An implicit-gradient-enhanced incremental-secant mean-field homogenization scheme for elasto-plastic composites with damage

• A meanfield homogenization for elasto-plastic material with damage is proposed.
• The mean-field homogenization relies on the newly developed incremental-secant method.
• This accounts for the unloading of one phase during the softening of the other one.
• The method is formulated in a non-local setting to ensure the solution uniqueness.
• The framework is used in a multi-scale way to simulate laminate responses.

This paper presents an incremental-secant mean-field homogenization (MFH) procedure for composites made of elasto-plastic constituents exhibiting damage. During the damaging process of one phase, the proposed method can account for the resulting unloading of the other phase, ensuring an accurate prediction of the scheme. When strain softening of materials is involved, classical finite element formulations lose solution uniqueness and face the strain localization problem. To avoid this issue the model is formulated in a so-called implicit gradient-enhanced approach, with a view toward macro-scale simulations. The method is then used to predict the behavior of composites whose matrix phases exhibit strain softening, and is shown to be accurate compared to unit cell simulations and experimental results. Then the convergence of the method upon strain softening, with respect to the mesh size, is demonstrated on a notched composite ply. Finally, applications consisting in a stacking plate, successively without and with a hole, are given as illustrations of the possibility of the method to be used in a multiscale framework.