Work on radiation transport in stochastic media has tended to focus on binary mixing with Markovian mixing statistics. However, although some real-world applications involve only two materials, others involve three or more. Therefore, we seek to provide a foundation for ongoing theoretical and numerical work with āN-aryā stochastic media comprised of discrete material phases with spatially homogenous Markovian mixing statistics. To accomplish this goal, we first describe a set of parameters and relationships that are useful to characterize such media. In doing so, we make a noteworthy observation: media that are frequently called Poisson media only comprise a subset of those that have Markovian mixing statistics. Since the concept of correlation length (as it has been used in stochastic media transport literature) and the hyperplane realization generation method are both tied to the Poisson property of the media, we argue that not all media with Markovian mixing statistics have a correlation length in this sense or are realizable with the traditional hyperplane generation method. Second, we describe methods for generating realizations of N-ary media with Markovian mixing. We generalize the chord- and hyperplane-based sampling methods from binary to N-ary mixing and propose a novel recursive hyperplane method that can generate a broader class of material structures than the traditional, non-recursive hyperplane method. Finally, we perform numerical studies that provide validation to the proposed N-ary relationships and generation methods in which statistical quantities are observed from realizations of ternary and quaternary media and are shown to agree with predicted values.
Two key mechanical processes exist in the formation of powder compacts. These include the complex kinematics of particle rearrangement as the powder is densified and particle deformation leading to mechanical failure and fragmentation. Experiments measuring the time varying forces across a densifying powder bed have been performed in powders of microcrystalline cellulose with mean particle sizes between 0.4 and 1.2 mm. In these experiments, diagnostics measured the applied and transmitted loads and the bulk powder density. Any insight into the particle behavior must be inferred from deviations in the smoothly increasing stress-density compaction relationship. By incorporating a window in the compaction die body, simultaneous images of particle rearrangement and fracture at the confining window are captured. The images are post-processed in MATLABĀ® to track individual particle motion during compression. Complimentary discrete element method (DEM) simulations are presented and compared to experiment. The comparison provides insight into applying DEM methods for simulating large or permanent particle deformation and suggests areas for future study.
In this paper we introduce a method to compare sets of full-field data using Alpert tree-wavelet transforms. The Alpert tree-wavelet methods transform the data into a spectral space allowing the comparison of all points in the fields by comparing spectral amplitudes. The methods are insensitive to translation, scale and discretization and can be applied to arbitrary geometries. This makes them especially well suited for comparison of field data sets coming from two different sources such as when comparing simulation field data to experimental field data. We have developed both global and local error metrics to quantify the error between two fields. We verify the methods on two-dimensional and three-dimensional discretizations of analytical functions. We then deploy the methods to compare full-field strain data from a simulation of elastomeric syntactic foam.
