Particle Discretization Scheme Research Articles

Numerical analysis of glass edge chipping by impact loading

This study presents numerical analyses for edge chipping by impact loading. As a numerical analysis method, we extend Particle Discretization Scheme Finite Element Method (PDS-FEM) developed by the authors to be able to simulate fracture due to impact loading. We performed simulations targeting edge chipping of soda-lime glass by impact of rigid steel sphere and examined the crack morphology while varying the diameter of the impactor, the impact velocity, and the impact distance. The proposed method successfully simulates the 3D complex crack pattern on edge chipping such as Hertzian cone crack and conchoidal chip scar. The method also reproduces the change of crack morphologies depending on the impact force and the impact distance. Also, a series of numerical analyses is presented to reveal the effect of the impactor geometry on the chip dimensions. The height of chip is independent of the impactor geometry while the width of chip depends on it. According to the agreement with experimental results, it is confirmed that the proposed method is capable of realizing edge chipping due to impact loading.

Mathematical model and numerical analysis method for dynamic fracture in a residual stress field.

Residual stress field is a self-equilibrium state of stress in the bulk solid material with the inhomogeneous field of the inelastic deformations. The high level of tensile residual stress often leads to dynamic fracture resulting in the instantaneous and catastrophic destruction of the materials because the cracks are fed with the strain energy initially stored in the bulk materials due to the residual stress. The dissipation of the strain energy with crack growth results in the release and the redistribution of the residual stress. In this paper, we propose an effective mathematical model and a numerical analysis method for dynamic fracture in residual stress field. We formulate the dynamic behavior of solid continuum with residual stress field in the context of particle discretization scheme finite element method. This formulation enables the appropriate evaluation of (i) release and redistribution of residual stress due to dynamic propagation of the cracks and (ii) the effect of the elastic wave on crack propagation, which are the most substantial problems on dynamic fracture in residual stress field. We perform the experiments and the simulations of dynamic fracture process in chemically tempered glass sheets with residual stress field to validate the proposed numerical analysis method. The simulation results show remarkable agreement with the experiments of the catastrophic failure of the glass sheets with residual stress field in all aspects of crack behavior. These results indicate that the proposed model and method can rigorously evaluate the release and the autonomous redistribution of the residual stress in the dynamic fracture process.

Application of PDS–FEM to simulate dynamic crack propagation and supershear rupture

Dynamic crack propagation problems, including intersonic rupture, are simulated with two Hamiltonian based formulations of particle discretization scheme (PDS) FEM: the traditional displacement momentum form and the strain momentum form, for which consistent momentum conserving and symplectic integration schemes are derived. Numerical results are verified, and validated by comparing with photoelastic observations of a dynamic mode-I crack captured with a 1 Mfps camera. Both methods are successful in accurately reproducing the crack patterns observed in classical 2D and 3D dynamic rupture scenarios, as well as the near crack tip stress field during the propagation. The two methods are found to be numerically indifferentiable, although the displacement based method offers a significantly better computational performance. As a demonstrative application, we simulate the super-shear rupture in earthquakes, modeling the contact at the fault surface by a linear slip weakening friction law. The Burridge–Andrews mechanism naturally appears in the simulations, making the crack front jump from the sub-Rayleigh regime to the intersonic regime and propagate while producing shear Mach cones.

Modeling and Simulating Methods for the Desiccation Cracking

The desiccation cracks can be observed on dry-out soil fields or other various materials under desiccation. These cracks have a net-like structure and tessellate the surface of the materials into polygonal cells. The averaged cell size changes systematically depending on the size of the specimen. In spite of the varieties of the materials, these fundamental features of the cell topology are conserved. This implies the existence of the governing mechanism behind the desiccation crack phenomenon regardless of the materials. In this paper, the desiccation crack phenomenon is modeled by the coupling of desiccation, deformation, and fracture. We perform simulations for the reproduction of the desiccation cracking based on this coupling model. In the simulations, the finite element analysis for the desiccation problem and the analysis of particle discretization scheme finite element method for the deformation and the fracture problems are weakly coupled. The results of the simulations show the satisfactory agreements with the experimental observations in terms of the geometry of the crack pattern, the increase tendency of the averaged cell size depending on the size of the specimen, and the hierarchical sequence of the cell formation. These agreements indicate that the proposed model and method capture the fundamental features and the mechanism of the desiccation cracking.

