scholarly journals The mechanics of brittle granular materials with coevolving grain size and shape

2021 ◽  
Vol 477 (2249) ◽  
Author(s):  
Giuseppe Buscarnera ◽  
Itai Einav
Keyword(s):  
Particle Shape ◽  
Elastic Strain Energy ◽  
Particle Morphology ◽  
Future Research ◽  
Shape Descriptors ◽  
State Variables ◽  
Energy Potential ◽  
Fracture Models ◽  
Engineering Models ◽  
Grain Size And Shape

The influence of particle shape on the mechanics of sand is widely recognized, especially in mineral processing and geomechanics. However, most existing continuum theories for engineering applications do not encompass the morphology of the grains and its evolution during comminution. Similarly, the relatively few engineering models accounting for grain-scale processes tend to idealize particles as spheres, with their diameters considered as the primary and sole geometric descriptor. This paper inspires a new generation of constitutive laws for crushable granular continua with arbitrary, yet evolving, particle morphology. We explore the idea of introducing multiple grain shape descriptors into Continuum Breakage Mechanics (CBM), a theory originally designed to track changes in particle size distributions during confined comminution. We incorporate the influence of these descriptors on the elastic strain energy potential and treat them as dissipative state variables. In analogy with the original CBM, and in light of evidence from extreme fragmentation in nature, the evolution of the additional shape descriptors is postulated to converge towards an attractor. Comparisons with laboratory experiments, discrete element analyses and particle-scale fracture models illustrate the encouraging performance of the theory. The theory provides insights into the feedback among particle shape, compressive yielding and inelastic deformation in crushable granular continua. These results inspire new questions that should guide future research into crushable granular systems using particle-scale imaging and computations.

scholarly journals Effect of Particle Morphology on Stiffness, Strength and Volumetric Behavior of Rounded and Angular Natural Sand

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3023
Author(s):  
Aashish Sharma ◽  
Alexia R. Leib-Day ◽  
Mohmad Mohsin Thakur ◽  
Dayakar Penumadu
Keyword(s):  
Particle Shape ◽  
Triaxial Compression ◽  
Particle Morphology ◽  
Mineralogical Composition ◽  
Friction Angle ◽  
Particle Crushing ◽  
Natural Sand ◽  
One Dimensional ◽  
Uniformity Coefficient ◽  
Crushing Behavior

Stress–strain and volume change behavior for clean sands which have distinct particle shape (rounded and angular) with very similar chemical (mineralogical) composition, size, and texture in one-dimensional (1D) compression and drained triaxial compression are presented. The effect of particle morphology on the crushing behavior in one-dimensional loading is explored using laser light diffraction technique which is suitable for particle crushing because of its high resolution and small specimen volume capability. Particle size distribution in both volume/mass and number distributions are considered for improved understanding associated with the process of comminution. Number distributions present a clearer picture of particle crushing. It is argued that particle crushing in granular assemblies initiates in larger particles, rather than in smaller particle. It was found that rounded sand specimens showed greater crushing than angular sand specimens with higher uniformity coefficient. In 1D compression, loose specimens compress approximately 10% more than dense specimens irrespective of particle shape. Densification of angular sand results in improvement in stiffness (approximately 40%) and is comparable to that of loose rounded sand. In general, density has a greater influence on the behavior of granular materials than particle morphology. The effect of particle shape was found to be greater in loose specimens than in dense specimens. The effect of grain shape on critical state friction angle is also quantified.

scholarly journals Gravel threshold of motion: a state function of sediment transport disequilibrium?

2016 ◽  
Vol 4 (3) ◽  
pp. 685-703 ◽  
Author(s):  
Joel P. L. Johnson
Keyword(s):  
Sediment Transport ◽  
Bedload Transport ◽  
Sediment Supply ◽  
Model Parameters ◽  
Morphologic Change ◽  
State Function ◽  
State Variables ◽  
Flume Experiments ◽  
Power Law Function ◽  
Grain Size And Shape

Abstract. In most sediment transport models, a threshold variable dictates the shear stress at which non-negligible bedload transport begins. Previous work has demonstrated that nondimensional transport thresholds (τc*) vary with many factors related not only to grain size and shape, but also with characteristics of the local bed surface and sediment transport rate (qs). I propose a new model in which qs-dependent τc*, notated as τc(qs)*, evolves as a power-law function of net erosion or deposition. In the model, net entrainment is assumed to progressively remove more mobile particles while leaving behind more stable grains, gradually increasing τc(qs)* and reducing transport rates. Net deposition tends to fill in topographic lows, progressively leading to less stable distributions of surface grains, decreasing τc(qs)* and increasing transport rates. Model parameters are calibrated based on laboratory flume experiments that explore transport disequilibrium. The τc(qs)* equation is then incorporated into a simple morphodynamic model. The evolution of τc(qs)* is a negative feedback on morphologic change, while also allowing reaches to equilibrate to sediment supply at different slopes. Finally, τc(qs)* is interpreted to be an important but nonunique state variable for morphodynamics, in a manner consistent with state variables such as temperature in thermodynamics.

