T he behavior of an infi nitely long flexib le fil a men t after transverse impact is treated theoret.icall y. The fil a ment is ass u med to have a tension-strain curve that is always co ncave dow nward, and to have no short-ti me creep or stress-rei fixation effects. Under most cond itions the impact in itiates a varia bl e strain t hat prop agates down the fil a ment between an "elasLic wave" fro nt a nd a " plastic wave" front. A tra nsverse wave, shaped li ke an inverLed V, then travels in t he co nstan t-strain region behin d the plastic-wave front. Under specia l condi tio ns t he transverse-wave front may propagate faster than the plastic-wave front, b ut the sh ape of t he tra nsverse wave r ema ins t he sam e. T he theory for both cases is worked out in d etail , an d some ill ustrative examples arc given.

Young' s modu lus and Poisso n's ratio have bee n measured simulta neo usly on a seri es of pa rti c ul a te co mposites co ntainin g vo lum e fra cti ons of fill e r up to 0.50. The co mpos ites co nsisted of small glass s ph e res im bedd ed in a ri gi d e poxy po lym e r matri x. The meas ured va lues we re com pared with th eOl·eti-cal valu es calc ul ated from c urre nt theories. A rece ntl y ge ne ralized a nd simplifi ed ve rs ion of van der Poe l' s th eo ry prov id ed th e bes t agreeme nt. It predicted va lu es of Youn g's modu lus for co mposites with fill er volume fractions up to 0.35. Meas ured valu es of Poisso n's ratio ex hibited sca tterin g, but we re co nsiste nt with value s calc ula ted from va n der Poel' s th eory.Key word s: Co mpos ite ma te ria ls; e las ti c consta nts; fill ed polym e rs; mec ha ni cal prope rti es; pa rti c ul a te co mposites; Poisso n's ratio ; Young' s modulu s.

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.

Van de r Poe l's me thod (Rh eol. Ac ta 1, 198 (1958)) for ca lc ulatin g the s hea r modu lu s of a par· ti c ulate co mposite agrees we ll with experim e ntal data, but its validit y has bee n qu es ti oned , and it wa s applicable only to co mpo sites in whi ch the matrix mate ria l is in co mpress ibl e. Th ese limitations a re removed in this paper in whic h an erro r in the origin a l derivation is corrected, a nd th e me thod ge ne ralize d to app ly to any matrix mat erial. Ca lc ulati ons using the co rrected theory s how that des pite th e e rror, a tabl e of s hea r mod ulu s va lu es publishe d wit h th e original th eory is s uffici e ntly correc t for most prac ti ca l purposes. Appli cability of th e ge ne ralized method to th e large c lass of co mpos ites having co mpress ibl e matri ces is di sc ussed. S hear moduli ca lc ul ated by th e correcte d a nd exte nd e d me th od are compared with corresponding va lues ca lc ulate d by othe r me thod s c urrentl y used.Key word s : Bu lk modulu s; co mpos ite mate rials ; e las tic co ns ta nts; fill e d polym ers; mechan ical prop· e rti es; partic ulate co mpo sites; shear modulu s; th eory of elasti cit y.

The behavior of an infinitely long flexible filament after transverse impact is treated theoretically. The filament is assumed to have a tension-strain curve which is always concave downwards and to have no short time creep or stress relaxation effects. Under most conditions the impact initiates a variable strain that propagates down the filament between an "elastic wave" front and a "plastic wave" front. A transverse wave, shaped like an inverted "V," then travels in the constant strain region behind the plastic wave front. Under special conditions the transverse wave front may propagate faster than the plastic wave front, but the shape of the transverse wave remains the same. The theory for both cases is worked out in detail and some illustrative examples given.