Simulation of local material properties based on moving-window GMC

Abstract When analyzing the behavior of composite materials under various loading conditions, the assumption is generally made that the behavior due to randomness in the material can be represented by a homogenized, or effective, set of material properties. This assumption may be valid when considering displacement, average strain, or even average stress of structures much larger than the inclusion size. The approach is less valid, however, when considering either behavior of structures of size at the scale of the inclusions or local stress of structures in general. In this paper, Monte Carlo simulation is used to assess the effects of microstructural randomness on the local stress response of composite materials. In order to achieve these stochastic simulations, the mean, variance and spectral density functions describing the randomly varying elastic properties are required as input. These are obtained here by using a technique known as moving-window generalized method of cells (moving-window GMC). This method characterizes a digitized composite material microstructure by developing fields of local effective material properties. Once these fields are generated, it is straightforward to obtain estimates of the associated probabilistic parameters required for simulation. Based on the simulated property fields, a series of local stress fields, associated with the random material sample under uniaxial tension, is calculated using finite element analysis. An estimation of the variability in the local stress response for the given random composite is obtained from consideration of these simulations.

[1]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[2]  R. K. Everett,et al.  Modeling of Non-Uniform Composite Microstructures , 1993 .

[3]  M. Grigoriu.  Applied Non-Gaussian Processes , 1995 .

[4]  Robert L. Mullen,et al.  Monte Carlo simulation of effective elastic constants of polycrystalline thin films , 1997 .

[5]  G. Povirk,et al.  Incorporation of microstructural information into models of two-phase materials , 1995 .

[6]  Masanobu Shinozuka,et al.  Simulation of Multi-Dimensional Gaussian Stochastic Fields by Spectral Representation , 1996 .

[7]  Martin Ostoja-Starzewski,et al.  Stochastic finite elements as a bridge between random material microstructure and global response , 1999 .

[8]  M. Ostoja-Starzewski.  Micromechanics as a Basis of Continuum Random Fields , 1994 .

[9]  M. Shinozuka,et al.  Digital Generation of Non‐Gaussian Stochastic Fields , 1988 .

[10]  Peter D. Lee,et al.  Morphological effects on the transverse permeability of arrays of aligned fibers , 1997 .

[11]  George N Frantziskonis,et al.  Stochastic modeling of heterogeneous materials – A process for the analysis and evaluation of alternative formulations , 1998 .

[12]  Ahsan Kareem,et al.  Simulation of Correlated Non-Gaussian Pressure Fields , 1998 .

[13]  M. Paley,et al.  Micromechanical analysis of composites by the generalized cells model , 1992 .

[14]  Teubner,et al.  Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and simulation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  J. Bendat,et al.  Random Data: Analysis and Measurement Procedures , 1971 .

[16]  Marc A. Maes,et al.  Random Field Modeling of Elastic Properties Using Homogenization , 2001 .

[17]  Roberts,et al.  Structure-property correlations in model composite materials. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  Salvatore Torquato,et al.  Local volume fraction fluctuations in heterogeneous media , 1990 .

[19]  Sarah C. Baxter,et al.  Characterization of Random Composites Using Moving-Window Technique , 2000 .

[20]  P. Spanos,et al.  Monte Carlo Treatment of Random Fields: A Broad Perspective , 1998 .

[21]  M. Shinozuka,et al.  Random fields and stochastic finite elements , 1986 .

[22]  S. Torquato,et al.  GEOMETRICAL-PARAMETER BOUNDS ON THE EFFECTIVE MODULI OF COMPOSITES , 1995 .

[23]  Pol D. Spanos,et al.  Markov chain models for life prediction of composite laminates , 1998 .

[24]  Jacob Aboudi,et al.  Micromechanical Analysis of Composites by the Method of Cells , 1989 .

[25]  Marek-Jerzy Pindera,et al.  An efficient implementation of the generalized method of cells for unidirectional, multi-phased composites with complex microstructures , 1999 .

[26]  M. Shinozuka,et al.  Digital simulation of random processes and its applications , 1972 .