Jamming Limit Research Articles

Influence of Fiber Volume Fraction on the Predictability of UD FRP Ply Behavior: A Validated Micromechanical Virtual Testing Approach.

Enhancing the understanding of the behavior, optimizing the design, and improving the predictability and reliability of manufactured unidirectional (UD) FRP plies, which serve as primary building blocks for structural FRP laminates and components, are crucial to achieving a safe and cost-effective design. This research investigated the influence of fiber volume fraction (vf) on the predictability and reliability of the homogenized elastic properties and damage initiation strengths of two different types of UD FRP plies using validated micromechanical virtual testing for representative volume element (RVE) models. Several sources of uncertainties were included in the RVE models. This study also proposed a modified algorithm for microstructure generation and explored the effect of vf on the optimal sizes of the RVE in terms of fiber number. Virtual tests were systematically conducted using full factorial DOE coupled with Monte Carlo simulation. The modified algorithm demonstrated exceptional performance in terms of convergence speed and jamming limit, significantly reducing the time required to generate microstructures. The developed RVE models accurately predicted failure modes, loci, homogenized elastic properties, and damage initiation strengths with a mean error of less than 5%. Also, it was found that increasing vf led to a concurrent increase in the optimal size of the RVE. While it was found that the vf had a direct influence on homogenized elastic properties and damage initiation strengths, it did not significantly affect the reliability and predictability of these properties, as indicated by low correlation coefficients and fluctuations in the coefficient of variation of normalized properties.

High‐fidelity random fiber distribution algorithm based on fiber spreading process

AbstractThe performance of fiber‐reinforced composites is not only determined by their constituents, but also by the spatial distribution of inclusions. The traditional random distribution algorithm only considers the randomness of its relative position, and every newly generated fiber has to be checked with all the existing fibers, which requires a large amount of calculation. In this paper, inspired by the spreading process that the fibers are not arranged randomly, but the forces acting on the upper and lower rows of fibers. A random fiber distribution algorithm based on partition randomness is proposed, and a microscopic model of in‐plane fibers with random distribution is established. The maximum volume fraction of fibers generated by the algorithm is 75%, and the generation time is less than 20s. Statistical characterization and finite element analysis of the structure generated by the algorithm are compared with the experimental data to verify the randomness and effectiveness of fibers. The algorithm overcomes the jamming limit of the traditional hard‐core method, and can efficiently generate random microstructure models with different volume fractions, which can be a promising alternative for modeling and analysis of unidirectional fiber‐reinforced composites.

Greedy-based approach for generating anisotropic random fiber distributions of unidirectional composites and transverse mechanical properties prediction

A novel adaptive greedy-based generation (GBG) algorithm is proposed to generate 2D random distribution of fibers for unidirectional composites. Inspired by greedy algorithm, the “fitness function” is introduced to better overcome the jamming limit of the traditional hard‐core method than most published algorithms and generate representative volume element (RVE) with high fiber volume fraction adaptively. The good agreement of statistical analysis with experiments suggests that the generated anisotropic RVEs is statistically equivalent to real composites. The influence of anisotropy on mechanical properties and progressive failure process is further revealed based on finite element method (FEM) using a progressive damage model. The results show that the predicted transverse elastic and strength properties are both anisotropic, which is not consistent with the traditional transverse isotropic hypothesis. The proposed algorithm can generate RVEs with high fiber volume fraction (up to 80%) and provide anisotropic RVEs statistically equivalent to real composites, and thus can serve as a promising method to guide the design and analysis of composites.

Predicting Defects in Soft Sphere Packings near Jamming Using the Force Network Ensemble.

Amorphous systems of soft particles above jamming have more contacts than are needed to achieve mechanical equilibrium. The force network of a granular system with a fixed contact network is thus underdetermined and can be characterized as a random instantiation within the space of the force network ensemble. In this Letter, we show that defect contacts that are not necessary for stability of the system can be uniquely identified by examining the boundaries of this space of allowed force networks. We further show that, for simulations in the near jamming limit, this identification is nearly always correct and that defect contacts are broken under decompression of the system.

