Force Propagation Research Articles

How do interparticle contact friction, packing density and degree of polydispersity affectforce propagation in particulate assemblies?

Interparticle contact friction, packing density and polydispersity are known to be majorcontributors to the macroscopic strength of particulate assemblies, that is, their bulkresistance to deformation. For example, when a solid object penetrates a particulatematerial, the penetration resistance (i.e. the force opposing the object) increasesconcomitantly with an increase in the degree of polydispersity, packing density andinterparticle friction. To establish the underlying mechanisms by which these propertiesgovern the macroscopic response, we characterize quantitatively force propagation at lengthscales beyond that of the interparticle contact region. Using data derived from discreteelement simulations of a two-dimensional granular assembly subject to indentation by arigid flat punch, we examine the properties of force chains and the force chain network asthey evolve during the course of the deformation. Findings indicate that increasinginterparticle friction, packing density and degree of polydispersity promotes theformation of straighter chains and a greater degree of branching in the force chainnetwork. Although the force chain length appears to be independent of friction andpolydispersity, on average, denser systems tend to favour shorter chains. Thus,straighter and shorter force chains, combined with a greater degree of branching inthe force chain network, result in a macroscopically stronger granular material.

Particle simulation of spontaneous crack generation problems in large‐scale quasi‐static systems

AbstractTo extend the application range of the distinct element method from a laboratory scale into a large scale such as a geological scale, we need to deal with an upscale issue associated with simulating spontaneous crack generation problems in large‐scale quasi‐static systems. Toward this direction, three important simulation issues, which may affect the quality of the particle simulation results of a quasi‐static system, have been addressed in details in this paper. The first simulation issue is how to determine the particle‐scale mechanical properties of a particle from the measured macroscopic mechanical properties of rocks. The second simulation issue is that the fictitious time, rather than the physical time, is used in the particle simulation of a quasi‐static problem. The third simulation issue is that the conventional loading procedure used in the distinct element method is conceptually inaccurate, at least from the force propagation point of view. A new loading procedure is proposed to solve the conceptual problem resulting from the third simulation issue. The proposed loading procedure is comprised of two main types of periods, a loading period and a frozen period. Using the proposed loading procedure, the parameter selection problem stemming from the first issue can be somewhat solved. Since the second issue is an inherent one, it is strongly recommended that a particle‐size sensitivity analysis of at least two different models, which have the same geometry but different smallest particle sizes, be carried out to confirm the particle simulation result of a large‐scale quasi‐static system. The related simulation results have demonstrated the usefulness and correctness of the proposed loading procedure for dealing with spontaneous crack generation problems in large‐scale quasi‐static geological systems. Copyright © 2006 John Wiley & Sons, Ltd.

Control of stress propagation in the cytoplasm by prestress and loading frequency.

One fundamental question in cell biology is how mechanical stresses are distributed inside the cytoplasm. Recently we have developed a synchronous detection approach to map cytoplasmic displacements and stresses using yellow fluorescent protein tagged mitochondria as fiducial markers of the cytoskeleton (CSK) in response to a localized load applied via an RGD-coated magnetic bead (7). We have shown that stresses are propagated to remote sites in the cytoplasm, a finding that contradicts continuum model predictions. Here we show that long distance force propagation in the cytoplasm was abolished when the contractile prestress in the CSK was lowered by relaxing agents and enhanced when the prestress was increased by contractile agonists. Surprisingly, when the loading frequency was varied from 0.03 Hz to 30 Hz, the total area of induced displacements (an index of the extent of stress propagation) first increased with loading frequency and then decreased with loading frequency. These results demonstrate that the long distance force propagation in living adherent cells might be controlled by the level of contractile prestress in the CSK and by the loading frequency.

Interactive cutting of deformable objects using force propagation approach and digital design analogy

Interactive cutting simulation of deformable objects is primarily achieved by modifying the mesh topology of the objects in real time. As cutting proceeds arbitrarily, it results in many possible cases of topological changes that make the design of generic cutting algorithms a tedious bookkeeping task. This paper presents an interactive cutting simulation approach based on mass–spring system. By the analogy of digital design, a systematic method is proposed to trace and manage the topology changes during interactive cutting. The dynamics of deformable objects and the cutting-induced deformation are simulated by the force propagation among the mass-points. In the meantime, adaptive mesh refinements by three processes—redistribution, remeshing and relaxation—are carried out in the process of interactive topology modification. The proposed method is scalable by controlling the extent of localized simulation. It is suitable for cutting simulation in virtual surgery and applications involving the cutting of soft deformable objects.

