Improved incrementally affine homogenization method for viscoelastic-viscoplastic composites based on an adaptive scheme

We proposed an adaptive incrementally affine method, a micromechanics-based mean-field homogenization scheme for viscoelastic-viscoplastic particle-reinforced composites, which is applicable for predicting the me-chanical response under complex loading conditions. The formulation is based on an incrementally affine scheme using algorithmic tangent operators while adaptively adjusting the mean strain of each constituent at every step of the loading process to reflect the changes in tangent operators and the shape of the reinforcing particles. We found that its prediction beyond the viscoelastic regime can be further improved by enforcing consistency be-tween the accumulated strain states of each phase and the concentration tensors, excluding accumulated affine strain and stress. It was inevitable that the plastic deformation of the composite was initiated earlier than what was predicted by the mean-field theory owing to the local stress concentration near the particles. Hence, we proposed a yield reduction method that enforces the earlier initiation of plastic deformation in the matrix phase when obtaining an effective mechanical response. We observed that the predictions of the adaptive incrementally affine scheme adjusted with the yield reduction agreed well with various numerical simulations of particle -reinforced composites considering viscoelastic, elastic-viscoplastic, and viscoelastic-viscoplastic matrices under uniaxial, cyclic, and biaxial loadings.