Matrix Crack Detection in Composite Plate with Spatially Random Material Properties using Fractal Dimension

Fractal dimension based damage detection method is investigated for a composite plate with random material properties. Composite material shows spatially varying random material properties because of complex manufacturing processes. Matrix cracks are considered as damage in the composite plate. Such cracks are often seen as the initial damage mechanism in composites under fatigue loading and also occur due to low velocity impact. Static deflection of the cantilevered composite plate with uniform loading is calculated using the finite element method. Damage detection is carried out based on sliding window fractal dimension operator using the static deflection. Two dimensional homogeneous Gaussian random field is generated using Karhunen-Loeve (KL) expansion to represent the spatial variation of composite material property. The robustness of fractal dimension based damage detection method is demonstrated considering the composite material properties as a two dimensional random field.

Iterated stochastic filters with additive updates for dynamic system identification: Annealing-type iterations and the filter bank

A nonlinear stochastic filtering scheme based on a Gaussian sum representation of the filtering density and an annealing-type iterative update, which is additive and uses an artificial diffusion parameter, is proposed. The additive nature of the update relieves the problem of weight collapse often encountered with filters employing weighted particle based empirical approximation to the filtering density. The proposed Monte Carlo filter bank conforms in structure to the parent nonlinear filtering (Kushner-Stratonovich) equation and possesses excellent mixing properties enabling adequate exploration of the phase space of the state vector. The performance of the filter bank, presently assessed against a few carefully chosen numerical examples, provide ample evidence of its remarkable performance in terms of filter convergence and estimation accuracy vis-a-vis most other competing filters especially in higher dimensional dynamic system identification problems including cases that may demand estimating relatively minor variations in the parameter values from their reference states. (C) 2014 Elsevier Ltd. All rights reserved.

Matrix crack detection in spatially random composite structures using fractal dimension

Fractal dimension based damage detection method is studied for a composite structure with random material properties. A composite plate with localized matrix crack is considered. Matrix cracks are often seen as the initial damage mechanism in composites. Fractal dimension based method is applied to the static deformation curve of the structure to detect localized damage. Static deflection of a cantilevered composite plate under uniform loading is calculated using the finite element method. Composite material shows spatially varying random material properties because of complex manufacturing processes. Spatial variation of material property is represented as a two dimensional homogeneous Gaussian random field. Karhunen-Loeve (KL) expansion is used to generate a random field. The robustness of fractal dimension based damage detection methods is studied considering the composite plate with spatial variation in material properties.

Low-Wear High-Friction Behavior of Copper Matrix Composites Dispersed With an In Situ Polymer Derived Ceramic

We show that copper-matrix composites that contain 20 vol. % of an in situ processed, polymer-derived, ceramic phase constituted from Si-C-N have unusual friction-and-wear properties. They show negligible wear despite a coefficient of friction (COF) that approaches 0.7. This behavior is ascribed to the lamellar structure of the composite such that the interlamellar regions are infused with nanoscale dispersion of ceramic particles. There is significant hardening of the composite just adjacent to the wear surface by severe plastic deformation.

A matrix model for QCD: QCD color is mixed

We use general arguments to show that colored QCD states when restricted to gauge invariant local observables are mixed. This result has important implications for confinement: a pure colorless state can never evolve into two colored states by unitary evolution. Furthermore, the mean energy in such a mixed colored state is infinite. Our arguments are confirmed in a matrix model for QCD that we have developed using the work of Narasimhan and Ramadas(3) and Singer.(2) This model, a (0 + 1)-dimensional quantum mechanical model for gluons free of divergences and capturing important topological aspects of QCD, is adapted to analytical and numerical work. It is also suitable to work on large N QCD. As applications, we show that the gluon spectrum is gapped and also estimate some low-lying levels for N = 2 and 3 (colors). Incidentally the considerations here are generic and apply to any non-Abelian gauge theory.

A matrix model for QCD

Gribov's observation that global gauge fixing is impossible has led to suggestions that there may be a deep connection between gauge fixing and confinement. We find an unexpected relation between the topological nontriviality of the gauge bundle and colored states in SU(N) Yang-Mills theory, and show that such states are necessarily impure. We approximate QCD by a rectangular matrix model that captures the essential topological features of the gauge bundle, and demonstrate the impure nature of colored states explicitly. Our matrix model also allows the inclusion of the QCD theta-term, as well as to perform explicit computations of low-lying glueball masses. This mass spectrum is gapped. Since an impure state cannot evolve to a pure one by a unitary transformation, our result shows that the solution to the confinement problem in pure QCD is fundamentally quantum information-theoretic.

