Dynamic mechanical behavior of filled polymers. I. Theoretical developments

A constitutive theory is developed for modeling the mechanical response of dynamically loaded filled-polymer composites. The basis for this work is Mo ri and Tanaka's effective medium theory. Expressions derived by Weng and co -workers are used for the elastic stiffness tensor of the composite. The fi ller is a low volume concentration of randomly positioned elastic ellipsoid al particles. Random and aligned orientations of the ellipsoids are conside red. The viscoelastic stress-strain behavior of the polymer matrix is model ed using the Boltzmann superposition principle with a Prony series represen tation for the stress relaxation functions. We argue that for rubbery polym ers it is reasonable to express the composite stress relaxation functions a s series expansions about the ratio of the polymer shear relaxation functio n to its bulk modulus. The smallness of this ratio allows accurate results to be obtained when truncating the expansion at first order. Inverse Laplac e transformations required by the theory can then be done analytically. The result of these manipulations is again a Prony series for the stress relax ation functions of the composite, but with series coefficients that are now functions of the filler concentration, ellipsoidal aspect ratio, and modul i. In the limit of low filler concentration the theory reduces to known res ults derived in classical suspension theory. (C) 2001 American Institute of Physics.