Numerical Modeling of Brittle Cracks Using Higher Order Particle Discretization Scheme–FEM

Higher order extension of Particle Discretization Scheme (HO-PDS), its implementation in FEM framework (HO-PDS-FEM) and applications in efficiently simulating cracks are presented in this paper. PDS is an approximation scheme which uses a conjugate domain tessellation pair like Voronoi and Delaunay in approximating a function and its derivatives. In approximating a function (or derivatives), HO-PDS first produces local polynomial approximations for the target function (or derivatives) within each element of respective tessellation. The approximations over the whole domain are then obtained by taking the union of those respective local approximations. These approximations are inherently discontinuous along the boundaries of the respective tessellation elements since the support of the local approximations is confined to the domain of respective tessellation elements and no continuity conditions are enforced. HO-PDS-FEM utilizes these inherent discontinuities in function approximation to efficiently model discontinuities such as cracks. Higher order PDS is implemented in FEM framework to solve boundary value problem of elastic solids, including mode-I crack problems. With several benchmark problems, it is shown that HO-PDS-FEM has higher expected accuracy and convergence rate. J-integral around a mode-I crack tip is calculated to demonstrate the improvement in the accuracy of the crack tip stress field. Further, it is shown that HO-PDS-FEM significantly improves the traction along the crack surfaces, compared to the zeroth-order PDS-FEM [Hori, M., Oguni, K. and Sakaguchi, H. [2005] “Proposal of FEM implemented with particle discretization scheme for analysis of failure phenomena,” J. Mech. Phys. Solids 53, 681–703].

Coupling analysis of pattern formation in desiccation cracks

Desiccation cracks are widely observed as a result of the drying process of the mixture of powder and water. These cracks have a net-like structure and tessellate the dry-out surface area into polygonal cells with typical size. Regardless of the choice of the materials and the minor details in the drying process, while some varieties can be observed, the basic topology of the cells (i.e., net-like structure and the polygonal cells) is persistently conserved. This stable and common feature in the desiccation crack patterns strongly suggests the existence of the common governing mechanism behind. In this paper, the pattern formation of desiccation cracks is regarded as the result of the coupling among (i) the change in water volume fraction due to desiccation, (ii) the equilibrium of deformation field corresponding to the inhomogeneous volume shrinkage, and (iii) the crack formation. Based on this assumption, a coupling model of desiccation, deformation, and fracture is proposed for the numerical analysis of the desiccation crack patterns. We perform the coupled analysis by using finite element method for the desiccation (described by the diffusion equation) and particle discretization scheme finite element method (PDS-FEM) for the seamless analysis of deformation and fracture. The results of the numerical analysis show satisfactory agreement with the experimental observation in terms of the basic topology of the cells and the hierarchical sequence of the crack propagation. These results indicate that the proposed approach captures the fundamental governing mechanism of the pattern formation of the desiccation crack phenomenon.

Stability analysis of soil liquefaction using a finite element method based on particle discretization scheme

Mathematically, liquefaction corresponds to the unstable solutions of the governing equations of soil dynamics. Stability analysis of these solutions facilitates the understanding of the triggering and development of liquefaction. This paper presents a numerical approach for stability analysis of the solutions of the governing equations. The governing equations are linearized for small perturbations and discretized using a finite element method (FEM) based on the particle discretization scheme (PDS). By solving the discretized governing equations with the developed PDS–FEM code, unstable solutions are captured for perturbations in the form of a three-dimensional spherical wave. The present approach considers the dilatancy effect and the detaching effect. The numerical results show that the dilatancy effect triggers and the detaching effect spatially expands the unstable solutions. The existence and expansion of the unstable solutions provide a new perspective on the triggering and development of liquefaction.

Large-Scale Numerical Simulation of an RC Tunnel Junction Member Using Particle Discretization Scheme FEM

This paper presents a large-scale numerical simulation of a reinforced concrete (RC) tunnel junction member using solid FEM. Particle discretization scheme (PDS), which uses two sets of non-overlapping characteristic functions to discretize displacement field and strain/stress field respectively, is employed to represent the multiple-cracking configurations of concrete. An efficient parallel FE program, called ADVENTURE, is used to implement PDS as well as a reformulated nonlinear concrete constitutive relation. A simplified tunnel junction member, in order to reveal its multiple-cracking behavior under the static load, is studied and the stochastic behavior of cracking is investigated; good agreements are achieved between the simulation results and experimental observations regarding the multiple cracking configurations.