A common stochastic accumulator with effector-dependent noise can explain eye-hand coordination

The computational architecture that enables the flexible coupling between otherwise independent eye and hand effector systems is not understood. By using a drift diffusion framework, in which variability of the reaction time (RT) distribution scales with mean RT, we tested the ability of a common stochastic accumulator to explain eye-hand coordination. Using a combination of behavior, computational modeling and electromyography, we show how a single stochastic accumulator to threshold, followed by noisy effector-dependent delays, explains eye-hand RT distributions and their correlation, while an alternate independent, interactive eye and hand accumulator model does not. Interestingly, the common accumulator model did not explain the RT distributions of the same subjects when they made eye and hand movements in isolation. Taken together, these data suggest that a dedicated circuit underlies coordinated eye-hand planning.

Unified Continuum Damage Model for Matrix Cracking in Composite Rotor Blades

This paper deals with modeling of the first damage mode, matrix micro-cracking, in helicopter rotor/wind turbine blades and how this effects the overall cross-sectional stiffness. The helicopter/wind turbine rotor system operates in a highly dynamic and unsteady environment leading to severe vibratory loads present in the system. Repeated exposure to this loading condition can induce damage in the composite rotor blades. These rotor/turbine blades are generally made of fiber-reinforced laminated composites and exhibit various competing modes of damage such as matrix micro-cracking, delamination, and fiber breakage. There is a need to study the behavior of the composite rotor system under various key damage modes in composite materials for developing Structural Health Monitoring (SHM) system. Each blade is modeled as a beam based on geometrically non-linear 3-D elasticity theory. Each blade thus splits into 2-D analyzes of cross-sections and non-linear 1-D analyzes along the beam reference curves. Two different tools are used here for complete 3-D analysis: VABS for 2-D cross-sectional analysis and GEBT for 1-D beam analysis. The physically-based failure models for matrix in compression and tension loading are used in the present work. Matrix cracking is detected using two failure criterion: Matrix Failure in Compression and Matrix Failure in Tension which are based on the recovered field. A strain variable is set which drives the damage variable for matrix cracking and this damage variable is used to estimate the reduced cross-sectional stiffness. The matrix micro-cracking is performed in two different approaches: (i) Element-wise, and (ii) Node-wise. The procedure presented in this paper is implemented in VABS as matrix micro-cracking modeling module. Three examples are presented to investigate the matrix failure model which illustrate the effect of matrix cracking on cross-sectional stiffness by varying the applied cyclic

Novel architecture for anomalous strengthening of a particulate filled polymer matrix composite

We propose an architecture for dramatically enhancing the stress bearing and energy absorption capacities of a polymer based composite. Different weight fractions of iron oxide nano-particles (NPs) are mixed in a poly(dimethylesiloxane) (PDMS) matrix either uniformly or into several vertically aligned cylindrical pillars. These composites are compressed up to a strain of 60% at a strain rate of 0.01 s(-1) following which they are fully unloaded at the same rate. Load bearing and energy absorption capacities of the composite with uniform distribution of NPs increase by similar to 50% upon addition of 5 wt% of NPs; however, these properties monotonically decrease with further addition of NPs so much so that the load bearing capacity of the composite becomes 1/6th of PDMS upon addition of 20 wt% of NPs. On the contrary, stress at a strain of 60% and energy absorption capacity of the composites with pillar configuration monotonically increase with the weight fraction of NPs in the pillars wherein the load bearing capacity becomes 1.5 times of PDMS when the pillars consisted of 20 wt% of NPs. In situ mechanical testing of composites with pillars reveals outward bending of the pillars wherein the pillars and the PDMS in between two pillars, located along a radius, are significantly compressed. Reasoning based on effects of compressive hydrostatic stress and shape of fillers is developed to explain the observed anomalous strengthening of the composite with pillar architecture.

Carbon-Nanohorn-Reinforced Polymer Matrix Composites: Synergetic Benefits in Mechanical Properties

Mechanical properties of single-walled carbon nanohoms (SWNH) and SWNH plus few-layer graphene (EG)-reinforced poly(vinyl alcohol) (PVA) matrix composites have been measured using the nanoindentation technique. The elastic modulus (E) and hardness (H) of PVA were found to improve by similar to 315% and similar to 135%, respectively, upon the addition of just 0.4 wt % SWNH. These properties were found to be comparable to those obtained upon the addition of 0.2 wt % single-walled nanotubes (SWNT) to PVA. Furthermore, upon binary addition of 0.2 wt % EG and 0.4 wt % SWNH to PVA, benefits in the form of similar to 400% and similar to 330% synergy in E and H, respectively, were observed, along with an increased resistance to viscoelastic deformation. The reasons for these improvements are discussed in terms of the dimensionality of nanocarbon, the effectiveness of nanocarbon and polymer matrix interaction, and the influence of nanocarbon on the degree of crystallinity of the polymer. The results from SWNH reinforcement in this study demonstrate the scope for a novel and, in contrast to SWNT composites, a commercially feasible opportunity for strengthening polymer matrices.

