Cutting and Fracturing Models without Remeshing

Abstract. A finite element simulation framework for cutting and fracturing model without remeshing is presented. The main idea of proposed method is adding a discontinuous function for the standard approximation to account for the crack. A feasible technique is adopted for dealing with multiple cracks and intersecting cracks. Several involved problems including extended freedoms of finite element nodes as well as mass matrix calculation are discussed. The presented approach is easy to simulate object deformation while changing topology. Moreover, previous methods developed in standard finite element framework, such as the stiffness warping method, can be extended and utilized

PyFrac: A planar 3D hydraulic fracture simulator

Fluid driven fractures propagate in the upper earth crust either naturally or in response to engineered fluid injections. The quantitative prediction of their evolution is critical in order to better understand their dynamics as well as to optimize their creation. We present a Python implementation of an open-source hydraulic fracture propagation simulator based on the implicit level set algorithm originally developed by Peirce & Detournay (2008) -- "An implicit level set method for modeling hydraulically driven fractures". Comp. Meth. Appl. Mech. Engng, (33-40):2858--2885. This algorithm couples a finite discretization of the fracture with the use of the near tip asymptotic solutions of a steadily propagating semi-infinite hydraulic fracture. This allows to resolve the multi-scale processes governing hydraulic fracture growth accurately, even with relatively coarse meshes. We present an overview of the mathematical formulation, the numerical scheme and the details of our implementation. A series of problems including a radial hydraulic fracture verification benchmark, the propagation of a height contained hydraulic fracture, the lateral spreading of a magmatic dyke and the handling of fracture closure are presented to demonstrate the capabilities, accuracy and robustness of the implemented algorithm

Simulating Fractures with Bonded Discrete Element Method

Along with motion and deformation, fracture is a fundamental behaviour for solid materials, playing a critical role in physically-based animation. Many simulation methods including both continuum and discrete approaches have been used by the graphics community to animate fractures for various materials. However, compared with motion and deformation, fracture remains a challenging task for simulation, because the material's geometry, topology and mechanical states all undergo continuous (and sometimes chaotic) changes as fragmentation develops. Recognizing the discontinuous nature of fragmentation, we propose a discrete approach, namely the Bonded Discrete Element Method (BDEM), for fracture simulation. The research of BDEM in engineering has been growing rapidly in recent years, while its potential in graphics has not been explored. We also introduce several novel changes to BDEM to make it more suitable for animation design. Compared with other fracture simulation methods, the BDEM has some attractive benefits, e.g. efficient handling of multiple fractures, simple formulation and implementation, and good scaling consistency. But it also has some critical weaknesses, e.g. high computational cost, which demand further research. A number of examples are presented to demonstrate the pros and cons, which are then highlighted in the conclusion and discussion

Tides modulate crevasse opening prior to a major calving event at Bowdoin Glacier, Northwest Greenland

This research is part of the Sun2ice project (ETH Grant ETH-12 16-2), supported by the Dr. Alfred and Flora Spälti and the ETH Zurich Foundation. Field work was funded by the Swiss National Science Foundation, grant 200021-153179/1, and the Japanese Ministry of Education, Culture, Sports, Science and Technology through the Arctic Challenge for Sustainability (ArCS) project. Implementation of the remeshing routine has been performed under the Project HPC-EUROPA3 (INFRAIA-2016-1-730897), with the support of the EC Research Innovation Action under the H2020 Programme.Retreat of calving glaciers worldwide has contributed substantially to sea-level rise in recent decades. Mass loss by calving contributes significantly to the uncertainty of sea-level rise projections. At Bowdoin Glacier, Northwest Greenland, most calving occurs by a few large events resulting from kilometre-scale fractures forming parallel to the calving front. High-resolution terrestrial radar interferometry data of such an event reveal that crevasse opening is fastest at low tide and accelerates during the final 36 h before calving. Using the ice flow model Elmer/Ice, we identify the crevasse water level as a key driver of modelled opening rates. Sea water-level variations in the range of local tidal amplitude (1 m) can reproduce observed opening rate fluctuations, provided crevasse water level is at least 4 m above the low-tide sea level. The accelerated opening rates within the final 36 h before calving can be modelled by additional meltwater input into the crevasse, enhanced ice cliff undercutting by submarine melt, ice damage increase due to tidal cyclic fatigue, crevasse deepening or a combination of these processes. Our results highlight the influence of surface meltwater and tides on crevasse opening leading to major calving events at grounded tidewater glaciers such as Bowdoin.Publisher PDFPeer reviewe

Impulse-based discrete element modelling of rock impact and fragmentation, with applications to block cave mining

