Simplified prediction of the monotonic uniaxial stress-strain curve of non-linear particulate composites

A variational estimate of the non-linear flow stress of two-phase materials is adapted to simplify predictions of the monotonic uniaxial response of an isotropic particle-reinforced metal. Simplifications to the model are: (i) calculation of the composite elastic and plastic strain is decoupled and (ii) when calculating the composite plastic strain, the reinforcement is taken to be perfectly rigid while the matrix is assumed to deform with no volume change according to a Hollomon power law. This simplified scheme yields analytical expressions that show good agreement with predictions of the full variational estimate, particularly if the Mori-Tanaka or the Torquato identical hard spheres models are used to predict the composite linear elastic modulus. More specifically, error introduced by the above assumptions is significantly less than the difference made by the choice of the appropriate elastic modulus prediction scheme. Use of the approach proposed here is thus justified in practical applications, given the considerable simplification they bring to the calculation.