scholarly journals Fast simulation of grain growth based on Orientated Tessellation Updating Method

2020 ◽  
Vol 21 (5) ◽  
pp. 513
Author(s):  
Daniel Weisz-Patrault ◽  
Sofia Sakout ◽  
Alain Ehrlacher
Keyword(s):  
Grain Growth ◽  
Growth Models ◽  
Computational Cost ◽  
Material Point ◽  
General Idea ◽  
Macroscopic Model ◽  
State Variables ◽  
Segregation Of Alloying Elements ◽  
Evolution Laws ◽  
Grain Size And Shape

This work is part of a more general idea consisting in developing a macroscopic model of grain growth whose state variables contain for each material point the statistical descriptors of the microstructure (e.g., disorientation, grain size and shape distributions). The strategy is to determine macroscopic free energy and dissipation potentials on the basis of a large number of computations at the scale of the polycrystal. The aim is to determine enriched macroscopic evolution laws. For sake of simplicity, this contribution only deals with grain growth of a single phased metal without diffusion or segregation of alloying elements. In order to test this upscaling strategy it is necessary to establish a simulation tool at the scale of the polycrystal. It should be sufficiently simple and fast to enable a large number of simulations of various microstructures, even if it leads to neglect some phenomena occurring at this scale. Usual grain growth models relying on mobile finite element modeling, level set functions, phase field or molecular dynamics are too computationally costly to be used within the proposed framework. Therefore, this paper focuses on the development of a “toy” model. Tessellation techniques are usually used to approximate polycrystalline microstructures. Therefore, one can approximate the real evolution of the microstructure as a succession of tessellation approximations. It then becomes quite natural to attempt to establish the evolution law of the microstructure directly on the parameters defining the tessellation. The obtained model is very light in terms of computational cost and enables to compute a large number of evolutions within the framework of the proposed statistical upscaling method.

scholarly journals Numerical Study of Particle Morphology Effect on the Angle of Repose for Coarse Assemblies Using DEM

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Jing Chen ◽  
Rui Gao ◽  
Yangzepeng Liu
Keyword(s):  
Particle Shape ◽  
Laboratory Tests ◽  
Sliding Friction ◽  
Numerical Study ◽  
Dominant Role ◽  
Particle Morphology ◽  
Angle Of Repose ◽  
Shape Effect ◽  
Shape Factors ◽  
Coefficient Of Sliding Friction

The morphologies of coarse particles are usually irregular and play a dominant role in the mechanical behaviors of the particle assemblies. This paper quantitatively studies the effect of particle shape on the angle of repose, which is an important macroscopic parameter for ballast materials, via laboratory tests and numerical simulations by means of the discrete element method (DEM). Forty ballast particle templates and four simply created clump templates are reconstructed using an image-based method and quantified with two shape factors, sphericity and convexity. A series of simulations are conducted with the coefficient of sliding friction between particles changing from 0.2 to 0.6 at an interval of 0.1 to study its influence on various shapes of particles, and an appropriate value of sliding friction coefficient is chosen for the comparison of particle shape effect. The results show that increasing sphericity and convexity can significantly decrease the angle of repose, and the real ballast model gives a more realistic angle of repose behaviors as that of laboratory tests compared to simply created models. By analyzing the characteristics of particle motions and contacts from a microscopic perspective, the mechanism of particle shape attributed to the formation of granular aggregation is also discussed and revealed in this research.

scholarly journals Mammoth grazers on the ocean's minuteness: a review of selective feeding using mucous meshes

2018 ◽  
Vol 285 (1878) ◽  
pp. 20180056 ◽  
Author(s):  
Keats R. Conley ◽  
Fabien Lombard ◽  
Kelly R. Sutherland
Keyword(s):  
Particle Size ◽  
Food Web ◽  
Surface Properties ◽  
Particle Shape ◽  
Feeding Strategy ◽  
Trophic Levels ◽  
Future Research ◽  
Selective Feeding ◽  
Ambient Seawater ◽  
Faecal Pellets

Mucous-mesh grazers (pelagic tunicates and thecosome pteropods) are common in oceanic waters and efficiently capture, consume and repackage particles many orders of magnitude smaller than themselves. They feed using an adhesive mucous mesh to capture prey particles from ambient seawater. Historically, their grazing process has been characterized as non-selective, depending only on the size of the prey particle and the pore dimensions of the mesh. The purpose of this review is to reverse this assumption by reviewing recent evidence that shows mucous-mesh feeding can be selective. We focus on large planktonic microphages as a model of selective mucus feeding because of their important roles in the ocean food web: as bacterivores, prey for higher trophic levels, and exporters of carbon via mucous aggregates, faecal pellets and jelly-falls. We identify important functional variations in the filter mechanics and hydrodynamics of different taxa. We review evidence that shows this feeding strategy depends not only on the particle size and dimensions of the mesh pores, but also on particle shape and surface properties, filter mechanics, hydrodynamics and grazer behaviour. As many of these organisms remain critically understudied, we conclude by suggesting priorities for future research.