Prestress mediates force propagation into the nucleus

Several reports show that the nucleus is 10 times stiffer than the cytoplasm. Hence, it is not clear if intra-nuclear structures can be directly deformed by a load of physiologic magnitudes. If a physiologic load could not directly deform intra-nuclear structures, then signaling inside the nucleus would occur only via the mechanisms of diffusion or translocation. Using a synchronous detection approach, we quantified displacements of nucleolar structures in cultured airway smooth muscle cells in response to a localized physiologic load (∼0.4 μm surface deformation) via integrin receptors. The nucleolus exhibited significant displacements. Nucleolar structures also exhibited significant deformation, with the dominant strain being the bulk strain. Increasing the pre-existing tensile stress (prestress) in the cytoskeleton significantly increased the stress propagation efficiency to the nucleolus (defined as nucleolus displacement per surface deformation) whereas decreasing the prestress significantly lowered the stress propagation efficiency to the nucleolus. Abolishing the stress fibers/actin bundles by plating the cells on poly- l-lysine-coated dishes dramatically inhibited stress propagation to the nucleolus. These results demonstrate that the prestress in the cytoskeleton is crucial in mediating stress propagation to the nucleolus, with implications for direct mechanical regulation of nuclear activities and functions.

Long-distance propagation of forces in a cell

A fundamental question in the field of mechanotransduction is how forces propagate inside a cell. Recent experiments have shown that a force of a physiological magnitude, applied via a focal adhesion, can propagate a long distance into the cell. This observation disagrees with existing models that regard the cell as a homogeneous body. We show that this “action at a distance” results from the inhomogeneity in the cell: a prestressed and stiff actin bundle guides the propagation of forces over long distances. Our models highlight the enormous ratios of the prestress and the modulus of the actin bundle to the modulus of the cytoskeleton network. For a normal cell, the models predict that forces propagate over characteristic lengths comparable to the size of the cell. The characteristic lengths can be altered, however, by treatments of the cell. We provide experimental evidence and discuss biological implications.

Measurement of grain–wall contact forces in a granular bed using frequency-scanning interferometry

Micro-mechanical theories have recently been developed to model the propagation of force through a granular material based on single grain interactions. We describe here an experimental technique, developed to validate such theories, that is able to measure the individual contact forces between the grains and the wall of the containing vessel, thereby avoiding the spatial averaging effect of conventional pressure transducers. The method involves measuring interferometrically the deflection of an interface within a triple-layer elastic substrate consisting of epoxy, silicone rubber, and glass. A thin coating of gold between the epoxy and rubber acts as a reflective film, with the reference wave provided by the glass/air interface. Phase shifting is carried out by means of a tunable laser. Phase difference maps are calculated using a 15-frame phase-shifting formula based on a Hanning window. The resulting displacement resolution of order 1 nm allows the wall stiffness to be increased by some two orders of magnitude compared to previously described methods in the literature.

On entropy estimates of contact forces in static granular assemblies

As an extension of previous work by others, this articles deals with maximum-entropy estimates for the statistics of static contact forces in assemblies of nearly rigid grains. As found in the previous works, the constraint of mean stress leads provisionally to a distribution of contact force that is exponential at large force. This behavior, found in various experiments and numerical simulations, does not depend on special models of force propagation postulated in the contemporary physics literature. Following K. Bagi [Behringer, R. Jenkins, J.T. (Eds.), Powders and Grains, Balkema, 1997, p. 251] consideration is also given to entropy maximization under the constraint of constant mean strain, which leads to a similar exponential tail in the distribution of particle displacements. In contrast to the previous works, it is emphasized that the exact form of the probability density depends on the statistical weight (a priori probability) assigned to elementary volumes in the state-space of contact forces or displacements. This leads to the conclusion that the large-force exponential is a general representation of maximum-entropy statistics arising from global constraints, whereas the state-space measure is dictated by local mechanics. A few examples of state-space measure are considered, and the resulting distributions are compared to previous experiment and simulation. A striking analogy is revealed between the force distribution in a static sphere assembly and the Maxwell–Boltzmann velocity distribution for gases. Based on the methods of statistical thermodynamics, a virtual-thermodynamic formalism is presented for complementary strain energies in granular statics. This involves no direct appeal to the concept of (static) granular temperature favored in certain statistical-physics literature. As a possible test of the general validity of the entropy principle in granular statics, the question is raised as to whether it can describe the heterogeneous two-phase structure found in photoelastic experiments and numerical simulations of granular assemblies.

