TY - JOUR
T1 - Effective stiffness tensor of composite media
T2 - II. Applications to isotropic dispersions
AU - Torquato, S.
N1 - Funding Information:
The author is thankful to L. Gibiansky for many useful discussions and his help in simplifying moduli expressions using the Y-transformation. The author gratefully acknowledges the support of the Air Force Office of Scientific Research under Grant No. F49620-96-1-0182 and the Office of Basic Energy Sciences, U.S. Department of Energy, under Grant No. DE-FG02-92ER14275.
PY - 1998/8/1
Y1 - 1998/8/1
N2 - Accurate approximate relations for the effective elastic moduli of two- and three-dimensional isotropic dispersions are obtained by truncating, after third-order terms, an exact series expansion for the effective stiffness tensor of d-dimensional two-phase composites (obtained in the first paper) that perturbs about certain optimal dispersions. Our third-order approximations of the effective bulk modulus Ke and shear modulus Ge are compared to benchmark data, rigorous bounds and popular self-consistent approximations for a variety of macroscopically isotropic dispersions in both two and three dimensions, for a wide range of phase moduli and volume fractions. Generally, for the cases considered, the third-order approximations are in very good agreement with benchmark data, always lie within rigorous bounds, and are superior to popular self-consistent approximations.
AB - Accurate approximate relations for the effective elastic moduli of two- and three-dimensional isotropic dispersions are obtained by truncating, after third-order terms, an exact series expansion for the effective stiffness tensor of d-dimensional two-phase composites (obtained in the first paper) that perturbs about certain optimal dispersions. Our third-order approximations of the effective bulk modulus Ke and shear modulus Ge are compared to benchmark data, rigorous bounds and popular self-consistent approximations for a variety of macroscopically isotropic dispersions in both two and three dimensions, for a wide range of phase moduli and volume fractions. Generally, for the cases considered, the third-order approximations are in very good agreement with benchmark data, always lie within rigorous bounds, and are superior to popular self-consistent approximations.
KW - Elastic material
KW - Microstructures
KW - Particulate reinforced material
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U2 - 10.1016/S0022-5096(97)00083-5
DO - 10.1016/S0022-5096(97)00083-5
M3 - Article
AN - SCOPUS:0032137019
SN - 0022-5096
VL - 46
SP - 1411
EP - 1440
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
IS - 8
ER -