Micromechanical modeling of coupled viscoelastic–viscoplastic composites based on an incrementally affine formulation

This study proposes a micromechanical modeling of inclusion-reinforced viscoelastic–viscoplastic composites, based on mean-field approaches. For this, we have generalized the so-called incrementally affine linearization method which was proposed by Doghri et al. (2010a) for elasto-viscoplastic materials. The proposal provides an affine relation between stress and strain increments via an algorithmic tangent operator. In order to find the incrementally affine expression, we start by the linearization of evolution equations at the beginning of a time step around the end time of the step. Next, a numerical integration of the linearized equations is required using a fully implicit backward Euler scheme. The obtained algebraic equations lead to an incrementally affine formulation which is form-similar to linear thermoelasticity, therefore known homogenization models for linear thermoelastic composites can be applied. The proposed method can deal with general viscoelastic–viscoplastic constitutive models with an arbitrary number of internal variables. The semi-analytical predictions are validated against finite element simulations and experimental results.