Simulation study of random sequential deposition of binary mixtures of lattice animals on a three-dimensional cubic lattice

Random sequential adsorption of mixtures of objects of various shapes on a three-dimensional (3D) cubic lattice is studied numerically by means of Monte Carlo simulations. Depositing objects are ‘lattice animals’, made of a certain number of nearest neighbor sites on a lattice. We analyzed binary mixtures composed of shapes of equal size, n = 3, 4, 5. We concentrate here on the influence of geometrical properties of the shapes on the jamming coverage θ J and on the temporal evolution of the density θ(t). The approach of the coverage θ(t) to the jamming limit θ J is found to be exponential, θ J − θ(t) ∼ exp(−t/σ), both for the mixtures and their components. The values of the relaxation time σ are determined by the number of different orientations m that lattice animals can take when placed on a cubic lattice. The value of the relaxation time σ for a mixture is approximately twice the relaxation time for the pure component shape with a larger number m of possible orientations. Depending on the local geometry of the objects making the mixture, the jamming coverage of a mixture θ J can be either greater than both single-component jamming coverages or it can be in between these values. The first case is the most common, while in the second case, the jamming density of the mixture is very close to the higher jamming density for the pure component shapes. For a majority of the investigated mixtures, a component with a larger number of orientations m has a larger value of the fractional jamming density.

Advances in the Rheological Characterization of Slurries of Elongated Particles

Inherent challenges regarding the rheological characterization of slurries of elongated particles have necessitated the development of alternatives to standardized rheometers. These methods of measurement, and the associated advances in the quantification of shear and normal stress measurements, are described. Also, recent advances in modeling and predictive capabilities are summarized. During shearing flows, confinement substantially influences the orientation distribution of the particles; this change in the microstructure impacts the rheology, even as the smallest confining dimension exceeds seven particle lengths. The slow development of the orientation distributions renders additional difficulties in evaluating the rheology. Achievements of the measurement methods include a universal shear viscosity as a function of concentration for a wide range of particle lengths to diameters (aspect ratios). The jamming limit (divergence of the viscosity with concentration) of the suspensions has been also shown to scale differently than for spheres. More general dynamics of the suspensions and the additional needs for measurement improvements are discussed.

Generation of random fiber distributions in fiber reinforced composites based on Delaunay triangulation

This paper presents a new method for generating the random fiber distributions of carbon fiber reinforced plastic with high volume fraction. The novelty is that an adaptive fiber shaking module is developed on the basis of Delaunay triangulation and combined with the proposed algorithm. The adaptability is to realize coordination between the parameters of fiber volume fraction and fiber spacing, in order to overcome the jamming limit and eliminate the unreasonable resin-rich zone that may appear at the boundary of the microstructures. The maximum fiber volume fraction reached is 67.43%. Statistical analysis is conducted on the generated microstructures, and there is a good agreement by comparing it with the statistical results of random sequential expansion algorithm and completely spatial random pattern. Finite element analysis is also performed to predict the elastic properties of the generated microstructures. It shows that a maximum absolute error is only 7.354% in elastic property by comparing with the experimental and simulation results in literatures. The proposed algorithm contributes to the further researches on the strength and micro-damage evolution of carbon fiber reinforced plastic.

Honeycomb-based method for generating random fiber distributions of fiber reinforced composites and transverse mechanical properties prediction

This paper proposes an innovative honeycomb-based algorithm to generate the random fiber distributions geometry of the unidirectional laminate with high fiber volume fraction, which can reach 75% or even higher. This algorithm overcomes the jamming limit appeared in traditional hard-core algorithms and lots of iterative computation required in most of the published algorithms. Then a progressive damage model is used to evaluate the prediction capacity of the fiber distribution model generated by the new algorithm. The present results are compared with the experimental and predicted ones from other different fiber distribution models. Moreover, load direction effect on the predicted results is discussed using the coefficient of variation. Finally, a fiber distribution is generated with the fiber volume fraction of 75% to validate the prediction capability of the honeycomb-based distribution model with high fiber volume fraction.