Deformable simulation using force propagation model with finite element optimization

A key challenge of deformable simulation is to satisfy the conflicting requirements of real-time interactivity and physical realism. In this paper, we present the mass–spring-based force propagation model (FPM) in which the simulation speed is tunable to maintain a balance between the two criteria. Deformation is modeled as a result of force propagation among the mass points in localized regions. Experiments have been performed to study the effects of the FPM parameters on the eventual deformation. Furthermore, a heuristic optimization technique is proposed to identify the model parameters for materials as specified by mechanical constants. We employ simulated annealing to tune the parameters automatically until the simulated shape of the FPM approximates the reference deformation as defined by the mathematically more rigorous finite element model. The proposed technique provides a feasible solution to the issue of parameter identification in mass–spring-based models.

Interactive deformation of soft tissues with haptic feedback for medical learning.

An effective deformable model based on a successive force propagation process is proposed. It avoids the laborious stiffness matrix formulation and is scalable simply by controlling the penetration depth. Mechanical tests are performed to evaluate its feasibility for modeling real tissues. An interactive system is developed using a commercial haptic device.

Anomalous force diffusion in nearly ordered packings of frictionless discs

We derive analytic expressions for force propagation in packings of frictionless discs with a narrow distribution of disc sizes, by expanding to first order about the known ordered solution. The distribution of contact forces P(f) is found to be narrow at the upper surface, and broaden at a rate that varies with depth, being superdiffusive near the surface until crossing over to a subdiffusive regime near the fixed base. Furthermore, the response to an isolated load propagates along the edge of a `cone,' as in the ordered case, but fluctuates under ensemble averaging by an amount that depends purely on height, not on the lateral position. Finally, we comment on ways in which the analytical framework presented here could be extended to a wider range of granular packings.

A flexible-arm as manipulator position and force detection unit

This paper presents a self-sensory robot arm to two basic sensing problems in control of flexible manipulators: detection of the position and orientation variations due to structural deformation and detection of the contact force of end-effector when manipulator interacts with its environment. Taking advantage of structural flexibility, a flexible robot arm with strain gauges distributed on it acts as a sensing unit. The position and orientation of flexible arm are expressed as a function of curvature of the arm. An interpolation technique gives this continuous curvature function from a finite set of measurements made with strain gauges. A relation between strain measurements and endpoint force of flexible arm is developed and the contact force of end-effector is then determined using a force propagation algorithm. The proposed technique and algorithm were implemented and evaluated in a laboratorial flexible arm. Experimental validations using a vision system and two force sensors have shown that the self-sensory flexible arm can provide accurate endpoint position and force in both static and dynamic loading situations.

Statistical mechanics of granular materials: stress propagation and distribution of contact forces

In a static granular material all particles are touching their neighbours and given a sufficiently high density a jammed state results. A new approach which employs statistical-mechanical concepts is offered for the description of such states. We investigate the simplest statically determinate problem and derive equations of stress propagation. The simplest Boltzmann type equation for the probability of contact force distribution is formulated and solved for model packings. The theory predicts a distribution for the probability of finding a contact force of magnitude f as e− f / ¯f which is in a good agreement with experimental data. We also propose a pathway to calculating the macroscopic stress tensor as a function of compactivity in a static and slowly sheared granular media.

Displacement of building cluster using field analysis method

This paper presents a field based method to deal with the displacement of building cluster, which is driven by the street widening. The compress of street boundary results in the force to push the building moving inside and the force propagation is a decay process. To describe the phenomenon above, the field theory is introduced with the representation model of isoline. On the basis of the skeleton of Delaunay triangulation, the displacement field is built in which the propagation force is related to the adjacency degree with respect to the street boundary. The study offers the computation of displacement direction and offset distance for the building displacement. The vector operation is performed on the basis of grade and other field concepts.

1119 レールの転がり損傷に関する研究

As far as the surface defects on the rail head, there are two kinds of defects called on "head check" and "dark spots" (shelling defects) in the Shinkansen's rail. In addition "White Phase" exists in the surface layer of rail head. The contents discussed in this paper are Contact Rolling Fatigue of Rails in the high-speed rail tracks. The authors have focused on "White Phase". It is clear that the initiation of "contact rolling defects" relates to Hertzian stress, Lubrication, tangential force etc. The main results obtained in the present study are as follows : (1) The occurrence of White Phase is attributed to alternate between water lubrication condition and dry condition. (2) The tangential force affect cracks initiation and propagation materially. (3) White Phase occurs in the origination of shelling early.

