1,720,990 research outputs found
Elastic sheets: Cracks by design
No full textDifferent methods exist to control fracture in thin media in order to produce some desired shape or curved edge. Commonly, inhomogeneities are placed along a specific path to guide a fracture, such as scoring a material's surface or introducing a sequence of perforations. In some circumstances, the ability to guide fractures without altering the material is advantageous or even necessary, and could provide a key design tool in areas such as flexible electronics, thin films and monolayer materials. Writing in Nature Materials, Mitchell, Irvine and colleagues explore the possibility of guiding crack paths in thin, elastic sheets by draping them on surfaces with non-zero Gaussian curvature1. The out-of-plane elastic deformation imposed by the surface curvature causes an inhomogeneous stress distribution within the sheet. If a small crack is introduced, the pre-load in the membrane can cause the fracture to grow spontaneously. Depending on how the substrate geometry is chosen, the crack growth can be made to conform to a curved path and possibly arrest after a desired crack length has been reached. This opens up the possibility of a new methodology for incising two-dimensional shapes from sheets by fracturing them over a tailored bumpy substrate surface
Foreword on the special issue: from discrete particles to continuum models of granular mechanics
No full textThe mechanics of granular materials have remained a challenge to describe since the days of Coulomb, both theoretically and computationally. Granular media arise in a number of everyday circumstances (e.g., raw materials, soils, food/agriculture, pharmaceuticals, vehicle mobility, debris removal) and remain the second-most handled material by weight in global industry. Hence, the challenge of coming up with accurate and efficient ways to simulate a collection of grains is an issue of great import to multiple disciplines. There are two major perspectives. Ideally, one would like a continuum model able to describe the behavior of large collections of grains in a numerically efficient fashion. There is also the discrete perspective, where modeling arises at the individual particle level and the motion of every grain is tracked and evolved under mechanical laws
Intrusion rheology in grains and other flowable materials
Full text linkThe interaction of intruding objects with deformable materials arises in many contexts, including locomotion in fluids and loose media, impact and penetration problems, and geospace applications. Despite the complex constitutive behaviour of granular media, forces on arbitrarily shaped granular intruders are observed to obey surprisingly simple, yet empirical 'resistive force hypotheses'. The physics of this macroscale reduction, and how it might play out in other media, has however remained elusive. Here, we show that all resistive force hypotheses in grains arise from local frictional yielding, revealing a novel invariance within a class of plasticity models. This mechanical foundation, supported by numerical and experimental validations, leads to a general analytical criterion to determine which rheologies can obey resistive force hypotheses. We use it to explain why viscous fluids are observed to perform worse than grains, and to predict a new family of resistive-force-obeying materials: cohesive media such as pastes, gels and muds.United States. Army Research Office (W911NF-14-1-0205)United States. Army Research Office (W911NF-15-1-0196
A hierarchy of granular continuum models: Why flowing grains are both simpleand complex
No full textranular materials have a strange propensity to behave as either a complex media or a simple media depending on the precise question being asked. This review paper offers a summary of granular flow rheologies for well-developed or steady-state motion, and seeks to explain this dichotomy through the vast range of complexity intrinsic to these models. A key observation is that to achieve accuracy in predicting flow fields in general geometries, one requires a model that accounts for a number of subtleties, most notably a nonlocal effect to account for cooperativity in the flow as induced by the finite size of grains. On the other hand, forces and tractions that develop on macro-scale, submerged boundaries appear to be minimally affected by grain size and, barring very rapid motions, are well represented by simple rate-independent frictional plasticity models. A major simplification observed in experiments of granular intrusion, which we refer to as the ‘resistive force hypothesis’ of granular Resistive Force Theory, can be shown to arise directly from rate-independent plasticity. Because such plasticity models have so few parameters, and the major rheological parameter is a dimensionless internal friction coefficient, some of these simplifications can be seen as consequences of scaling
Nonlocal Constitutive Relation for Steady Granular Flow
No full textExtending recent modeling efforts for emulsions, we propose a nonlocal fluidity relation for flowing granular materials, capturing several known finite-size effects observed in steady flow. We express the local Bagnold-type granular flow law in terms of a fluidity ratio and then extend it with a particular Laplacian term that is scaled by the grain size. The resulting model is calibrated against a sequence of existing discrete element method data sets for two-dimensional annular shear, where it is shown that the model correctly describes the divergence from a local rheology due to the grain size as well as the rate-independence phenomenon commonly observed in slowly flowing zones. The same law is then applied in two additional inhomogeneous flow geometries, and the predicted velocity profiles are compared against corresponding discrete element method simulations utilizing the same grain composition as before, yielding favorable agreement in each case
Effect of particle surface friction on nonlocal constitutive behavior of flowing granular media
