Mitigating kinematic locking in the material point method

Mast, Carter M.; Mackenzie‐Helnwein, Peter; Arduino, Pedro; Miller, Gregory R.; Shin, W.

doi:10.1016/j.jcp.2012.04.032

Cited by 87 publications

(49 citation statements)

References 45 publications

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“…For example, explicit nature of the presented MPM formulation only allows for adoptation of linear elements; however, the first derivative of shape functions for these elements are discontinuous which can lead to numerical noise in the calculation known as particle crossing problem [3]. Several improvements including using Generalized Interpolation [1], Spline shape function [2], anti-locking approach [25,26] and mixed integration [6] were proposed to treat such problem. Here, the computationally efficient method of mixed integration was implemented.…”

Section: Materials Point Methodsmentioning

confidence: 99%

Numerical evaluation of mean-field homogenisation methods for predicting shale elastic response

2016

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Numerical evaluation of mean-field homogenisation methods for predicting shale elastic responseReceived: date / Accepted: date Abstract Homogenisation techniques have been successfully used to estimate the mechanical response of synthetic composite materials, due to their ability to relate the macroscopic mechanical response to the material microstructure. The adoption of these mean-field techniques in geo-composites such as shales is attractive, partly because of the practical difficulties associated with the experimental characterisation of these highly heterogeneous materials. In this paper, numerical modelling has been undertaken to investigate the applicability of homogenisation methods in predicting the macroscopic, elastic response of clayey rocks. The rocks are considered as two-level composites consisting of a porous clay matrix at the first level and a matrix-inclusion morphology at the second level . The simulated microstructures ranged from a simple system of one inclusion/void embedded in a matrix to complex, random microstructures. The effectiveness and limitations of the different homogenisation schemes were demonstrated through a comparative evaluation of the macroscopic elastic response, illustrating the appropriate schemes for upscaling the microstructure of shales. Based on the numerical simulations and existing experimental observations, a randomly distributed pore system for the micro-structure of porous clay matrix has been proposed which can be used for the subsequent development and validation of shale constitutive models and their flow properties. Finally, the homogenisation techniques were used to predict the experimental measurements of elastic response. The developed methodology is proved to be a valuable too for verifying the accuracy and performance of the homogenisation techniques.

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Section: Materials Point Methodsmentioning

confidence: 99%

Numerical evaluation of mean-field homogenisation methods for predicting shale elastic response

2016

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“…There is a large literature base considering MPM applications-the interested reader is referred to three recent publications [13,14,22] that summarize previous applications, extensions, and numerical implementation details. In the specific context of granular flow, it is important to recognize the works of [15,32,33] in which the MPM is used to simulate granular media in various contexts.…”

Section: Materials Point Methods Representation Of Landslides and Debrimentioning

confidence: 99%

“…The final step in the cycle (lower left part of the figure) is updating the particle velocity and position, after which, the procedure begins again and repeats for a prescribed time duration. This work employs a locking-free variant of the MPM described in [14], with a suitable extension for use with an elastoplastic integration algorithm [16]. This approach minimizes the well-known cell-crossing error phenomenon and results in a robust and simple algorithm well-suited for the systems modeled in this paper.…”

Section: Materials Point Methods Representation Of Landslides and Debrimentioning

confidence: 99%

“…The code has been validated using closed form solutions and experimental results. A complete validation study can be found in [14,15].…”

Section: Materials Point Methods Representation Of Landslides and Debrimentioning

confidence: 99%

“…Each example employs a locking-free variant of the MPM described in [14], with a suitable extension for use with elastoplastic materials as described in [16].…”

Section: Constitutive Modelmentioning

confidence: 99%

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Avalanche and landslide simulation using the material point method: flow dynamics and force interaction with structures

Mast¹,

Arduino

Miller

et al. 2014

Comput Geosci

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In this paper, the material point method (MPM) is presented as a tool for simulating large deformation, gravity-driven landslides. The primary goal is to assess the interaction of these flow-like events with the built environment. This includes an evaluation of earthen mounds when energy dissipating devices are placed in the path of a snow avalanche. The effectiveness of the embankments is characterized using displacement, velocity, mass, and energy measures. A second example quantifies the force interaction between a landslide and a square rigid column. Multiple slide approach angles are considered, and various aspects of the impact force are discussed.

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Particle Methods in Computational Fluid Dynamics

Idelsohn

Oñate

Becker

2017

Encyclopedia of Computational Mechanics Second Edition

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Particle methods in computational fluid dynamics (CFD) are numerical tools for the solution of the equations of fluid dynamics, obtained by replacing the fluid continuum with a finite set of particles. One of the key attributes of particle methods is that pure advection is treated exactly. The convection of properties eases the solution of multi‐material problems, simplifying the detection of interfaces. The use of particles also allows to bridge the gap between the continuum and fragmentation in a natural way, for example, in fracture or droplets problems. Particle methods can be roughly classified into two types: (i) those based on probabilistic models, which represent macroscopic properties as statistical behaviors of microscopic particles, and (ii) those based on deterministic models, implying that the state in every point at a given time is perfectly defined. This chapter covers the most common deterministic particle methods. The layout of this chapter is as follows. First we present the governing equations for the motion of fluids. Then, we describe the basic concepts of two methods that rely only on the particles to obtain the field of variables and their derivatives: smoothed particle hydrodynamics (SPH) and the moving particle semi‐implicit method (MPS). The next sections describe three methods that use the particles in combination with a finite element method (FEM) mesh to improve the accuracy. First the material point method (MPM) is described, followed by a more detailed evaluation of the particle finite element method (PFEM) and the finite element method second generation (PFEM‐2). For each of the particle methods, the advantages and disadvantages of the strategies are evaluated. The chapter concludes with an overview of the DEM and the coupling of the DEM with the FEM for the analysis of particulate flows and their interaction with structures.

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Mitigating kinematic locking in the material point method

Cited by 87 publications

References 45 publications

Numerical evaluation of mean-field homogenisation methods for predicting shale elastic response

Numerical evaluation of mean-field homogenisation methods for predicting shale elastic response

Avalanche and landslide simulation using the material point method: flow dynamics and force interaction with structures

Particle Methods in Computational Fluid Dynamics

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