method, in which an optimization method using a relaxed stopping criteria is applied on a coarse grid, and then the coarse grid is refined to generate a better initial guess in the fine grid, will further speed up the convergence and lower the energy. Numerical tests show that our preconditioned two-grid optimization methods converges fast and has nearly linear complexity.
Ecology Letters (2011) 14: 179-186 ABSTRACT: Allee effects are important dynamical mechanisms in small-density populations in which per capita population growth rate increases with density. When ...positive density dependence is sufficiently severe (a ‘strong' Allee effect), a critical density arises below which populations do not persist. For spatially distributed populations subject to dispersal, theory predicts that the occupied area also exhibits a critical threshold for population persistence, but this result has not been confirmed in nature. We tested this prediction in patterns of population persistence across the invasion front of the European gypsy moth (Lymantria dispar) in the United States in data collected between 1996 and 2008. Our analysis consistently provided evidence for effects of both population area and density on persistence, as predicted by the general theory, and confirmed here using a mechanistic model developed for the gypsy moth system. We believe this study to be the first empirical documentation of critical patch size induced by an Allee effect.
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