TY - JOUR
T1 - New method to generate three-point bounds on effective properties of composites
T2 - Application to viscoelasticity
AU - Gibiansky, L. V.
AU - Torquato, S.
N1 - Funding Information:
The authors thank Graeme Milton for helpful discussions. We gratefully acknowledge the support of the Air Force Office of Scientific Research under Grant No. F49620-96-1-0182.
PY - 1998/4
Y1 - 1998/4
N2 - The general goal of this paper is to develop a new approach for bounding the effective moduli (e.g. elastic moduli, conductivity, or thermal expansion coefficients) of composite materials. Specifically, this paper aims to: (1) formulate a procedure that combines the translation method and the Beran procedure into one powerful method that has the advantages of both approaches; and (2) apply the new method to study effective properties of viscoelastic composites. The new method enables one to get the most restrictive three-point geometrical-parameter bounds. In particular, we obtain new three-point bounds on the complex bulk modulus of an isotropic viscoelastic composite. The new bounds are given by the outermost of several circular arcs in the complex bulk modulus plane. They take into account three-point statistical information and thus are much more restrictive than previously known two-point bounds.
AB - The general goal of this paper is to develop a new approach for bounding the effective moduli (e.g. elastic moduli, conductivity, or thermal expansion coefficients) of composite materials. Specifically, this paper aims to: (1) formulate a procedure that combines the translation method and the Beran procedure into one powerful method that has the advantages of both approaches; and (2) apply the new method to study effective properties of viscoelastic composites. The new method enables one to get the most restrictive three-point geometrical-parameter bounds. In particular, we obtain new three-point bounds on the complex bulk modulus of an isotropic viscoelastic composite. The new bounds are given by the outermost of several circular arcs in the complex bulk modulus plane. They take into account three-point statistical information and thus are much more restrictive than previously known two-point bounds.
KW - A. dissipation
KW - B. inhomogeneous material
KW - B. viscoelastic material
KW - C. variational calculus
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U2 - 10.1016/S0022-5096(97)00044-6
DO - 10.1016/S0022-5096(97)00044-6
M3 - Article
AN - SCOPUS:0032043039
SN - 0022-5096
VL - 46
SP - 749
EP - 783
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
IS - 4
ER -