An equivalent domain integral method for three-dimensional mixed-mode fracture problems

A general formulation of the equivalent domain integral (EDI) method for mixed mode fracture problems in cracked solids is presented. The method is discussed in the context of a 3-D finite element analysis. The J integral consists of two parts: the volume integral of the crack front potential over a torus enclosing the crack front and the crack surface integral due to the crack front potential plus the crack face loading. In mixed mode crack problems the total J integral is split into J sub I, J sub II, and J sub III representing the severity of the crack front in three modes of deformations. The direct and decomposition methods are used to separate the modes. These two methods were applied to several mixed mode fracture problems, were analyzed, and results were found to agree well with those available in the literature. The method lends itself to be used as a post-processing subroutine in a general purpose finite element program

Treatment of singularities in cracked bodies

Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields of the form rho = C sub o (theta, z) r to the -1/2 power + D sub o (theta, phi) R to the lambda rho power. The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 pct (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second term is dominant at the free surface and becomes nearly zero away from the the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer varied from 0 pct to about 5 pct of the total specimen thickness as Poisson's ratio varied from 0.0 to 0.45. Because there are two singular stress fields near the free surface, the strain energy release rate (G) is an appropriate parameter to measure the severity of the crack

Implementation of equivalent domain integral method in the two-dimensional analysis of mixed mode problems

An equivalent domain integral (EDI) method for calculating J-intergrals for two-dimensional cracked elastic bodies is presented. The details of the method and its implementation are presented for isoparametric elements. The total and product integrals consist of the sum of an area of domain integral and line integrals on the crack faces. The line integrals vanish only when the crack faces are traction free and the loading is either pure mode 1 or pure mode 2 or a combination of both with only the square-root singular term in the stress field. The EDI method gave accurate values of the J-integrals for two mode I and two mixed mode problems. Numerical studies showed that domains consisting of one layer of elements are sufficient to obtain accurate J-integral values. Two procedures for separating the individual modes from the domain integrals are presented. The procedure that uses the symmetric and antisymmetric components of the stress and displacement fields to calculate the individual modes gave accurate values of the integrals for all problems analyzed. The EDI method when applied to a problem of an interface crack in two different materials showed that the mode 1 and mode 2 components are domain dependent while the total integral is not. This behavior is caused by the presence of the oscillatory part of the singularity in bimaterial crack problems. The EDI method, thus, shows behavior similar to the virtual crack closure method for bimaterial problems

Detection of Cognitive States from fMRI data using Machine Learning Techniques

Over the past decade functional Magnetic Resonance Imaging (fMRI) has emerged as a powerful technique to locate activity of human brain while engaged in a particular task or cognitive state. We consider the inverse problem of detecting the cognitive state of a human subject based on the fMRI data. We have explored classification techniques such as Gaussian Naive Bayes, k-Nearest Neighbour and Support Vector Machines. In order to reduce the very high dimensional fMRI data, we have used three feature selection strategies. Discriminating features and activity based features were used to select features for the problem of identifying the instantaneous cognitive state given a single fMRI scan and correlation based features were used when fMRI data from a single time interval was given. A case study of visuo-motor sequence learning is presented. The set of cognitive states we are interested in detecting are whether the subject has learnt a sequence, and if the subject is paying attention only towards the position or towards both the color and position of the visual stimuli. We have successfully used correlation based features to detect position-color related cognitive states with 80% accuracy and the cognitive states related to learning with 62.5% accuracy

Methods and Approaches for Characterizing Learning Related Changes Observed in functional MRI Data — A Review

Brain imaging data have so far revealed a wealth of information about neuronal circuits involved in higher mental functions like memory, attention, emotion, language etc. Our efforts are toward understanding the learning related effects in brain activity during the acquisition of visuo-motor sequential skills. The aim of this paper is to survey various methods and approaches of analysis that allow the characterization of learning related changes in fMRI data. Traditional imaging analysis using the Statistical Parametric Map (SPM) approach averages out temporal changes and presents overall differences between different stages of learning. We outline other potential approaches for revealing learning effects such as statistical time series analysis, modelling of haemodynamic response function and independent component analysis. We present example case studies from our visuo-motor sequence learning experiments to describe application of SPM and statistical time series analyses. Our review highlights that the problem of characterizing learning induced changes in fMRI data remains an interesting and challenging open research problem

A Multi-disciplinary Approach to the Investigation of Aspects of Serial Order in Cognition

Serial order processing or Sequence processing underlies many human activities such as speech, language, skill learning, planning, problem solving, etc. Investigating the\ud neural bases of sequence processing enables us to understand serial order in cognition and helps us building intelligent devices. In the current paper, various\ud cognitive issues related to sequence processing will be discussed with examples. Some of the issues are: distributed versus local representation, pre-wired versus\ud adaptive origins of representation, implicit versus explicit learning, fixed/flat versus hierarchical organization, timing aspects, order information embedded in sequences, primacy versus recency in list learning and aspects of sequence perception such as recognition, recall and generation. Experimental results that give evidence for the involvement of various brain areas will be described. Finally, theoretical frameworks based on Markov models and Reinforcement Learning paradigm will be presented. These theoretical ideas are useful for studying sequential phenomena in a principled way

High resolution nuclear magnetic resonance studies of hen's egg yolk plasma lipoproteins

High resolution nuclear magnetic resonance spectra of native or protease-treated hen's egg yolk plasma (very low density lipoproteins) were taken either in water or deuterated water; the protease-treated samples showed a sharpening of choline methyl proton signal of phospholipid, indicating the hindrance of the choline head-group rotation by the phospholipids in the native very low density lipoproteins. With both native and the protease-treated egg yolk plasma, elevated temperatue increased the signal intensity and produced line-sharpening of Q choline methyl protons and the - CH2-C=O-protons of the methylene group adjacent to the carboxyl group of esterified fatty acids, indicating prior restriction of mobility of these groups. Total extracted lipids of egg yolk plasma containing traces of chloroform, methanol and water (which keep the sample in one phase) also gave similar temperature dependence. Addition of water to the same sample and sonication resulted in the loss of temperature dependence. Frozen and thawed protease-treated egg yolk plasma also behaved in a similar manner. The absence of temperature dependence in these latter two samples is believed to be due to formation of bilayers of phospholipids following phase separation of triglycerides and phospholipids. The results support a model in which the lipoprotein particles of the egg yolk plasma have a lipid-core structure containing triglycerides in the centre with a monomolecular layer of lecithin at the surface, the polar heads of which are surrounded by proteins