An elasto-plastic self-consistent model for damaged polycrystalline materials: Theoretical formulation and numerical implementation

An advanced elastoplastic framework accounting for induced plastic anisotropy fully coupled with ductile damage

“…A detailed description of the numerical scheme used to integrate the single crystal constitutive equations with damage effect has been provided in [45,67]. Once the constitutive equations are integrated at the single crystal scale, the self-consistent scheme is then used to obtain the macroscopic response from the microscopic one.…”

“…This model assumes that the strain field is homogeneous through the polycrystalline aggregate. It has been coupled in several contributions [43][44][45] with the FE method to simulate different forming processes. In reality, the assumption of the strain field homogeneity cannot be fulfilled due to the grain boundaries and the differences observed in the crystallographic orientation between the different grains or crystals.…”

“…Consequently, more sophisticated and accurate mean-field schemes have been developed in the literature to accurately describe the mechanical behavior of polycrystalline media. In this area, one can quote the self-consistent scheme [45][46][47]. This scheme considers each grain as an ellipsoidal inclusion surrounded by an infinite homogeneous effective medium having the average properties of the real polycrystal.…”

“…Moreover, the equilibrium condition across the grain boundaries is satisfied within the self-consistent approach. This scheme has been coupled in several recent contributions with the FE method [45,[48][49][50]. The fullfield homogenization approaches are generally based on solving the multiscale equations by means of -5-the FE method, after spatial discretization of the studied polycrystalline aggregate [51][52][53].…”

Regularized Yield Surfaces for Crystal Plasticity of Metals

“…Until recently, return mapping algorithms for yield surfaces with high exponents have not been numerically stable. In a recent publication, Paux et al [15] avoid this problem by combining the best part of the two available methods, using the regularized yield surface to obtain a smooth, unique tangent modulus, while using the highly efficient Schmid model for the integration of the single crystal constitutive equations. However, progress has recently been reported related to stable, efficient return-mapping algorithms for yield surfaces with high exponents.…”