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Material Point Method (material + point_method)
Selected AbstractsThe modelling of anchors using the material point methodINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2005C. J. Coetzee Abstract The ultimate capacity of anchors is determined using the material point method (MPM). MPM is a so-called meshless method capable of modelling large displacements, deformations and contact between different bodies. A short introduction to MPM is given and the derivation of the discrete governing equations. The analysis of a vertically loaded anchor and one loaded at 45° is presented. The load,displacement curves are compared to that obtained from experiments and the effect of soil stiffness and anchor roughness is investigated. The results of the vertically loaded anchor are also compared to an analytical solution. The displacement of the soil surface above the anchor was measured and compared to the numerical predictions. Convergence with mesh refinement is demonstrated and the effect of mesh size and dilatancy angle on the shear band width and orientation is indicated. The results show that MPM can model anchor pull out successfully. No special interface elements are needed to model the anchor,soil interface and the predicted ultimate capacities were within 10% of the measured values. Copyright © 2005 John Wiley & Sons, Ltd. [source] Decoupling and balancing of space and time errors in the material point method (MPM)INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010Michael Steffen Abstract The material point method (MPM) is a computationally effective particle method with mathematical roots in both particle-in-cell and finite element-type methods. The method has proven to be extremely useful in solving solid mechanics problems involving large deformations and/or fragmentation of structures, problem domains that are sometimes problematic for finite element-type methods. Recently, the MPM community has focused significant attention on understanding the basic mathematical error properties of the method. Complementary to this thrust, in this paper we show how spatial and temporal errors are typically coupled within the MPM framework. In an attempt to overcome the challenge to analysis that this coupling poses, we take advantage of MPM's connection to finite element methods by developing a ,moving-mesh' variant of MPM that allows us to use finite element-type error analysis to demonstrate and understand the spatial and temporal error behaviors of MPM. We then provide an analysis and demonstration of various spatial and temporal errors in MPM and in simplified MPM-type simulations. Our analysis allows us to anticipate the global error behavior in MPM-type methods and allows us to estimate the time-step where spatial and temporal errors are balanced. Larger time-steps result in solutions dominated by temporal errors and show second-order temporal error convergence. Smaller time-steps result in solutions dominated by spatial errors, and hence temporal refinement produces no appreciative change in the solution. Based upon our understanding of MPM from both analysis and numerical experimentation, we are able to provide to MPM practitioners a collection of guidelines to be used in the selection of simulation parameters that respect the interplay between spatial (grid) resolution, number of particles and time-step. Copyright © 2009 John Wiley & Sons, Ltd. [source] A computational model for impact failure with shear-induced dilatancyINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2003Z. Chen Abstract It has been observed in plate impact experiments that some brittle solids may undergo elastic deformation at the shock wave front, and fail catastrophically at a later time when they are shocked near but below the apparent Hugoniot elastic limit. Because this phenomenon appears to have features different from those of usual inelastic waves, it has been interpreted as the failure wave. To design an effective numerical procedure for simulating impact failure responses, a three-dimensional computational damage model is developed in this paper. The propagation of the failure wave behind the elastic shock wave is described by a non-linear diffusion equation. Macroscopic shear-induced dilatancy is assumed and treated as a one-to-one measure of the mean intensity of microcracking. The damage evolution in time is determined based on the assumption that the deviatoric strain energy in the elastically compressed material (undamaged) is converted, through the damaging process, into the volumetric potential energy in the comminuted and dilated material. For the ease in large-scale simulations, the coupled damage diffusion equation and the stress wave equation are solved via a staggered manner in a single computational domain. Numerical solutions by using both the finite element method and the material point method, i.e. with and without a rigid mesh connectivity, are presented and compared with the experimental data available. It is shown that the model simulations capture the essential features of the failure wave phenomenon observed in shock glasses, and that the numerical solutions for localized failure are not mesh-dependent. Copyright © 2003 John Wiley & Sons, Ltd. [source] Solving time-dependent PDEs using the material point method, a case study from gas dynamicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2010L. T. Tran Abstract The material point method (MPM) developed by Sulsky and colleagues is currently being used to solve many challenging problems involving large deformations and/or fragementations with some success. In order to understand the properties of this method, an analysis of the considerable computational properties of MPM is undertaken in the context of model problems from gas dynamics. The MPM method in the form used here is shown both theoretically and computationally to have first-order accuracy for a standard gas dynamics test problem. Copyright © 2009 John Wiley & Sons, Ltd. [source] A hybrid immersed boundary and material point method for simulating 3D fluid,structure interaction problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008Anvar Gilmanov Abstract A numerical method is developed for solving the 3D, unsteady, incompressible Navier,Stokes equations in curvilinear coordinates containing immersed boundaries (IBs) of arbitrary geometrical complexity moving and deforming under forces acting on the body. Since simulations of flow in complex geometries with deformable surfaces require special treatment, the present approach combines a hybrid immersed boundary method (HIBM) for handling complex moving boundaries and a material point method (MPM) for resolving structural stresses and movement. This combined HIBM & MPM approach is presented as an effective approach for solving fluid,structure interaction (FSI) problems. In the HIBM, a curvilinear grid is defined and the variable values at grid points adjacent to a boundary are forced or interpolated to satisfy the boundary conditions. The MPM is used for solving the equations of solid structure and communicates with the fluid through appropriate interface-boundary conditions. The governing flow equations are discretized on a non-staggered grid layout using second-order accurate finite-difference formulas. The discrete equations are integrated in time via a second-order accurate dual time stepping, artificial compressibility scheme. Unstructured, triangular meshes are employed to discretize the complex surface of the IBs. The nodes of the surface mesh constitute a set of Lagrangian control points used for tracking the motion of the flexible body. The equations of the solid body are integrated in time via the MPM. At every instant in time, the influence of the body on the flow is accounted for by applying boundary conditions at stationary curvilinear grid nodes located in the exterior but in the immediate vicinity of the body by reconstructing the solution along the local normal to the body surface. The influence of the fluid on the body is defined through pressure and shear stresses acting on the surface of the body. The HIBM & MPM approach is validated for FSI problems by solving for a falling rigid and flexible sphere in a fluid-filled channel. The behavior of a capsule in a shear flow was also examined. Agreement with the published results is excellent. Copyright © 2007 John Wiley & Sons, Ltd. [source] | ||||||||||