Simulation Studies of Random Sequential Adsorption (RSA) of Mixture of Two-Component Circular Discs

We study Random Sequential Adsorption (RSA) of mixture of two-component circular discs on a two-dimensional continuum substrate by computer simulation for different values of radius ratio $${r}_{A}/{r}_{B}$$ , $$({r}_{A}<{r}_{B})$$ , and relative rate constant $$k = {k}_{A}/{k}_{B}$$ between the discs. For smaller values of radius ratio and all values of relative rate constant between the discs, the approach of instantaneous surface coverage $$\theta (t)$$ to the jammed state surface coverage $$\theta (\infty )$$ of larger and smaller discs, is found to obey a power law behavior $$\theta \left(\infty \right)-\theta (t)\sim {t}^{-p}$$ , separately. For larger values of radius ratio and relative rate constant $$k$$ , the approach is found to obey same power law. Total surface coverage of binary mixture $$\theta (\infty )$$ for all the cases is found always greater than 54.7%, the one component jamming limit. Also, it is found that for a given radius ratio $${r}_{A}/{r}_{B}$$ , there is an optimum value of relative rate constant $$k = {k}_{A}/{k}_{B}$$ for which jamming coverage $$\theta (\infty )$$ is maximum. Also, our study shows that in case of adsorption of a binary mixture of circular discs of a given radius ratio $${r}_{A}/{r}_{B}$$ , relative rate constant $$k$$ can be fixed in order to get maximum or desired surface coverage. Microstructural properties of the coverings formed by RSA of binary mixture of circular discs are studied by analyzing radial distribution function and volume distribution of pores.

Density distribution functions of random sequential adsorption on a [formula omitted] lattice

Random sequential adsorption (RSA) is an irreversible random deposition process with short range exclusion interaction. It is shown that the distribution function of the occupation densities at the jamming limit of a RSA process on a 2×n lattice converges for n→∞ to a Gaussian around an average density. The second moment decreases like 1∕n.

Enhanced stability of free viscous films due to surface viscosity

The stability of a thin liquid film bounded by two free surfaces is examined in the presence of insoluble surface-active agents. This study is broadly aimed at understanding enhanced stability of emulsions with the increasing surface concentration of surface-active agents. Surface-active agents not only cause gradients in surface tension but could also render surface viscosity to be significant, which could vary with surface concentration. We employ two phenomenological models for surface viscosity, a linear viscosity model and a nonlinear viscosity model. In the latter, surface viscosity diverges at a critical concentration, which is termed the “jamming” limit. We show that rupture can be significantly delayed with high surface viscosity. An analysis of the “jamming” limit reveals that Γi(nl)&amp;gt;3D/M provides a simple criterion for enhanced stability, where Γi(nl), D, and M are the normalized initial surfactant concentration, disjoining pressure number, and Marangoni number, respectively. Nonlinear simulations suggest that high surface viscosity renders free films remarkably stable in the jamming limit, and their free surfaces behave like immobile interfaces consistent with experimental observations. Furthermore, it is shown that rupture times can be arbitrarily increased by tuning the initial surfactant concentration, offering a fluid dynamical route to stabilization of thin films.

Random sequential adsorption of lattice animals on a three-dimensional cubic lattice

