Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

A number of image processing techniques IPTs have been implemented for detecting civil infrastructure defects to partially replace human-conducted onsite inspections. These IPTs are primarily used to manipulate images to extract defect features, such as cracks in concrete and steel surfaces. However, the extensively varying real-world situations e.g., lighting and shadow changes can lead to challenges to the wide adoption of IPTs. To overcome these challenges, this article proposes a vision-based method using a deep architecture of convolutional neural networks CNNs for detecting concrete cracks without calculating the defect features. As CNNs are capable of learning image features automatically, the proposed method works without the conjugation of IPTs for extracting features. The designed CNN is trained on 40 K images of 256 × 256 pixel resolutions and, consequently, records with about 98% accuracy. The trained CNN is combined with a sliding window technique to scan any image size larger than 256 × 256 pixel resolutions. The robustness and adaptability of the proposed approach are tested on 55 images of 5,888 × 3,584 pixel resolutions taken from a different structure which is not used for training and validation processes under various conditions e.g., strong light spot, shadows, and very thin cracks. Comparative studies are conducted to examine the performance of the proposed CNN using traditional Canny and Sobel edge detection methods. The results show that the proposed method shows quite better performances and can indeed find concrete cracks in realistic situations.

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Deep Learning-Based Crack Damage Detection Using Convolutional Neural Networks

Numerical Initial Value Problems in Ordinary Differential Equations

An overview of the extended/generalized finite element method (GEFM/XFEM) with emphasis on methodological issues is presented. This method enables the accurate approximation of solutions that involve jumps, kinks, singularities, and other locally non-smooth features within elements. This is achieved by enriching the polynomial approximation space of the classical finite element method. The GEFM/XFEM has shown its potential in a variety of applications that involve non-smooth solutions near interfaces: Among them are the simulation of cracks, shear bands, dislocations, solidification, and multi-field problems. Copyright © 2010 John Wiley & Sons, Ltd.

The extended/generalized finite element method: An overview of the method and its applications

The extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: (1) fracture, (2) dislocations, (3) grain boundaries and (4) phases interfaces. These methods facilitate the modeling of complicated geometries and the evolution of such geometries, particularly when combined with level set methods, as for example in the simulation growing cracks or moving phase interfaces. The state of the art for these problems is described along with the history of developments.

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A review of extended/generalized finite element methods for material modeling

From diffuse damage to sharp cohesive cracks: A coupled XFEM framework for failure analysis of quasi-brittle materials

An extended finite element method (XFEM) coupled with a Monte Carlo approach is proposed to quantify the uncertainty in the homogenized effective elastic properties of multiphase materials. The methodology allows for an arbitrary number, aspect ratio, location and orientation of elliptic inclusions within a matrix, without the need for fine meshes in the vicinity of tightly packed inclusions and especially without the need to remesh for every different generated realization of the microstructure. Moreover, the number of degrees of freedom in the enriched elements is dynamically reallocated for each Monte Carlo sample run based on the given volume fraction. The main advantage of the proposed XFEM-based methodology is a major reduction in the computational effort in extensive Monte Carlo simulations compared with the standard FEM approach. Monte Carlo and XFEM appear to work extremely efficiently together. The Monte Carlo approach allows for the modeling of the size, aspect ratios, orientations, and spatial distribution of the elliptical inclusions as random variables with any prescribed probability distributions. Numerical results are presented and the uncertainty of the homogenized elastic properties is discussed. Copyright © 2011 John Wiley & Sons, Ltd.

Uncertainty quantification in homogenization of heterogeneous microstructures modeled by XFEM

The modeling of progressive delamination by means of a discrete damage zone model within the extended finite element method is investigated. This framework allows for both bulk and interface damages to be conveniently traced, regardless of the underlying mesh alignment. For discrete interfaces, a new mixed-mode force---separation relation, which accounts for the coupled interaction between opening and sliding modes, is proposed. The model is based on the concept of Continuum Damage Mechanics and is shown to be thermodynamically consistent. An integral-type nonlocal damage is adopted in the bulk to regularize the softening material response. The resulting nonlinear equations are solved using a Newton scheme with a dissipation-based arc-length constraint, for which an analytical Jacobian is derived. Several benchmark delamination studies, as well as failure analyses of a fiber/epoxy unit cell, are presented and discussed in detail. The proposed model is validated against available analytical/experimental data and is found to be robust and mesh insensitive.

Progressive delamination analysis of composite materials using XFEM and a discrete damage zone model

This paper investigates the extended finite element method (XFEM)-GA detection algorithm proposed by Rabinovich et al. (Int. J. Numer. Meth. Engng 2007; 71(9):1051–1080; Int. J. Numer. Meth. Engng 2009; 77(3):337–359) on elastostatic problems with different types of flaws. This algorithm is designed for non-destructive assessment of structural components. Trial flaws are modeled using the XFEM as the forward problem and genetic algorithms (GAs) are employed as the optimization method to converge to the true flaw location and size. The main advantage of the approach is that XFEM alleviates the need for re-meshing the domain at every new iteration of the inverse solution process and GAs have proven to be robust and efficient optimization techniques in particular for this type of problems.



In this paper the XFEM-GA methodology is applied to elastostatic problems where flaws are considered as straight cracks, circular holes and non-regular-shaped holes. Measurements are obtained from strain sensors that are attached to the surface of the structure at specific locations and provide the target solution to the GA. The results show convergence robustness and accuracy provided that a sufficient number of sensors are employed and sufficiently large flaws are considered. Copyright © 2009 John Wiley & Sons, Ltd.

Haim Waisman

Papers

From diffuse damage to sharp cohesive cracks: A coupled XFEM framework for failure analysis of quasi-brittle materials

Uncertainty quantification in homogenization of heterogeneous microstructures modeled by XFEM

Progressive delamination analysis of composite materials using XFEM and a discrete damage zone model

Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms

A unified model for metal failure capturing shear banding and fracture