TY - JOUR

T1 - Stiffness tensor random fields through upscaling of planar random materials

AU - Sena, Michael P.

AU - Ostoja-Starzewski, Martin

AU - Costa, Luis

N1 - Funding Information:
This work was made possible by the support from Sandia-DTRA (Grant HDTRA1-08-10-BRCWMD ) and the NSF (Grant CMMI-1030940 ). Also, the support of the first author as a Timoshenko Distinguished Visitor in the Division of Mechanics and Computation, Stanford University, is gratefully acknowledged. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000 .

PY - 2013

Y1 - 2013

N2 - Unique effective material properties are not possible for random heterogeneous materials at intermediate length scales, which is to say at some mesoscale above the microscale yet prior to the attainment of the representative volume element (RVE). Focusing on elastic moduli in particular, a micromechanical analysis based on the Hill-Mandel condition leads to the conclusion that two fields, stiffness and compliance, are required to bound the response of the material. In particular, we analyze means and correlation coefficients of a random planar material with a two-phase microstructure of random checkerboard type. We employ micromechanics, which can be viewed as an upscaling, smoothing procedure using the concept of a mesoscale "window", and random field theory to compute the correlation structure of 4th-rank tensor fields of stiffness and compliance for a given mesoscale. Results are presented for various correlation distances, volume fractions, and contrasts in stiffness between phases. The main contribution of this research is to provide the data for developing analytical correlation functions, which can then be used at any mesoscale to generate micromechanically based inputs into analytical and computational mechanics models.

AB - Unique effective material properties are not possible for random heterogeneous materials at intermediate length scales, which is to say at some mesoscale above the microscale yet prior to the attainment of the representative volume element (RVE). Focusing on elastic moduli in particular, a micromechanical analysis based on the Hill-Mandel condition leads to the conclusion that two fields, stiffness and compliance, are required to bound the response of the material. In particular, we analyze means and correlation coefficients of a random planar material with a two-phase microstructure of random checkerboard type. We employ micromechanics, which can be viewed as an upscaling, smoothing procedure using the concept of a mesoscale "window", and random field theory to compute the correlation structure of 4th-rank tensor fields of stiffness and compliance for a given mesoscale. Results are presented for various correlation distances, volume fractions, and contrasts in stiffness between phases. The main contribution of this research is to provide the data for developing analytical correlation functions, which can then be used at any mesoscale to generate micromechanically based inputs into analytical and computational mechanics models.

KW - Compliance tensor

KW - Correlation structure

KW - Mesoscale

KW - Random fields

KW - Random microstructure

KW - Stiffness tensor

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U2 - 10.1016/j.probengmech.2013.08.008

DO - 10.1016/j.probengmech.2013.08.008

M3 - Article

AN - SCOPUS:84886302915

SN - 0266-8920

VL - 34

SP - 131

EP - 156

JO - Probabilistic Engineering Mechanics

JF - Probabilistic Engineering Mechanics

ER -