The properties of the random sequential adsorption of objects of various shapes on simple three-dimensional (3D) cubic lattice are studied numerically by means of Monte Carlo simulations. Depositing objects are "lattice animals," made of a certain number of nearest-neighbor sites on a lattice. The aim of this work is to investigate the impact of the geometrical properties of the shapes on the jamming density θ_{J} and on the temporal evolution of the coverage fraction θ(t). We analyzed all lattice animals of size n=1, 2, 3, 4, and 5. A significant number of objects of size n⩾6 were also used to confirm our findings. Approach of the coverage θ(t) to the jamming limit θ_{J} is found to be exponential, θ_{J}-θ(t)∼exp(-t/σ), for all lattice animals. It was shown that the relaxation time σ increases with the number of different orientations m that lattice animals can take when placed on a cubic lattice. Orientations of the lattice animal deposited in two randomly chosen places on the lattice are different if one of them cannot be translated into the other. Our simulations performed for large collections of 3D objects confirmed that σ≅m∈{1,3,4,6,8,12,24}. The presented results suggest that there is no correlation between the number of possible orientations m of the object and the corresponding values of the jamming density θ_{J}. It was found that for sufficiently large objects, changing of the shape has considerably more influence on the jamming density than increasing of the object size.

How clay particulates affect flow cessation and the coiling stability of yield stress-matched cementing suspensions

The remarkable increase in the flow resistance of dense suspensions can hinder 3D-printing processes on account of flow cessation in the extruder, and filament fragility/rupture following deposition. Understanding the nature of rheological changes that occur is critical to manipulate flow conditions or to dose flow modifiers for 3D-printing. Therefore, this paper elucidates the influences of clay particulates on controlling flow cessation and the shape stability of dense cementing suspensions that typically feature poor printability. A rope coiling method was implemented with varying stand-off distances to probe the buckling stability and tendency to fracture of dense suspensions that undergo stretching and bending during deposition. The contributions of flocculation and short-term percolation due to the kinetics of structure formation to deformation rate were deconvoluted using a stepped isostress method. It is shown that the shear stress indicates a divergence with a power-law scaling when the particle volume fraction approaches the jamming limit; φ → φj ≈ φmax. Such a power-law divergence of the shear stress decreases by a factor of 10 with increasing clay dosage. Such behavior in clay-containing suspensions arises from a decrease in the relative packing fraction (φ/φmax) and the formation of fractally-architected aggregates with stronger interparticle interactions, whose uniform arrangement controls flow cessation in the extruder and suspension homogeneity, thereby imparting greater buckling stability. The outcomes offer new insights for assessing/improving the extrudability and printability behavior during slurry-based 3D-printing process.

An efficient method to generate random distribution of fibers in continuous fiber reinforced composites

AbstractThis paper presents a new method based on iterative improvement to generate the random microstructure of continuous fiber reinforced composite with high fiber volume fraction (up to 70%), overcoming the jamming limit of the traditional random sequential adsorption (RSA) method. The novelty of the proposed method lies in an iterative improvement of the generated microstructure through separating initially randomly set positions of the fibers. Without complex heuristic steps, this algorithm can generate different fiber distributions with fast speed and good randomness. The offset magnitude of the separation process is adjusted according to fiber volume fractions to speed up the generation. Statistical analysis is performed on the generated fiber distribution. Five descriptors including Voronoi polygon area, nearest neighbor distances, nearest neighbor orientation, Ripley's K function and pair distribution function are used to compare the proposed algorithm and the RSA with completely spatial random distribution for both short and far distances. Fiber distributions generated by this new algorithm are proved to have good randomness. An finite element analysis (FEA) example is also presented to predict the effective elastic property of the carbon fiber epoxy composites, and a reasonable agreement with the experimental result is achieved. The proposed algorithm provides a useful tool to generate micromechanical models that can be used to predict and understand the mechanical behavior of fiber reinforced composites.

A novel FastRSA algorithm: Statistical properties and evolution of microstructure