Extension to Elasto-Plastic Version of a Fracture Mechanics Method

This paper develops a three dimensional elastic fracture analysis method, PDS-FEM (Particle Discretization Scheme Finite Element Method), to its elasto-plastic version. The Newton-Raphson iteration method is adopted for solving material nonlinearity, and the conjugate gradient method is applied to solve the linear equations of FEM. In order to apply the fracture analysis method to the engineering scale analysis, CPU based parallel computing technology is applied, and the computation speed is highly advanced. In this trial test, a simple stress based failure criterion is employed for the failure analysis of a cantilever steel beam. The numerical results without fracture match well with the commercial FEM software, ANSYS’s, which verifies the accuracy of the developed platform.

Three Dimensional Dynamic Analysis of Crack Growth in Unreinforced Baked Brick Shear Wall

This paper presents the 3D dynamic crack growth simulation of unreinforced baked brick shear wall by using particle discretization scheme finite element method (PDS-FEM), which is efficient and capable of computing bifurcation/branching in cracking. The technology of fast modelling of bricks and cements by applying VB script in AUTOCAD is illustrated briefly. The shear wall including mortar joints is modelled in detail. The model parameters are calibrated by using standard static tests. Since the computation cost is high in structural level fracture analysis, parallel computation technology is employed. Finally, with two-phase failure criterion of mortar under multi-dimension stress state, the performance of low and high loading speed is compared. The numerical results verify the availability of dynamic fracture analysis of masonry structure by using PDS-FEM.

Implementation of Finite Element Method with Higher Order Particle Discretization Scheme

Implementation of Finite Element Method with Higher Order Particle Discretization Scheme

Crack propagation analysis using PDS-FEM and comparison with fracture experiment

This paper presents the formulation of PDS-FEM (particle discretization scheme finite element method) in three dimensional setting and Monte-Carlo simulation of crack propagation by PDS-FEM. The probability density function of the crack paths in a plate with two parallel initial cracks located in an anti-symmetric manner is computed in order to evaluate the statistical and spatial distribution of the crack paths, and it is shown that the crack path in an ideally homogeneous plate is unstable. The simulation results are compared with experimental data. Besides, Monte-Carlo simulation of crack propagation in a heterogeneous elasto-plastic cylinder (as a simplified model of concrete) under uniaxial tension has been carried out and its statistical behavior is discussed.

Numerical analysis of growing crack problems using particle discretization scheme

AbstractThis paper presents the particle discretization scheme (PDS) to analyze brittle failure of solids. The scheme uses characteristic functions of Voronoi and Delaunay tessellations to discretize a function and its derivatives, respectively. A discretized function has numerous discontinuities so that these discontinuities are utilized as a candidate of crack path segment in modeling propagating cracks, without making any extra computation to accommodate new displacement discontinuities. When the scheme is implemented to a finite element method (FEM), the resulting stiffness matrix coincides with the one that is obtained by using linear elements. The accuracy of computing a stress intensity factor at a crack tip is examined. It is shown that the accuracy is better than that of a FEM with linear elements when the rotational degree of freedom is included in discretizing displacement functions. Three three‐dimensional growing crack problems are solved by means of the PDS and the results are presented. Copyright © 2009 John Wiley & Sons, Ltd.

3D dynamic crack propagation analysis with PDS-FEM

This paper briefly explains a recently developed numerical technique called PDS-FEM and its dynamic extension. PDS-FEM is a simple and efficient numerical technique for modeling propagation crack in brittle materials. The discretization scheme used in this new numerical technique is called particle discretization scheme (PDS). PDS uses characteristic functions of Voronoi and Delaunay tessellations to discretize function and its derivatives, respectively. The uses of non-overlapping shape functions facilitate simple and numerically efficient failure treatment. We considered the dynamic extension of PDS-FEM and simulated several real life experiments, to illustrate the potential of simulating dynamic crack propagation of problems requiring fine domain discretizations.