Average Overlap for Clustering Incomplete Data using Symmetric Non-Negative Matrix Factorization

Clustering techniques which can handle incomplete data have become increasingly important due to varied applications in marketing research, medical diagnosis and survey data analysis. Existing techniques cope up with missing values either by using data modification/imputation or by partial distance computation, often unreliable depending on the number of features available. In this paper, we propose a novel approach for clustering data with missing values, which performs the task by Symmetric Non-Negative Matrix Factorization (SNMF) of a complete pair-wise similarity matrix, computed from the given incomplete data. To accomplish this, we define a novel similarity measure based on Average Overlap similarity metric which can effectively handle missing values without modification of data. Further, the similarity measure is more reliable than partial distances and inherently possesses the properties required to perform SNMF. The experimental evaluation on real world datasets demonstrates that the proposed approach is efficient, scalable and shows significantly better performance compared to the existing techniques.

A hybrid method for stochastic response analysis of a vibrating structure

Response analysis of a linear structure with uncertainties in both structural parameters and external excitation is considered here. When such an analysis is carried out using the spectral stochastic finite element method (SSFEM), often the computational cost tends to be prohibitive due to the rapid growth of the number of spectral bases with the number of random variables and the order of expansion. For instance, if the excitation contains a random frequency, or if it is a general random process, then a good approximation of these excitations using polynomial chaos expansion (PCE) involves a large number of terms, which leads to very high cost. To address this issue of high computational cost, a hybrid method is proposed in this work. In this method, first the random eigenvalue problem is solved using the weak formulation of SSFEM, which involves solving a system of deterministic nonlinear algebraic equations to estimate the PCE coefficients of the random eigenvalues and eigenvectors. Then the response is estimated using a Monte Carlo (MC) simulation, where the modal bases are sampled from the PCE of the random eigenvectors estimated in the previous step, followed by a numerical time integration. It is observed through numerical studies that this proposed method successfully reduces the computational burden compared with either a pure SSFEM of a pure MC simulation and more accurate than a perturbation method. The computational gain improves as the problem size in terms of degrees of freedom grows. It also improves as the timespan of interest reduces.

In-situ synthesized poly(vinyl butyral)/MMT-clay nanocomposites: The role of degree of acetalization and clay content on thermal, mechanical and permeability properties of PVB matrix

Poly(vinyl butyral) - MMT clay nanocomposites were synthesized in situ with three different degrees of acetalization and with varying clay content for each vinyl butyral polymer ratio. The clay nano-platelet galleries were expanded, as determined by X-ray diffraction and TEM analysis. The glass transition temperature of the polymer nanocomposites were found to be similar to 56 degrees C and similar to 52 degrees C for the neat polymer and the 4% clay loaded samples, respectively. The 4 wt% clay loaded film showed higher strength and low strain to failure. The dynamic mechanical analysis also confirmed the improved stability of the matrix. The matrix with 0.5 butyral to alcohol ratio for 4 wt% clay exhibited good water vapor transmission compared to all other compositions. The encapsulated devices with 2.5 and 4 wt% clay loaded films increases the device life time and the efficiencies of these films were 50% higher than their encapsulated pristine polymer films. (C) 2015 Elsevier Ltd. All rights reserved.

Eye-hand coordination during a double-step task: evidence for a common stochastic accumulator

Many studies of reaching and pointing have shown significant spatial and temporal correlations between eye and hand movements. Nevertheless, it remains unclear whether these correlations are incidental, arising from common inputs (independent model); whether these correlations represent an interaction between otherwise independent eye and hand systems (interactive model); or whether these correlations arise from a single dedicated eye-hand system (common command model). Subjects were instructed to redirect gaze and pointing movements in a double-step task in an attempt to decouple eye-hand movements and causally distinguish between the three architectures. We used a drift-diffusion framework in the context of a race model, which has been previously used to explain redirect behavior for eye and hand movements separately, to predict the pattern of eye-hand decoupling. We found that the common command architecture could best explain the observed frequency of different eye and hand response patterns to the target step. A common stochastic accumulator for eye-hand coordination also predicts comparable variances, despite significant difference in the means of the eye and hand reaction time (RT) distributions, which we tested. Consistent with this prediction, we observed that the variances of the eye and hand RTs were similar, despite much larger hand RTs (similar to 90 ms). Moreover, changes in mean eye RTs, which also increased eye RT variance, produced a similar increase in mean and variance of the associated hand RT. Taken together, these data suggest that a dedicated circuit underlies coordinated eye-hand planning.

Necessary and sufficient conditions for optimality in constrained general sum stochastic games

In this paper we first derive a necessary and sufficient condition for a stationary strategy to be the Nash equilibrium of discounted constrained stochastic game under certain assumptions. In this process we also develop a nonlinear (non-convex) optimization problem for a discounted constrained stochastic game. We use the linear best response functions of every player and complementary slackness theorem for linear programs to derive both the optimization problem and the equivalent condition. We then extend this result to average reward constrained stochastic games. Finally, we present a heuristic algorithm motivated by our necessary and sufficient conditions for a discounted cost constrained stochastic game. We numerically observe the convergence of this algorithm to Nash equilibrium. (C) 2015 Elsevier B.V. All rights reserved.