Multiple scale eigendeformation-based reduced order homogenization

SUMMARYIn this work a spectral stochastic computational scheme is proposed that links the global properties of multi-phase periodic composites to the geometry and random material properties of their microstructural components. To propagate the uncertainties associated with the material properties to the microstructural response the scheme benefits from a combination of homogenization theory built into a finite element framework and the spectral representation of uncertainty based on Hermite Chaos where a probabilistic characterization of the solutions to a set of local problems defined on the period cell is first sought. A full stochastic description of the global (effective) properties is then obtained by averaging the solutions to the forgoing set of local problems over the unit cell. A representative subset of results is compared with the results obtained using Monte Carlo simulation to demonstrate the accuracy of the proposed procedure.

Section: Introductionmentioning

confidence: 99%

A multi‐scale spectral stochastic method for homogenization of multi‐phase periodic composites with random material properties

Tootkaboni

Graham‐Brady

2010

“…, hereafter referred as the NIAR report. A nonlinear two‐scale analysis has been conducted using the reduced order homogenization method For validation, a nonintrusive stochastic multiscale solver based on the sparse grid collocation approach is employed.…”

Section: Numerical Studiesmentioning

confidence: 99%

An adaptive stochastic inverse solver for multiscale characterization of composite materials

Fish

McAuliffe

2016

Self Cite

Summary We present an adaptive variant of the measure‐theoretic approach for stochastic characterization of micromechanical properties based on the observations of quantities of interest at the coarse (macro) scale. The salient features of the proposed nonintrusive stochastic inverse solver are identification of a nearly optimal sampling domain using enhanced ant colony optimization algorithm for multiscale problems, incremental Latin‐hypercube sampling method, adaptive discretization of the parameter and observation spaces, and adaptive selection of number of samples. A complete test data of the TORAY T700GC‐12K‐31E and epoxy #2510 material system from the National Institute for Aviation Research report is employed to characterize and validate the proposed adaptive nonintrusive stochastic inverse algorithm for various unnotched and open‐hole laminates. Copyright © 2016 John Wiley & Sons, Ltd.

“…The coarse‐scale stress in the reduced order spatial homogenization theory is updated by the fine‐scale partitioned eigenstrain and partitioned eigenseparation . The coarse‐scale eigenstrain evolution equation will be constructed from the reduced order constitutive equations of partitioned eigenstrain and partitioned eigenseparation …”

Section: Spatio‐temporal Homogenizationmentioning

confidence: 99%

Multiscale fatigue life prediction model for heterogeneous materials

Fish

Bailakanavar

Powers

et al. 2012

Self Cite

SUMMARY A multiscale fatigue life prediction model is developed for heterogeneous materials. The proposed model combines a two‐scale asymptotic homogenization approach in time with a ‘block cycle jump’ technique into a unified temporal multiscale framework that can be effectively utilized for arbitrary material architectures and constitutive equations of microphases. The unified temporal multiscale approach in combination with a spatial multiscale approach based on the reduced order homogenization is characterized for high temperature ceramic matrix composites. Copyright © 2012 John Wiley & Sons, Ltd.