AN EVALUATION OF STRAIN AMPLIFICATION CONCEPTS VIA MONTE-CARLO SIMULATIONS OF AN IDEAL COMPOSITE

In the modeling of carbon-black filled elastomers it is important to h ave a good estimate of the state of the elastomer itself, since many n onlinear effects originate in the matrix material. A common notion in such estimates is the idea of a ''strain amplification'' factor that r elates a macroscopically imposed strain state to the average strain st ate in the elastomer matrix material. In this paper Mullins and Tobin' s interpretation of the Guth-Gold and Smallwood's amplification factor , and a more recent proposal by Govindjee and Simo will be examined. A ll three theories are compared to the results of a series of Monte Car lo simulations on an ideal composite with a Neo-Hookean matrix and sem i-rigid inclusions. Tt is shown that for the idealized material, one c an not interpret the Guth-Gold and Smallwood amplification factors as an estimate of the strain state of the matrix material. The theory of Govindjee and Simo, on the other hand, is shown to accurately predict the strain state of the matrix.