Thermodynamic Formulation of Endochronic Cyclic Viscoplasticity With Damage- Application to Eutectic Sn/Pb Solder Alloy

2007 ◽  
Vol 23 (4) ◽  
pp. 433-444 ◽  
Author(s):  
C. F. Lee ◽  
Y. C. Chen
Keyword(s):  
Internal State ◽  
Low Cycle Fatigue ◽  
Cyclic Stress ◽  
Irreversible Thermodynamics ◽  
Damage Parameter ◽  
Fatigue Tests ◽  
Future Research ◽  
Mathematical Form ◽  
State Variables ◽  
Endochronic Theory

AbstractIn this paper, an endochronic theory of cyclic viscoplasticy with damage is established based on the irreversible thermodynamics of continuous media with internal state variables containing an isotropic damage parameter. The constitutive equations derived have the same mathematical form as those of convectional endochronic theory without damage, except the effective stress with damage is used. This result coincides with the Lemaitre's statements of stain equivalence principle.Using the experimental cyclic stress-strain curves of 63Sn/37Pb solder bars, corrected from the uniaxially constant displacement amplitude cyclic tests under MTS Tytron microtester, the computational results of cyclic stess-strain curves with several degrees of damage can reproduce the experimental data quite well. Based on compressive buckling appeared in the vicinity of the compressive end parts of the hysteresis loop, the critical values of damage are determined between 0.3 and 0.4.The evolution equation of damage proposed in terms of the intrinsic damage time scale and its results in the modified Coffin-Manson LCF law can be extended in the future research for a statistical theory of life distribution under low cycle fatigue tests.

scholarly journals Upper Bounds on Return Predictability

2017 ◽  
Vol 52 (2) ◽  
pp. 401-425 ◽  
Author(s):  
Dashan Huang ◽  
Guofu Zhou
Keyword(s):  
Stock Returns ◽  
Upper Bounds ◽  
Future Research ◽  
State Variables ◽  
Discount Factors ◽  
Predictive Regressions ◽  
Market Portfolio ◽  
Stochastic Discount Factors ◽  
Highly Correlated ◽  
Using Data

Can the degree of predictability found in data be explained by existing asset pricing models? We provide two theoretical upper bounds on theR2of predictive regressions. Using data on the market portfolio and component portfolios, we find that the empiricalR2s are significantly greater than the theoretical upper bounds. Our results suggest that the most promising direction for future research should aim to identify new state variables that are highly correlated with stock returns instead of seeking more elaborate stochastic discount factors.

scholarly journals Particle shape characterisation and classification using automated microscopy and shape descriptors in batch manufacture of particulate solids

Particuology ◽  
2016 ◽  
Vol 24 ◽  
pp. 61-68 ◽  
Author(s):  
Yang Zhang ◽  
Jing J. Liu ◽  
Lei Zhang ◽  
Jorge Calderon De Anda ◽  
Xue Z. Wang
Keyword(s):  
Particle Shape ◽  
Shape Descriptors ◽  
Particulate Solids ◽  
Automated Microscopy

Deformation Kinetics of Steady Creep in Sn/Pb Solder Alloys With Applications

2004 ◽  
Vol 20 (2) ◽  
pp. 85-93 ◽  
Author(s):  
C. F. Lee ◽  
M. K. Chang ◽  
W. K. Chung
Keyword(s):  
Constitutive Equation ◽  
Internal State ◽  
Tensile Creep ◽  
Future Research ◽  
State Variables ◽  
Steady Creep ◽  
Solder Alloys ◽  
Creep Tests ◽  
Shear Creep ◽  
Deformation Kinetics

AbstractIn this paper, a constitutive equation of steady creep rates:is derived based on a liaison of the theory of irreversible thermodynamics of continuous media with internal state variables (ISV); and the deformation kinetics. In steady creep, only one ISV is used, whose evolution equation is derived by the concepts of deformation kinetics, in which micromotions are generated by a group of atoms climbing over a tilted potential barrier of the highest height ε0.Applications of the constitutive equation in the cases of some Sn/Pb solder alloys-63Sn/37Pb, 60Sn/40Pb and 97.5Pb/2.5Sn under shear creep tests; and 98Pb/2Sn under tensile creep tests, show that the theoretical results can describe the experimental data quite well. These results pave the way for future research in the comparisons of creep resistance among solders with various Sn/Pb compositions and in the generalization of three-dimensional constitutive equation.

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