19 research outputs found
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Prediction of Incipient Damage Sites in Composites using Classifiers
This paper describes a method for predicting locations in a two-phase material where effective elastic strain is concentrated above a specified threshold value by virtue of the local arrangement of phases and a specified set of boundary conditions. This prediction is made entirely based on knowledge of the material properties of the phases, their spatial arrangement, and the boundary conditions, and does not require numerical solution of the equations of elasticity. The example problem is a 2D idealization of a fiber- or particle-reinforced composite in which the fibers/particles are randomly placed in the matrix and the boundary conditions correspond to uniaxial extension. The method relies on a moving window implementation of a decision tree classifier that predicts, for all points in the material, whether the effective elastic strain will exceed a specified threshold value. The classifier operates on a set of attributes that are the coefficients of a series expansion of a discretized version of the phase geometry. The basis vectors appearing in this series expansion of the phase geometry are derived from a principal components analysis of a set of training samples for which the mechanical response is calculated using finite element analysis. These basis vectors allow the accurate representation of the phase geometry with many fewer parameters than is typical, and, because the training samples contain information regarding the mechanical response of the material, also allow prediction of the response using a classifier that takes a relatively small number of input attributes. The predictive classifier is tested on simulated two-phase material samples that are not part of the original training set, and correctly predicts whether efffective elastic strain will be elevated above a specified threshold with greater than 90% accuracy
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Statistics and probabilistic modeling of simulated intergranular cracks
Using Monte Carlo simulation, the statistical properties of intergranular crack trajectories in polycrystalline materials are estimated. The polycrystalline microstructures are two dimensional and are modeled by a Poisson–Voronoi tessellation for the grain geometry and a uniform orientation distribution function for the crystallographic orientation. A heuristic is introduced for determining the path of crack propagation when the crack tip arrives at a grain boundary triple junction. This heuristic applies a combination of two criteria for determining the direction of crack propagation, the maximum circumferential stress criterion, and a criterion in which the crack is assumed to propagate in the direction with the least material resistance. The resistance of grain boundaries is assumed to be related to the crystallographic misorientation at the grain boundary. The trajectories of microcracks can be treated as a random process, and simulation results indicate that the crack process exhibits linear variance growth, the rate of which is related to the importance attached to the circumferential stress and the material resistance in determining the direction of propagation. The rate of variance growth is shown to vary with the average grain diameter, so that microcracks in polycrystals with small grain size will exhibit less spatial uncertainty. The statistics and distributions of the increments of the crack process are also given. Through a small change made to the normalization applied to non-dimensionalize the statistics, the results are extended to polycrystals that have spatially varying grain size. Finally, a probabilistic model is proposed that is able to produce synthetic crack trajectories that replicate the important statistical properties of the simulated cracks. Such a model may prove useful in studies of the transition from micro to macrocracking
Burrowing in marine muds by crack propagation: kinematics and forces
The polychaete Nereis virens burrows through muddy sediments by exerting dorsoventral forces against the walls of its tongue-depressor-shaped burrow to extend an oblate hemispheroidal crack. Stress is concentrated at the crack tip, which extends when the stress intensity factor (KI) exceeds the critical stress intensity factor (KIc). Relevant forces were measured in gelatin, an analog for elastic muds, by photoelastic stress analysis, and were 0.015±0.001 N (mean ± s.d.; N=5). Measured elastic moduli (E) for gelatin and sediment were used in finite element models to convert the forces in gelatin to those required in muds to maintain the same body shapes observed in gelatin. The force increases directly with increasing sediment stiffness, and is 0.16 N for measured sediment stiffness of E=2.7×104 Pa. This measurement of forces exerted by burrowers is the first that explicitly considers the mechanical behavior of the sediment. Calculated stress intensity factors fall within the range of critical values for gelatin and exceed those for sediment, showing that crack propagation is a mechanically feasible mechanism of burrowing. The pharynx extends anteriorly as it everts, extending the crack tip only as far as the anterior of the worm, consistent with wedge-driven fracture and drawing obvious parallels between soft-bodied burrowers and more rigid, wedge-shaped burrowers (i.e. clams). Our results raise questions about the reputed high energetic cost of burrowing and emphasize the need for better understanding of sediment mechanics to quantify external energy expenditure during burrowing
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Variability of the Compressive Strength of Parallel Strand Lumber