No full textA recently proposed nonlocal rheology for dense granular flow, based on the concept of nonlocal granular fluidity, has demonstrated predictive capabilities in multiple geometries. This work is concerned with determining how the parameters of this continuum model arise from the properties of the grains themselves. We perform a controlled study investigating how the surface friction of the grains influences the continuum parameters, with a focus on how the nonlocal amplitude, the model’s one new parameter, is affected. This is achieved comparing two-dimensional discrete-element simulations of flowing disks to numerical solutions of the model in planar shear and several annular shear geometries. A multi-step calibration scheme for the continuum parameter extraction is developed and implemented. Results indicate the nonlocal amplitude varies less than an order of magnitude over a wide range of surface frictions, with a slight tendency to increase as surface friction decreases, particularly in a regime of small surface friction. Our data also show that the stress and flow-rate variables deviate little from a local relationship as surface friction vanishes, which corroborates certain existing experimental findings
Modeling growth paths of interacting crack pairs in elastic media
Full text linkThe problem of predicting the growth of a system of cracks, each crack influencing the growth of the others, arises in multiple fields. We develop an analytical framework toward this aim, which we apply to the 'En-Passant' family of crack growth problems, in which a pair of initially parallel, offset cracks propagate nontrivially toward each other under far-field opening stress. We utilize boundary integral and perturbation methods of linear elasticity, linear elastic fracture mechanics, and common crack opening criteria to calculate the first analytical model for curved En-Passant crack paths. The integral system is reduced under a hierarchy of approximations, producing three methods of increasing simplicity for computing crack paths. The last such method is a major highlight of this work, using an asymptotic matching argument to predict crack paths based on superposition of simple, single-crack fields. Within the corresponding limits of the three methods, all three are shown to agree with each other. We provide comparisons to exact results and existing experimental data to verify certain approximation steps
A predictive, size-dependent continuum model for dense granular flows
No full textDense granular materials display a complicated set of flow properties, which differentiate them from ordinary fluids. Despite their ubiquity, no model has been developed that captures or predicts the complexities of granular flow, posing an obstacle in industrial and geophysical applications. Here we propose a 3D constitutive model for well-developed, dense granular flows aimed at filling this need. The key ingredient of the theory is a grain-size-dependent nonlocal rheology—inspired by efforts for emulsions—in which flow at a point is affected by the local stress as well as the flow in neighboring material. The microscopic physical basis for this approach borrows from recent principles in soft glassy rheology. The size-dependence is captured using a single material parameter, and the resulting model is able to quantitatively describe dense granular flows in an array of different geometries. Of particular importance, it passes the stringent test of capturing all aspects of the highly nontrivial flows observed in split-bottom cells—a geometry that has resisted modeling efforts for nearly a decade. A key benefit of the model is its simple-to-implement and highly predictive final form, as needed for many real-world applications.Massachusetts Institute of Technology. Dept. of Mechanical Engineerin
Modeling tensorial conductivity of particle suspension networks
No full textSignificant microstructural anisotropy is known to develop during shearing flow of attractive particle suspensions. These suspensions, and their capacity to form conductive networks, play a key role in flow-battery technology, among other applications. Herein, we present and test an analytical model for the tensorial conductivity of attractive particle suspensions. The model utilizes the mean fabric of the network to characterize the structure, and the relationship to the conductivity is inspired by a lattice argument. We test the accuracy of our model against a large number of computer-generated suspension networks, based on multiple in-house generation protocols, giving rise to particle networks that emulate the physical system. The model is shown to adequately capture the tensorial conductivity, both in terms of its invariants and its mean directionality
Nonlocal modeling of granular flows down inclines
No full textFlows of granular media down a rough inclined plane demonstrate a number of nonlocal phenomena. We apply the recently proposed nonlocal granular fluidity model to this geometry and find that the model captures many of these effects. Utilizing the model's dynamical form, we obtain a formula for the critical stopping height of a layer of grains on an inclined surface. Using an existing parameter calibration for glass beads, the theoretical result compares quantitatively to existing experimental data for glass beads. This provides a stringent test of the model, whose previous validations focused on driven steady-flow problems. For layers thicker than the stopping height, the theoretical flow profiles display a thickness-dependent shape whose features are in agreement with previous discrete particle simulations. We also address the issue of the Froude number of the flows, which has been shown experimentally to collapse as a function of the ratio of layer thickness to stopping height. While the collapse is not obvious, two explanations emerge leading to a revisiting of the history of inertial rheology, which the nonlocal model references for its homogeneous flow response.National Science Foundation (U.S.) (NSF-CBET-1253228
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