Improved incrementally affine method for viscoelastic-viscoplastic composite by utilizing an adaptive scheme

Abstract

We propose a micromechanics-based mean-field homogenization scheme for the viscoelastic-viscoplastic particulate-reinforced composite which is applicable to predict its mechanical response under complex loading conditions. We apply a formulation based on an incrementally affine scheme by using algorithmic tangent operators, while adaptively adjusting the strain of each constituent at every step of the loading process to ensure the consistency of the accumulated strain state and the concentration tensor. We name the method adaptive incrementally affine method. Despite mathematically rigorous derivation, the method has some errors in plastic deformation regime. We propose an assumption for better prediction which dropping out the affine strain and affine stress in adaptive scheme. We show that the adaptive incrementally affine scheme is able to predict the viscoelastic response very well. Still, it is inevitable that the plastic deformation of the composite is initiated earlier than our mean-field theoretical prediction because of the local stress concentration near the particulate. Hence, we propose a yield reduction method that enforces the earlier initiation of the plastic deformation in the matrix phase when obtaining an effective mechanical response. We show that the predictions from the adaptive incrementally affine scheme adjusted with the yield reduction match well with various numerical simulations on particulate-reinforced composites considering viscoelastic, elastic-viscoplastic, and viscoelastic-viscoplastic matrices under uniaxial, cyclic, and bi-axial loadings.