Measurement of the compressive strength of parallel strand lumber (PSL) is conducted on specimens of varying size with nominally identical mesostructure. The mean of the compressive strength is found to vary inversely with the specimen size, and the coefficient of variation of the strength is found to decrease with increasing specimen size, and to be smaller than the coefficient of variation of strength for solid lumber. The correlation length of the compressive strength is approximately 0.5 m, and this correlation length leads to significant specimen-to-specimen variation in mean strength. A computational model is developed that includes the following properties of the PSL mesostructure: the strand length, the grain angle, the elastic constants, and the parameters of the Tsai-Hill failure surface. The computational model predicts the mean strength and coefficient of variation reasonably well, and predicts the correct form of correlation decay, but overpredicts the correlation length for compressive strength, likely because of sensitivity to the distribution of strand length used in the model. The estimates of the statistics of the PSL compressive strength are useful for reliability analysis of PSL structures, and the computational model, although still in need of further development, can be used in evaluating the effect of mesostructural parameters on PSL compressive strength
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Worms as wedges: Effects of sediment mechanics on burrowing behavior
Recent studies document linear elastic response of muddy marine sediments to load and deformation on temporal and spatial scales relevant to animal movement, with burrowers making openings for movement in such sediments by fracture. Cracks propagate through linear elastic solids in mode I (opening-mode crack growth) when the stress intensity factor (KI) at the crack tip exceeds the material\u27s fracture toughness (KIc). Fracture mechanics depend on material stiffness as well as fracture toughness, and we prepared a range of transparent gels that varied in stiffness and fracture toughness to assess the dependence of burrowing behavior on these material properties. When the polychaete Nereis virens elongated its burrow, it altered its body shape and behavior across these gels in a manner consistent with fracture mechanics theory. We modeled burrow elongation as stable, wedge-driven crack growth, and calculated that KI values at the tips of the burrows reached KIc values of most gels without pharynx eversion and exceeded KIc when the pharynx was everted. In materials with higher fracture toughnesses, worms everted their pharynges to become thicker and blunter wedges, as predicted from simple wedge theory. In stiff materials with low toughness, worms moved their heads from side-to-side to extend crack edges laterally, relieving elastic forces compressing them and allowing them to maintain body shape more easily. This solution extends the crack in small increments that each require relatively little force. We introduce a dimensionless “wedge” number to characterize the relative importance of work to fracture the material and extend the burrow and work to maintain body shape against the elastic restoring force of the material. The mechanism of burrowing by crack propagation is utilized across a range of material properties found in natural muds, and variation in these properties strongly influences burrowing behaviors. These results demonstrate how quantifying the mechanical properties of muds can improve our understanding of bioturbation. On spatial and temporal scales relevant to burrower activity, variations in these properties may impact particle mixing by influencing burrower behavior
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Random composites characterization using a classifier model
A new method is introduced for characterizing and analyzing materials with random heterogeneous microstructure. The method begins with classifiers which process information from high-fidelity analyses of small-sized simulated microstructures. These classifiers are subsequently used in a multipass moving window to identify subregions of potentially critical microscale behavior such as strain concentrations. In the derivation of the method, it is shown how information theory-based concepts can be formulated in a Bayesian decision theory framework that addresses microstructural issues. Furthermore, it is shown how a sequence of classifiers can be constructed to refine the analysis of microstructure. While the method presented herein is general, a relatively simple example of a two-dimensional, two-phase composite is used to illustrate the analysis steps
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Variance decomposition and global sensitivity for structural systems
This paper applies the Sobol\u27 decomposition of a function of many random variables to a problem in structural mechanics, namely the collapse of a two story two bay frame under gravity load. Prior to introduction of this example application, the Sobol\u27 decomposition itself is reviewed and extended to cover teh case in which th einput random variables have Gaussian distribution. Then, all illustrative example is given for a polynomial function of 3 random variables. In the structural example, the Sobol\u27 decomposition is used to decompose the variance of the response, the collapse load, into contributions from the individual input variables. This decomposition reveals the relative importance of the individual member yield stresses in determining the collapse load of the frame. In applying the Sobol\u27 decomposition to this structural problem the following issues are addressed: Caluculation of the components of the Sobol\u27 decomposition by Monte Carlo simulation: the effect of input distribution on the Sobol\u27 decomposition; convergence of estimates of the Sobol\u27 decomposition with sameple size using various sampling schemes; the possibility of model reductino guided by the results of the Sobol\u27 decomposition
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Measurement and Stochastic Computational Modeling of the Elastic Properties of Parallel Strand Lumber
This paper describes a model for the spatial variation of the elastic modulus of parallel strand lumber (PSL) that is based on bending experiments and also describes a validated stochastic computational model that incorporates orthotropic elasticity and uncertainty in strand geometry and material properties. The PSL exhibits significant variability both within members and between members, but this variability is less than that of equivalent sawn-wood members, and decreases with increasing member size. The correlation length of the elastic modulus is found to be several meters and is independent of the cross-sectional size. The variance of PSL elastic modulus is found to scale inversely with the number of strands in the cross section. The validated computational model is flexible enough to allow preliminary exploration of the properties of new mixes of species and strand sizes in PSL material design