A state-of-the-art review of the X-FEM for computational fracture mechanics
TL;DR: In this paper, the authors present a review of the extended finite element method X-FEM for computational fracture mechanics, and discuss the basic ideas and formulation for the newly developed XFEM method.
About: This article is published in Applied Mathematical Modelling.The article was published on 2009-12-01 and is currently open access. It has received 131 citations till now. The article focuses on the topics: Computational mechanics & Extended finite element method.
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Proceedings Article•
03 May 2021
TL;DR: MeshGraphNets is introduced, a framework for learning mesh-based simulations using graph neural networks that can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation, and can accurately predict the dynamics of a wide range of physical systems.
Abstract: Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike favorable trade-offs between accuracy and efficiency. However, high-dimensional scientific simulations are very expensive to run, and solvers and parameters must often be tuned individually to each system studied. Here we introduce MeshGraphNets, a framework for learning mesh-based simulations using graph neural networks. Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation. Our results show it can accurately predict the dynamics of a wide range of physical systems, including aerodynamics, structural mechanics, and cloth. The model's adaptivity supports learning resolution-independent dynamics and can scale to more complex state spaces at test time. Our method is also highly efficient, running 1-2 orders of magnitude faster than the simulation on which it is trained. Our approach broadens the range of problems on which neural network simulators can operate and promises to improve the efficiency of complex, scientific modeling tasks.
295 citations
TL;DR: Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results.
Abstract: This paper presents a new numerical integration technique oil arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint quadrature rule defined oil this unit disk is used. This method eliminates the need for a two-level isoparametric mapping Usually required. Moreover, the positivity of the Jacobian is guaranteed. Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results.
186 citations
TL;DR: In this paper, a review of the major areas where rock mechanics research can facilitate geothermal systems development are reviewed with particular emphasis on EGS design and management, including experimental and theoretical investigations as well as numerical and analytical solutions.
Abstract: Rock mechanics and geomechanical studies can provide crucial information for economic geothermal reservoir development. Although significant progress has been made in reservoir geomechanics, technical challenges specific to the geothermal area (high temps, data collection, experimentation issues) have prevented widespread use of geomechanics in geothermal reservoir development. However, as the geothermal industry moves to develop more challenging resources using the concept of enhanced geothermal systems (EGS), and to maximize productivity from conventional resources, the need for improved understanding of geomechanical issues and developing specific technologies for geothermal reservoirs has become critical. Rock mechanics research and improved technologies can impact areas related to in-situ stress characterization, initiation and propagation of artificial and natural fractures, and the effects of coupled hydro-thermo-chemo-mechanical processes on fracture permeability and induced seismicity. Rock mechanics/geomechanics research, including experimental and theoretical investigations as well as numerical and analytical solutions, has an important role in optimizing reservoir design and heat extraction strategies for sustainable geothermal energy development. A number of major areas where rock mechanics research can facilitate geothermal systems development are reviewed in this paper with particular emphasis on EGS design and management.
171 citations
TL;DR: In this paper, the linear free flexural vibration of cracked material plates is studied using the extended finite element method using a 4-noded quadrilateral plate bending element based on field and edge consistency requirement with 20 degrees of freedom per element.
141 citations
TL;DR: The basics and principles of the MLPG method, the meshless local approximation techniques for trial and test functions, applications to elasticity and elastodynamics, plasticity, fracture and crack analysis, heat transfer and fluid flow, coupled problems involving multiphase materials, and techniques for increasing the accuracy and computational effectiveness are presented.
Abstract: A review is presented for analysis of problems in engineering & the sciences, with the use of the meshless local Petrov-Galerkin (MLPG) method. The success of the meshless methods lie in the local nature, as well as higher order continuity, of the trial function approximations, high adaptivity and a low cost to prepare input data for numerical analyses, since the creation of a finite element mesh is not required. There is a broad variety of meshless methods available today; however the focus is placed on the MLPG method, in this paper. The MLPG method is a fundamental base for the derivation of many meshless formulations, since the trial and test functions can be chosen from different functional spaces. In the last decade, a broad community of researchers and scientists contributed to the development and implementation of the MLPG method in a wide range of scientific disciplines. This paper first presents the basics and principles of the MLPG method, the meshless local approximation techniques for trial and test functions, applications to elasticity and elastodynamics, plasticity, fracture and crack analysis, heat transfer and fluid flow, coupled problems involving multiphase materials, and techniques for increasing the accuracy and computational effectiveness. Various applications to 2-D planar problems, axisymmetric problems, plates and shells or 3-D problems are included. An increased number of published papers in literature in the recent years can be considered as a measure of the growing research activity in the general scope of the MLPG method, and thus, several trends and ideas for future research interest are also outlined.
103 citations
Cites methods from "A state-of-the-art review of the X-..."
...Interesting application of the MLPG method in cloth simulation has been presented by Yuan et al. (2008). The micro-mechanical material model of woven fabric composite material has been proposed in [Wen and Alliabadi (2010)]....
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References
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TL;DR: The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.
13,020 citations
TL;DR: In this article, a displacement-based approximation is enriched near a crack by incorporating both discontinuous elds and the near tip asymptotic elds through a partition of unity method.
Abstract: SUMMARY An improvement of a new technique for modelling cracks in the nite element framework is presented. A standard displacement-based approximation is enriched near a crack by incorporating both discontinuous elds and the near tip asymptotic elds through a partition of unity method. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robustness of the proposed technique. Copyright ? 1999 John Wiley & Sons, Ltd.
5,815 citations
TL;DR: In this article, a minimal remeshing finite element method for crack growth is presented, where Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack.
Abstract: A minimal remeshing finite element method for crack growth is presented. Discontinuous enrichment functions are added to the finite element approximation to account for the presence of the crack. This method allows the crack to be arbitrarily aligned within the mesh. For severely curved cracks, remeshing may be needed but only away from the crack tip where remeshing is much easier. Results are presented for a wide range of two-dimensional crack problems showing excellent accuracy. Copyright © 1999 John Wiley & Sons, Ltd.
4,185 citations
TL;DR: In this article, the basic ideas and the mathematical foundation of the partition of unity finite element method (PUFEM) are presented and a detailed and illustrative analysis is given for a one-dimensional model problem.
3,276 citations
TL;DR: In this paper, the authors investigated the C rack-tip strain singularities with the aid of an energy line integral exhibiting path independence for all contours surrounding a crack tip in a two-dimensional deformation field of an elastic material (or elastic/plastic material treated by a deformation theory).
Abstract: C rack-tip strain singularities are investigated with the aid of an energy line integral exhibiting path independence for all contours surrounding a crack tip in a two-dimensional deformation field of an elastic material (or elastic/plastic material treated by a deformation theory). It is argued that the product of stress and strain exhibits a singularity varying inversely with distance from the tip in all materials. Corresponding near crack tip stress and strain fields are obtained for the plane straining of an incompressible elastic/plastic material hardening according to a power law. A noteworthy feature of the solution is the rapid rise of triaxial stress concentration above the flow stress with increasing values of the hardening exponent. Results are presented graphically for a range of hardening exponents, and the interpretation of the solution is aided by a discussion of analogous results in the better understood anti-plane strain case.
2,890 citations