While the Random Sequential Adsorption (RSA) process for the generation of 2D geometries containing discrete entities has been extensively studied, both in terms of numerical simulations and in terms of its statistical properties, all the mechanisms involved are not fully understood, especially in dense configurations of elongated particles. This is mainly due to the very slow asymptotic approach to high packing configurations, especially when highly elongated particles are involved, which makes the creation of such configurations a time consuming task. For the estimation of the statistical properties of such configurations we therefore have to resort to extrapolations that do not always give accurate results. In this work we reveal the interaction of the mechanisms that come into play in the RSA process. We specifically show that the overall result of an RSA process is the summary outcome of these interwoven mechanisms, namely those involving the formation and destruction of Particle Area, Overlap Area and Influence Area – terms which we introduce and define in this work – resulting in a behavior that often appears counter-intuitive. We also show the shift of their importance as the particle aspect ratio α varies and explain how nematic structures are created when high aspect ratio particles are involved as well as the mechanisms behind their appearance. Following this, we propose a new algorithm for the process of random sequential adsorption (named FastRSA) which is capable of creating very high count configurations through all the range of particle aspect ratios and which follows Feder’s law with a θ∼τ−1∕2 behavior instead of the θ∼τ−1∕3 of the classic approach, where τ is the number of attempts to place a particle and θ is the degree of packing. We show how the new algorithm can be coupled with the classic RSA approach and point out the benefits of such a coupling. Use of the FastRSA algorithm has enabled us to study the evolution of the extent of packing using actual geometries, without the need to resolve to extrapolations and assumptions. For the case of highly elongated particles, this is the first time in our knowledge that estimations of maximum packing from actual configurations near the jamming limit have been obtained.

Phase-resolving simulation of dense bubble clusters under periodic shear

The paper studies the response of a cluster of bubbles to osmotic pressure, and steady and oscillatory shearing by detailed numerical simulations. In contrast to other investigations, the movement of the interstitial fluid is fully resolved. To that end, an immersed-boundary method is employed, yielding the trajectory of each bubble and the flow and pressure field of the fluid. Additionally, a physically motivated collision model ensures realistic bubble interactions. Furthermore, a suitable numerical configuration is proposed which allows imposing osmotic pressure and shear in a way that integrates well into the simulation without generating artefacts. This method allows for the realistic investigation of the compression of bubbles across the jamming limit, demonstrating the influence of the inertia of the interstitial fluid. Applying oscillatory shearing with varying osmotic pressure, shear stress and frequency, the occurrence of shear bands is demonstrated and the influence on rheometric measurements is discussed.

Combined Lattice–Boltzmann and rigid-body method for simulations of shear-thickening dense suspensions of hard particles

We present a high-fidelity simulation model for dense suspensions of spherical and non-spherical particles suspended in a Lattice–Boltzmann Method (LBM) based fluid. The non-spherical particles are composed of an arbitrary number of overlapping spheres of different sizes and arbitrary relative positions in the particle reference frame which stay fixed during the simulation. This approach allows to approximate a wide range of rigid particle shapes. Fluid Structure Interactions (FSI) are realized using a hybrid of immersed-boundary methods and bounce-back schemes, that employs coupling coefficients dependent upon particle overlap with the fluid lattice, resulting in smooth hydrodynamic interactions when particles move over the lattice. Numerical lubrication breakdown is overcome by applying appropriate corrections for small inter-particle gaps and hydrodynamic interactions are resolved down to scales much smaller than the LBM lattice spacing. For improved numerical stability in the limit of stiff particle-particle interactions, a generalized-α method together with a dynamically refined time-step is used for rigid body dynamics. An unbounded shear flow with large shear rates is realized by splitting the computational domain into multiple co-moving reference frames coupled through Galilean transformations of both fluid and particle phase. For fast simulations of hundreds of particles over physical times-spans of seconds, the LBM sub-model and FSI computations are accelerated on GPUs and MPI/OpenMP are used to parallelize the computation over networked/shared-memory resources. All these innovations together lead to a very powerful simulation environment for sheared dense suspensions, facilitating study of rheology close to the jamming limit. In this paper we present benchmark results and simulations of continuous and discontinuous shear-thickening of dense polydisperse frictional suspensions, demonstrating the accuracy and predictive power of the model over a large range of volume fractions of suspended particles and a large range of shear rates.

Higher-order corrections to the effective potential close to the jamming transition in the perceptron model.