OS11W0289 Study on contact rolling fatigue of rails

As far as the surface defects on the rail head, there are two kinds of defects called on "head check" and "dark spots" (shelling defects) in the Shinkansen's rail. In addition "White Phase" exists in the surface layer of rail head. The contents discussed in this paper are Contact Rolling Fatigue of Rails in the high-speed rail tracks. The authors have focused on "White Phase". It is clear that the initiation of "contact rolling defects" relates to Hertzian stress, Lubrication, tangential force etc. The main results obtained in the present study are as follows: (1) The occurrence of White Phase is attributed to alternate between water lubrication condition and dry condition. (2) The tangential force affect cracks initiation and propagation materially. (3) White Phase occurs in the origination of shelling early.

Effects of Flow on Measurements of Interactions in Colloidal Suspensions

A hydrodynamic mechanism of interactions of colloidal particles is considered. The mechanism is based on the assumption of tiny background flows in the experimental cells during measurements by Grier et al. Both trivial (shear flow) and nontrivial (force propagation through viscous fluid) effects are taken into account for two colloidal particles near a wall bounding the solvent. Expressions for the radial (attractive or repulsive) forces and the polar torques are obtained. Quantitative estimates of the flow needed to produce the observed strength of attractive force are given; other necessary conditions are also considered. The following conclusion is made: the mechanism suggested most likely is not responsible for the attractive interactions observed in the experiments of Grier et al.; however, it may be applicable in other experimental realizations and should be kept in mind while conducting colloidal measurements of high sensitivity. Several distinctive features of the interactions due to this mechanism are identified.

Models of soil compaction due to traffic and their evaluation

Soil compaction by wheeling may cause considerable damage to the structure of the tilled soil and the subsoil and consequently to crop production, workability and the environment. Soil compaction models are reviewed and their evaluation under laboratory or field conditions is discussed. The development of a compaction model includes: (i) modelling the propagation of the loading forces within the soil resulting from forces applied at the soil surface from farm vehicles; (ii) modelling soil stress–strain behaviour. Models predict stress distribution in the soil induced by farm vehicle and change in soil structure: increase in dry bulk density and rut depth formation. We conclude that models based on Boussinesq equations for stress propagation are useful since they use a small number of parameters. They have been successfully evaluated in field conditions for homogeneous soil under a wide range of soil and water conditions. The difference between simulations and observations becomes more apparent when dealing with heterogeneous structures (clods, firm subsoil). The models based on the finite element method (FEM) have been shown to be more adequate for modelling the 3D distribution of stress within the soil induced by wheeling and the complex stress–strain behaviour of soil. Nevertheless, these models require more mechanical parameters and have been evaluated under limited conditions in laboratory bins or in the field with low compaction intensities. This review stresses the need to test FEM soil compaction models, so as to extend the range of conditions where these models can be applied.

Footprints in sand: the response of a granular material to local perturbations.

We experimentally determine ensemble-averaged responses of granular packings to point forces, and we compare these results to recent models for force propagation in a granular material. We use 2D granular arrays consisting of photoelastic particles: either disks or pentagons, thus spanning the range from ordered to disordered packings. A key finding is that spatial ordering of the particles is a key factor in the force response. Ordered packings have a propagative component that does not occur in disordered packings.

Thermoacoustic Energy Effects in Electrical Arcs

Electrical arcs commonly occur in electrical injury incidents. Historically, safe work distances from an energized surface along with personal barrier protection have been employee safety strategies used to minimize electrical arc hazard exposures. Here, the two-dimensional computational simulation of an electrical arc explosion is reported using color graphics to depict the temperature and acoustic force propagation across the geometry of a hypothetical workroom during a time from 0 to 50 ms after the arc initiation. The theoretical results are compared to the experimental findings of staged tests involving a mannequin worker monitored for electrical current flow, temperature, and pressure, and reported data regarding neurologic injury thresholds. This report demonstrates a credible link between electrical explosions and the risk for pressure (acoustic) wave trauma. Our ultimate goal is to protect workers through the design and implementation of preventive strategies that properly account for all electrical arc-induced hazards, including electrical, thermal, and acoustic effects.