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arXiv 2020年

作者： Tuckman, Philip J. VanderWerf, Kyle Yuan, Ye Zhang, Shiyun Zhang, Jerry Shattuck, Mark D. O’Hern, Corey S. Department of Physics Yale University New HavenCT06520 United States Department of Mechanics and Engineering Science College of Engineering Peking University Beijing100871 China Department of Mechanical Engineering and Materials Science Yale University New HavenCT06520 United States Benjamin Levich Institute and Physics Department City College of New York New YorkNY10031 United States Department of Physics Yale University Department of Applied New HavenCT06520 United States Graduate Program in Computational Biology and Bioinformatics Yale University New HavenCT06520 United States

We investigate the mechanical response of packings of purely repulsive, frictionless disks to quasistatic deformations. The deformations include simple shear strain at constant packing fraction and at constant pressure, "polydispersity" strain (in which we change the particle size distribution) at constant packing fraction and at constant pressure, and isotropic compression. For each deformation, we show that there are two classes of changes in the interparticle contact networks: jump changes and point changes. Jump changes occur when a contact network becomes mechanically unstable, particles "rearrange", and the potential energy (when the strain is applied at constant packing fraction) or enthalpy (when the strain is applied at constant pressure) and all derivatives are discontinuous. During point changes, a single contact is either added to or removed from the contact network. For repulsive linear spring interactions, second- and higher-order derivatives of the potential energy/enthalpy are discontinuous at a point change, while for Hertzian interactions, third- and higher-order derivatives of the potential energy/enthalpy are discontinuous. We illustrate the importance of point changes by studying the transition from a hexagonal crystal to a disordered crystal induced by applying polydispersity strain. During this transition, the system only undergoes point changes, with no jump changes. We emphasize that one must understand point changes, as well as jump changes, to predict the mechanical properties of jammed packings. Copyright © 2020, The Authors. All rights reserved.

关键词： Potential energy

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Jammed packings of 3D superellipsoids with tunable packing fraction, contact number, and ordering

arXiv

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arXiv 2019年

作者： Yuan, Ye VanderWerf, Kyle Shattuck, Mark D. O’Hern, Corey S. Department of Mechanics and Engineering Science College of Engineering Peking University Beijing100871 China Department of Mechanical Engineering and Materials Science Yale University New HavenCT06520 United States Department of Physics Yale University New HavenCT06520 United States Benjamin Levich Institute and Physics Department City College of New York New YorkNY10031 United States Department of Applied Physics Yale University New HavenCT06520 United States Graduate Program in Computational Biology and Bioinformatics Yale University New HavenCT06520 United States

We carry out numerical studies of static packings of frictionless superellipsoidal particles in three spatial dimensions. We consider more than 200 different particle shapes by varying the three shape parameters that define superellipsoids. We characterize the structural and mechanical properties of both disordered and ordered packings using two packing-generation protocols. We perform athermal quasi-static compression simulations starting from either random, dilute configurations (Protocol 1) or thermalized, dense configurations (protocol 2), which allows us to tune the orientational order of the packings. In general, we find that the contact numbers at jamming onset for superellipsoid packings are hypostatic, with zJ f and df = 5 or 6 depending on whether the particles are axi-symmetric or not. Over the full range of orientational order, we find that the number of quartic modes of the dynamical matrix for the packings always matches the number of missing contacts relative to the isostatic value. This result suggests that there are no mechanically redundant contacts for ordered, yet hypostatic packings of superellipsoidal particles. Additionally, we find that the packing fraction at jamming onset for diordered packings of superellipsoidal particles can be collapsed using two particle shape parameters, e.g. the asphericity A and reduced aspect ratio β of the particles. Copyright © 2019, The Authors. All rights reserved.

关键词： Jamming

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Hypostatic jammed packings of frictionless nonspherical particles

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Physical Review E 2018年第1期97卷 012909-012909页

作者： Kyle VanderWerf Weiwei Jin Mark D. Shattuck Corey S. O'Hern Department of Physics Yale University New Haven Connecticut 06520 USA Department of Mechanics and Engineering Science Peking University Beijing 100871 China Department of Mechanical Engineering & Materials Science Yale University New Haven Connecticut 06520 USA Benjamin Levich Institute and Physics Department The City College of New York New York New York 10031 USA Department of Applied Physics Yale University New Haven Connecticut 06520 USA Graduate Program in Computational Biology and Bioinformatics Yale University New Haven Connecticut 06520 USA