Impulse-based methods efficiently and accurately model high-frequency collisions of complex shapes based on the enforcement of non-penetrating constraints. It does not rely on penalty parameters nor requires the computation of penetration between bodies. This work presents a novel necessary condition for energy conservation in impulse-based methods. In previous versions of the impulse methods, such as sequential and simultaneous impulse methods, the relative velocity at the contact points after collision is directly derived from the relative velocity before collision, in a purely simultaneous or sequential manner. This work presents a novel energy tracking method (ETM), in which the relative velocities are iteratively but gradually adjusted, simultaneously modelling their interaction at each iteration. ETM ensures the energy conservation while capturing the propagation of forces during collision. The ETM is applied to model the dynamics of fragment collision in the context of fragmentation. Two approaches of fragmentation are proposed: a finite-discrete element approach, and a low cost, fragmentation pattern-based approach. The first approach models the growth of fractures using the finite element method (FEM) and advanced re-meshing technology. This finite-discrete element approach suffers from the drawback of massive computational cost. The low-cost, fragmentation pattern-based approach separate colliding bodies directly. The fragmentation pattern is generated using Weibull distribution equations, the patterns and size distributions computed using full finite/discrete element simulations and experimental results. This work investigates the influence of fragmentation on the frequency of hang-up events and on the gravity flow of rock fragments within a block caving system. Numerical results indicate that models that do not consider fragmentation tend to overestimate the frequency of hang-up accidents.Open Acces

An extended finite element model for modelling localised fracture of reinforced concrete beams in fire

Open Access funded by Engineering and Physical Sciences Research Council under a Creative Commons license.A robust finite element procedure for modelling the localised fracture of reinforced concrete beams at elevated temperatures is developed. In this model a reinforced concrete beam is represented as an assembly of 4-node quadrilateral plain concrete, 3-node main reinforcing steel bar, and 2-node bond-link elements. The concrete element is subdivided into layers for considering the temperature distribution over the cross-section of a beam. An extended finite element method (XFEM) has been incorporated into the concrete elements in order to capture the localised cracks within the concrete. The model has been validated against previous fire test results on the concrete beams.The Engineering and Physical Sciences Research Council of Great Britain under Grant No. EP/I031553/1

リンカイ エンセイ ハカイ キジュンチ ノ ケッテイ ト センダン ウチヌキ カコウ ニオケル ハカイ カイシテン ノ ヨソク

博士(工学)佐賀大

2D finite elements for the computational analysis of crack propagation in brittle materials and the handling of double discontinuities

Crack growth simulations by way of the traditional Finite Element Method claim progressive remeshing to fit the geometry of the fracture, severely increasing the computational effort. Methods such as the eXtended Finite Element Method (XFEM) allow to overcome this limitation by means of nodal shape functions multiplied by Heaviside step function to enrich finite element nodes. Through the medium of a discontinuous field, the entire geometry of the discontinuity can be modelled regardless of the mesh, avoiding remeshing. In this paper two shell-type XFEM elements (a three-node triangular element and a four-node quadrangular element) to evaluate crack propagation in brittle materials are presented. These elements have been implemented into the widespread opensource framework OpenSees to evaluate crack propagation into a plane shell subjected to monotonically increasing loads. Moreover, in the perspective of fracture propagation simulations, the problem of managing multiple cracks without remeshing or operating subdivisions on the integration domain has been investigated and a four-node quadrangular finite element for the computational analysis of double crossed discontinuities by the means of equivalent polynomials is presented in this paper. Equivalent polynomials allow to overcome inaccuracies on the results when performing standard numerical integration (e.g. Gauss-Legendre quadrature rule) over the entire domain of XFEM elements, without the need of defining integration subdomains. The presented work and the computational strategy behind it may be extremely useful not only in the field of fracture mechanics, but also to solve complex geometry problems or material discontinuities

Meshless animation of fracturing solids

We present a new meshless animation framework for elastic and plastic materials that fracture. Central to our method is a highly dynamic surface and volume sampling method that supports arbitrary crack initiation, propagation, and termination, while avoiding many of the stability problems of traditional mesh-based techniques. We explicitly model advancing crack fronts and associated fracture surfaces embedded in the simulation volume. When cutting through the material, crack fronts directly affect the coupling between simulation nodes, requiring a dynamic adaptation of the nodal shape functions. We show how local visibility tests and dynamic caching lead to an efficient implementation of these effects based on point collocation. Complex fracture patterns of interacting and branching cracks are handled using a small set of topological operations for splitting, merging, and terminating crack fronts. This allows continuous propagation of cracks with highly detailed fracture surfaces, independent of the spatial resolution of the simulation nodes, and provides effective mechanisms for controlling fracture paths. We demonstrate our method for a wide range of materials, from stiff elastic to highly plastic objects that exhibit brittle and/or ductile fracture. Copyright © 2005 by the Association for Computing Machinery, Inc