TY - JOUR
T1 - Frequency-dependent scaling from mesoscale to macroscale in viscoelastic random composites
AU - Zhang, Jun
AU - Ostoja-Starzewski, Martin
N1 - Publisher Copyright:
© 2016 The Author(s) Published by the Royal Society. All rights reserved.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - This paper investigates the scaling from a statistical volume element (SVE; i.e. mesoscale level) to representative volume element (RVE; i.e. macroscale level) of spatially random linear viscoelasticmaterials, focusing on the quasi-static properties in the frequency domain. Requiring the material statistics to be spatially homogeneous and ergodic, the mesoscale bounds on the RVE response are developed from the Hill-Mandel homogenization condition adapted to viscoelastic materials. The bounds are obtained from two stochastic initial-boundary value problems set up, respectively, under uniform kinematic and traction boundary conditions. The frequency and scale dependencies of mesoscale bounds are obtained through computational mechanics for composites with planar random chessboard microstructures. In general, the frequency-dependent scaling to RVE can be described through a complex-valued scaling function, which generalizes the concept originally developed for linear elastic random composites. This scaling function is shown to apply for all different phase combinations on random chessboards and, essentially, is only a function of the microstructure and mesoscale.
AB - This paper investigates the scaling from a statistical volume element (SVE; i.e. mesoscale level) to representative volume element (RVE; i.e. macroscale level) of spatially random linear viscoelasticmaterials, focusing on the quasi-static properties in the frequency domain. Requiring the material statistics to be spatially homogeneous and ergodic, the mesoscale bounds on the RVE response are developed from the Hill-Mandel homogenization condition adapted to viscoelastic materials. The bounds are obtained from two stochastic initial-boundary value problems set up, respectively, under uniform kinematic and traction boundary conditions. The frequency and scale dependencies of mesoscale bounds are obtained through computational mechanics for composites with planar random chessboard microstructures. In general, the frequency-dependent scaling to RVE can be described through a complex-valued scaling function, which generalizes the concept originally developed for linear elastic random composites. This scaling function is shown to apply for all different phase combinations on random chessboards and, essentially, is only a function of the microstructure and mesoscale.
KW - Mesoscale bounds
KW - Random composite
KW - Representative volume element
KW - Scaling function
KW - Viscoelasticity
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U2 - 10.1098/rspa.2015.0801
DO - 10.1098/rspa.2015.0801
M3 - Article
C2 - 27274689
AN - SCOPUS:84968698111
SN - 1364-5021
VL - 472
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2188
M1 - 0801
ER -