A kinematic and incremental integration model for the micromechanical numerical analysis of dual-phase materials

A kinematic model suitable for the numerical analysis of dual-phase materials and, in particular, for composite materials is presented. Due to the non-linear character of the behavior of most materials, the model must be presented in an incremental form. The kinematic model is based on the decomposition of the transformation gradient in thermoelastic and plastic parts. Thus, the velocity gradient tensor is also decomposed in an elastic and a plastic part. Two different constitutive models are implemented in order to test the model. The dual-phase material modeled is an Al-SiC metal matrix composite (MMC). The reinforcement constitutive model is chosen to be thermoelastic and the matrix model is thermoelastic-viscoplastic. A forward gradient time integration procedure is described and implemented in order to calculate the increments of the state variables, namely the plastic strain increment and the stress increments in both materials. The proposed model is tested with one three-dimensional example: a cylindrical fiber MMC with 11% reinforcement volume fraction. The numerical results are compared with results obtained by other authors. Very good accordance can be observed between the results obtained with the incremental model proposed in this paper and those presented by other authors.