Micro-Macro Description for Elastoplasticity of Materials with Lamellar Microstructure Using Anisotropic Eshelby Tensor

The elastoplastic behavior of dual-phase materials with lamellar microstructure is analyzed using a micro-macro approach. It involves the Hill's self-consistent scheme incorporating general anisotropic Eshelby tensor, and it can take into account both inherent and plastic deformation induced anisotropies. A high-precision numerical algorithm related to rotational ellipsoidal inclusion and anisotropic Eshelby tensors is developed. The elastoplastic behavior of both macroscopically anisotropic and isotropic materials is analyzed and compared with the result using isotropic Eshelby tensor. It shows that the difference between the result with an isotropic Eshelby tensor and that with an anisotropic Eshelby tensor is negligible if plastic deformation is not severe. The effect of the shape of the ellipsoidal lamellar inclusion on the material responses, the computation time and the convergence of numerical processes are also investigated. It shows that the convergence of the numerical process with a general anisotropic Eshelby tensor is as good as that with an isotropic Eshelby tensor, but for the former the computation time is much more. The shape of the ellipsoidal inclusion also strongly affects the computation time.