This report describes the efforts to characterize and model General Plastics TF6070 and EF4000 flexible polyurethane foams under room temperature, large deformation quasi-static cyclic mechanical loading conditions. Densities from three to fifteen pound per cubic foot (PCF) are examined, which correspond to relative densities of approximately 4 to 20%. These foams are open cell structured and flexible at room temperature with a glass transition transition less than -30Ā°C, and they fully recover their original shape when unloaded (at room temperature). Uniaxial compression tests were conducted with accompanying lateral image series for Digital Image Correlation (DIC) analysis with the goal of extracting transverse strain responses. Due to difficulties with DIC analysis at large strains, lateral strains were instead extracted for each test via edge tracking. The experimental results exhibit a nonlinear elastic response and anisotropic material behavior (particularly for the lower densities). Some hysteresis is observed that is different between the first and subsequent cycles of deformation indicating both a small degree of permanent damage (reduced stiffness during reloading) and viscoelasticity. These inelastic mechanisms are not considered in the modeling and calibration in this report. This work considers only the rate independent, room temperature foam behavior. Individual foam densities were calibrated for loading in two directions, parallel and perpendicular to the foam bubble rise direction, since the mechanical behavior is different in these two directions. The Flex Foam constitutive model was used for all parameterizations despite the fact that the model is isotropic. A review of the constitutive model is given as well as necessary data reduction procedures to parameterize it for each foam density and orientation are discussed. Finally, two different parameterizations are developed that take the undeformed foam density as an input that span all densities considered. These two parameterized models represent foams loaded in the rise and transverse directions respectively. We summarize the assumptions and limitations of the parameterizations provided in this report to guide analysis choices with them. All parameterizations presented herein have the following traits, room temperature, rate independent, damage-free, and non-dissipative . Isotropy (even if they are representing anisotropic data). Supplied Sierra Solid Mechanics Flex Foam Model Inputs are in units: pounds, inches, Celsius, and seconds
Intuition tells us that a rolling or spinning sphere will eventually stop due to the presence of friction and other dissipative interactions. The resistance to rolling and spinning or twisting torque that stops a sphere also changes the microstructure of a granular packing of frictional spheres by increasing the number of constraints on the degrees of freedom of motion. We perform discrete element modeling simulations to construct sphere packings implementing a range of frictional constraints under a pressure-controlled protocol. Mechanically stable packings are achievable at volume fractions and average coordination numbers as low as 0.53 and 2.5, respectively, when the particles experience high resistance to sliding, rolling, and twisting. Only when the particle model includes rolling and twisting friction were experimental volume fractions reproduced.
Thermal sprayed metal coatings are used in many industrial applications, and characterizing the structure and performance of these materials is vital to understanding their behavior in the field. X-ray Computed Tomography (CT) machines enable volumetric, nondestructive imaging of these materials, but precise segmentation of this grayscale image data into discrete material phases is necessary to calculate quantities of interest related to material structure. In this work, we present a methodology to automate the CT segmentation process as well as quantify uncertainty in segmentations via deep learning. Neural networks (NNs) are shown to accurately segment full resolution CT scans of thermal sprayed materials and provide maps of uncertainty that conservatively bound the predicted geometry. These bounds are propagated through calculations of material properties such as porosity that may provide an understanding of anticipated behavior in the field.
In this work, we investigated microstructural features of elastomeric foam with the goal of identifying descriptors other than porosity that have a significant effect on the macroscale mechanical response. X-ray computed tomography (XCT) provided three-dimensional images of several flexible polyurethane foam samples prior to mechanical testing. The samples were then compressed to approximately 80% engineering strain. Stereo digital image correlation was used to measure the three-dimensional surface displacement data, from which strain was determined. The strain data, which were calculated with respect to the undeformed coordinates, were then overlaid on the corresponding surface generated from XCT. Heterogeneities in the strain-field were cross-correlated with topological quantities such as pore size distribution. A statistically significant correlation was identified between the distance transform of the pore phase and strain fluctuations.
Using random walk analyses we explore diffusive transport on networks obtained from contacts between isotropically compressed, monodisperse, frictionless sphere packings generated over a range of pressures in the vicinity of the jamming transition pā0. For conductive particles in an insulating medium, conduction is determined by the particle contact network with nodes representing particle centers and edges contacts between particles. The transition rate is not homogeneous, but is distributed inhomogeneously due to the randomness of packing and concomitant disorder of the contact network, e.g., the distribution of the coordination number. A narrow escape time scale is used to write a Markov process for random walks on the particle contact network. This stochastic process is analyzed in terms of spectral density of the random, sparse, Euclidean and real, symmetric, positive, semidefinite transition rate matrix. Results show network structures derived from jammed particles have properties similar to ordered, euclidean lattices but also some unique properties that distinguish them from other structures that are in some sense more homogeneous. In particular, the distribution of eigenvalues of the transition rate matrix follow a power law with spectral dimension 3. However, quantitative details of the statistics of the eigenvectors show subtle differences with homogeneous lattices and allow us to distinguish between topological and geometric sources of disorder in the network.