Stress triaxiality and Lode angle along surfaces of elastoplastic structures

Expressions for the stress triaxiality and the Lode angle along surfaces of elastoplastic structures are established in case of monotonic loading. The stress triaxiality is shown to be governed by the accumulated plastic strain when traction free boundary condition is considered. The exact expressions obtained are generalized to any loading thanks to the proposal of a multiaxiality rule or heuristics whose two parameters are determined from elastic computations of the structure considered: a first one with the elastic properties of the material, a second one quasi-incompressible. The multiaxiality rule proposed can then deal with both plane strain and plane stress conditions. The stress triaxiality at the surface is shown related to the Lode angle. The corresponding expressions are validated on different structures and loadings. Finally, two applications are presented: the enhancement of energetic methods for plasticity post-processing and the enhancement of homogenization localization laws.