Simplification of van der Poel's formula for the shear modulus of a particulate composite

Abstract

T he coe ffi c ient s in va n del" Poe!'s equa ti on fo r c alc ul atin g th e sh ear modulu s of a parti c ul atc c om pos it e have b ee n g r~a tl y sim p lifi ed. ma kin g the ca lc ul ati o n mu c h less un w ield y. Approx im ate so lut lO nso f va n d~r Poe l s equati on are al so de ri ved. and it is show n th at on e of th e low o rd er app rox i. mat lOns IS K e~'n e r s equ ati on. or I-I as hin a nd S htrik ma n's equ ati o n fur th e hi g hes t lowe r bo und. Th e K eln el appl OX I llHlt lO1l IS oft en too lo w In va lu e when th e vu lu me fr action of fill er exceeds 0.2. but it c an be used to. provide fu r~h er s imp lifi ca t IO n In va n der Poe l' s equ ation . or it c an be used as a first ap prOX i ma t IOn In a New ton s me th ud of so luti on . Key wu rd s: Co m posi te m ateri a ls : elas ti c co n stant s: fi ll ed po ly me r s: mec hani ca l p ro perti es; pa;" tl c ul ate co m posit es; shea r nwd ulu s; th eo r y o f e lasti c it y.

A micromechanical model for effective elastic properties of particulate composites with imperfect interfacial bonds

“…3. Smith (1974Smith ( , 1975, Christensen and Lo (1979), Hashin and Rosen (1964) and Hashin (1962Hashin ( , 1963Hashin ( , 1968Hashin ( , 1990Hashin ( , 1991a eventually improved on the CSA model. The CSA assumes that the particles are spherical and, moreover, that the action on the particle is transmitted through a spherical interphase shell.…”

“…Based on the Van der PoelÕs (1958) formula for the shear modulus of a particulate composite, Smith (1974Smith ( , 1975 also proposed the condition for determining the effective shear modulus of the CSA as follows:…”

The effect of filler particles on the texture of food gels

“…This second-order equation requires some calculations, and a simplified version (Equation (9.1)) of this formula is often used instead (Smith, 1975).…”

Estimation of the effective thermoelastic moduli of fibrous nanocomposites with cylindrically anisotropic phases

“…The classical GSCM, initiated by Kerner [20] and Van der Poel [39], extended by Smith [34,35] and completed by Christensen and Lo [10], is applicable only to composites made of isotropic phases without interface stress.…”

“…(1) 4 , we use the continuity conditions of the displacements u r and u θ and the stresses σ rr and σ r θ across the interface at r = r 2 and the interface conditions (34), (35), (37), and (38) at r = r 1 . These conditions yield eight linear equations which can be written in the matrix form…”