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 have a good estimate of the state of the elastomer itself, since many nonlinear effects originate in the matrix material. A common notion in such estimates is the idea of a ''strain amplification'' factor that relates a macroscopically imposed strain state to the average strain state 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. All three theories are compared to the results of a series of Monte Carlo simulations on an ideal composite with a Neo-Hookean matrix and semi-rigid inclusions. Tt is shown that for the idealized material, one can 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.