In view of the results achieved in a previously related work [A. Altieri, S. Franz, and G. Parisi, J. Stat. Mech. (2016) 093301]10.1088/1742-5468/2016/09/093301, regarding a Plefka-like expansion of the free energy up to the second order in the perceptron model, we improve the computation here focusing on the role of third-order corrections. The perceptron model is a simple example of constraint satisfaction problem, falling in the same universality class as hard spheres near jamming and hence allowing us to get exact results in high dimensions for more complex settings. Our method enables to define an effective potential (or Thouless-Anderson-Palmer free energy), namely a coarse-grained functional, which depends on the generalized forces and the effective gaps between particles. The analysis of the third-order corrections to the effective potential reveals that, albeit irrelevant in a mean-field framework in the thermodynamic limit, they might instead play a fundamental role in considering finite-size effects. We also study the typical behavior of generalized forces and we show that two kinds of corrections can occur. The first contribution arises since the system is analyzed at a finite distance from jamming, while the second one is due to finite-size corrections. We nevertheless show that third-order corrections in the perturbative expansion vanish in the jamming limit both for the potential and the generalized forces, in agreement with the isostaticity argument proposed by Wyart and coworkers. Finally, we analyze the relevant scaling solutions emerging close to the jamming line, which define a crossover regime connecting the control parameters of the model to an effective temperature.

Modified Random Sequential Adsorption Model for Understanding Kinetics of Proteins Adsorption at a Liquid-Solid Interface.

In this Article, we experimentally measure the adsorption kinetics of human serum albumin (HSA) on a hydrophobic hexadecanethiolated gold surface. We use micromachined quartz crystal resonators with fundamental frequency of 83 MHz to accomplish these measurements in real time. In this work, we focus on two key results: (i) asymptotic behavior of the sensor responses upon HSA adsorption and (ii) the jamming limit of adsorbed layer formed by both single-injection and multi-injection experiments with the same value of final concentration. We develop a new interface-depletion modified random sequential adsorption (RSA) model to elucidate the adsorption kinetics and the transport properties of the protein molecules. Analysis of the experimentally measured data shows that the results can be explained on the basis of the exponentially depleting interfacial layer RSA model. To better understand the origin of the formation of the interfacial depletion region where the supply of protein molecules is dramatically reduced, we performed a series of molecular dynamics (MD) simulations using the ReaxFF method. These simulations predict that the resulting adsorption of the protein molecules on the thiolated surface results in a specific orientation at the interface and the diffusion constant of the protein molecules in this layer is significantly reduced. This interplay between the surface adsorption rate and the reduced diffusion coefficient leads to the depletion of the protein molecules in the interfacial layer where the concentration of the protein molecules is much less than the bulk concentration and explains the observed slowdown of the HSA adsorption characteristics on a hydrophobic surface.

Kinetics of particle deposition at heterogeneous surfaces

The random sequential adsorption (RSA) approach is used to analyze adsorption of spherical particles of fixed diameter d0 on nonuniform surfaces covered by square cells arranged in a square lattice pattern. To characterize such pattern two dimensionless parameters are used: the cell size α and the cell–cell separation β, measured in terms of the particle diameter d0. Adsorption is assumed to occur if the particle (projected) center lies within a cell area. We focus on the kinetics of deposition process in the case when no more than a single disk can be placed onto any square cell (α<1∕2≈0.707). We find that the asymptotic approach of the coverage fraction θ(t) to the jamming limit θJ is algebraic if the parameters α and β satisfy the simple condition, β+α∕2<1. If this condition is not satisfied, the late time kinetics of deposition process is not consistent with the power law behavior. However, if the geometry of the pattern approaches towards “noninteracting conditions” (β>1), when adsorption on each cell can be decoupled, approach of the coverage fraction θ(t) to θJ becomes closer to the exponential law. Consequently, changing the pattern parameters in the present model allows to interpolate the deposition kinetics between the continuum limit and the lattice-like behavior. Structural properties of the jammed-state coverings are studied in terms of the radial distribution function g(r) and spatial distribution of particles inside the cell. Various, non-trivial spatial distributions are observed depending on the geometry of the pattern.