We perform computational studies of static packings of a variety of nonspherical particles including circulo-lines, circulo-polygons, ellipses, asymmetric dimers, dumbbells, and others to determine which shapes form packings with fewer contacts than degrees of freedom (hypostatic packings) and which have equal numbers of contacts and degrees of freedom (isostatic packings), and to understand why hypostatic packings of nonspherical particles can be mechanically stable despite having fewer contacts than that predicted from naive constraint counting. To generate highly accurate force- and torque-balanced packings of circulo-lines and cir-polygons, we developed an interparticle potential that gives continuous forces and torques as a function of the particle coordinates. We show that the packing fraction and coordination number at jamming onset obey a masterlike form for all of the nonspherical particle packings we studied when plotted versus the particle asphericity A, which is proportional to the ratio of the squared perimeter to the area of the particle. Further, the eigenvalue spectra of the dynamical matrix for packings of different particle shapes collapse when plotted at the same A. For hypostatic packings of nonspherical particles, we verify that the number of “quartic” modes along which the potential energy increases as the fourth power of the perturbation amplitude matches the number of missing contacts relative to the isostatic value. We show that the fourth derivatives of the total potential energy in the directions of the quartic modes remain nonzero as the pressure of the packings is decreased to zero. In addition, we calculate the principal curvatures of the inequality constraints for each contact in circulo-line packings and identify specific types of contacts with inequality constraints that possess convex curvature. These contacts can constrain multiple degrees of freedom and allow hypostatic packings of nonspherical particles to be mechanically stable.

关键词： Granular materials Granular packing Jamming

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Hypostatic jammed packings of frictionless nonspherical particles

arXiv

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arXiv 2017年

作者： VanderWerf, Kyle Jin, Weiwei Shattuck, Mark D. O'Hern, Corey S. Department of Physics Yale University New HavenCT06520 United States Benjamin Levich Institute and Physics Department City College of New York New YorkNY10031 United States Department of Mechanics and Engineering Science Peking University Beijing100871 China Department of Mechanical Engineering & Materials Science Yale University New HavenCT06520 United States Department of Applied Physics Yale University New HavenCT06520 United States Graduate Program in Computational Biology and Bioinformatics Yale University New HavenCT06520 United States

We perform computational studies of static packings of a variety of nonspherical particles including circulo-lines, circulo-polygons, ellipses, asymmetric dimers, dumbbells, and others to determine which shapes form packings with fewer contacts than degrees of freedom (hypostatic packings) and which have equal numbers of contacts and degrees of freedom (isostatic packings), and to understand why hypostatic packings of nonspherical particles can be mechanically stable despite having fewer contacts than that predicted from naïve constraint counting. To generate highly accurate force- and torque-balanced packings of circulo-lines and -polygons, we developed an interparticle potential that gives continuous forces and torques as a function of the particle coordinates. We show that the packing fraction and coordination number at jamming onset obey a master-like form for all of the nonspherical particle packings we studied when plotted versus the particle asphericity A, which is proportional to the ratio of the squared perimeter to the area of the particle. Further, the eigenvalue spectra of the dynamical matrix for packings of different particle shapes collapse when plotted at the same A. For hypostatic packings of nonspherical particles, we verify that the number of "quartic" modes along which the potential energy increases as the fourth power of the perturbation amplitude matches the number of missing contacts relative to the isostatic value. We show that the fourth derivatives of the total potential energy in the directions of the quartic modes remain nonzero as the pressure of the packings is decreased to zero. In addition, we calculate the principal curvatures of the inequality constraints for each contact in circulo-line packings and identify specific types of contacts with inequality constraints that possess convex curvature. These contacts can constrain multiple degrees of freedom and allow hypostatic packings of nonspherical particles to be mechanically stable. C

关键词： Degrees of freedom (mechanics)

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INCLUSION AND MISFIT EFFECTS IN HYDROSTATIC TENSION

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JOURNAL OF APPLIED mechanics-TRANSACTIONS OF THE ASME 1988年第2期55卷 355-360页

作者： wilner, B Benjamin Wilner Engineering Science and Mechanics Program School of Civil Engineering Georgia Institute of Technology Atlanta GA 30332

A study of the effect of an elastic spherical particle embedded in an infinite elastic-plastic matrix subject to hydrostatic tension is presented. Two types of particles will be considered: (1) a perfectly fitting inclusion, (2) a misfitting one. A numerical solution is developed to solve the governing equations. Various combinations of elastic constants and power hardening coefficients are studied for different load levels. The analysis is concentrated on the interfacial normal stresses and its dependence on the different parameters.

关键词： Hydrostatics Tension Particulate matter Stress Hardening Elastic constants Equations Fittings

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