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.

}, keywords = {classification, composites, damage initiation, elasticity, Micromechanics, pattern recognition, stochastic mechanics}, doi = {10.1177/1056789508096614}, author = {Arwade, Sanjay R. and Louhghalam, Arghavan} } @article {11227, title = {Variance decomposition and global sensitivity for structural systems}, journal = {Engineering Structures}, volume = {32}, year = {2010}, month = {01/2010}, pages = {1-10}, chapter = {1}, abstract = {This paper applies the Sobol\’ 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\’ decomposition itself is reviewed and extended to cover the case in which the input random variables have Gaussian distribution. Then, an illustrative example is given for a polynomial function of 3 random variables.

In the structural example, the Sobol\’ 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\’ decomposition to this structural problem the following issues are addressed: Calculation of the components of the Sobol\’ decomposition by Monte Carlo simulation; the effect of input distribution on the Sobol\’ decomposition; convergence of estimates of the Sobol\’ decomposition with sample size using various sampling schemes; the possibility of model reduction guided by the results of the Sobol\’ decomposition.

}, keywords = {Monte Carlo simulation, Sensitivity analysis, Sobol{\textquoteright} decomposition, Structural collapse analysis, Uncertainty quantification, Variance decomposition}, doi = {10.1016/j.engstruct.2009.08.011}, author = {Arwade, Sanjay R. and Moradi, Mohammadreza and Louhghalam, Arghavan} }