Gradient plasticity with the tangential-subloading surface model and the prediction of shear-band thickness of granular materials

An extended gradient elastoplastic constitutive equation is formulated, which is capable of describing the plastic strain rate due to the rate of stress inside the yield surface and the inelastic strain rate due to the stress rate component tangential to the subloading surface by incorporating the tangential-subloading surface model. Based on the extended constitutive equation, the post-localization analysis of granular materials is performed to predict the shear-band thickness. It is revealed that the shear-band thickness is almost determined by the gradient coefficient characterizing the inhomogeneity of deformation, although the stress–strain curve is strongly dependent on material properties.     

Multi-scale analysis in elasto-viscoplasticity coupled with damage

The purpose of this study is to present a micromechanical approach, based on the transformation field analysis (TFA), proposed by Dvorak, which has been generalized at Onera in order to analyze the nonlinear behavior of heterogeneous materials in elasto-viscoplasticity coupled with damage. In such analysis, the macroscopic constitutive equations are not purely phenomenological but are built up from multi-scale approaches starting from the knowledge of the properties of the constituents at the microscopic or mesoscopic scales. The model can take into account some local characteristics that can evolve during the thermo-mechanical applied loads or the manufacturing process, like the grain size for metallic alloys or the fiber volume fraction for composites.The determination of some specific tensors which are present in this formulation is closely linked to the microstructure morphology of heterogeneous materials constituting the macroscopic structure. For example, an Eshelby’s based approach is more appropriate to characterize polycrystalline materials with a random microstructure, while the homogenization of periodic media technique can be used for composite materials with a sufficiently regular microstructure. The proposed methodologies allowing to perform this nonlinear analysis across the scales are illustrated with examples based on the behavior of structures reinforced with a long fiber unidirectional metal matrix composite.