Minkowski plasticity in 3D frames: Decoupled construction of the cross-section yield surface and efficient stress update strategy

This work makes the Minkowski sum of ellipsoids into a consolidated tool for the representation of the yield surface of arbitrarily shaped composite cross sections under axial force and biaxial bending and shows how best to use it within the incremental nonlinear analysis of three-dimensional frames. A geometric interpretation of each term of the sum allows us to construct complex convex surfaces using a low number of ellipsoids, each of them evaluated in a robust and efficient decoupled manner. Specialized algorithms, which exploit the parameterization of the yield surface in terms of a cross-section collapse mechanism, are proposed for an efficient stress update based on the elastic predictor–return mapping scheme on a three-dimensional beam finite element. The derivation of the algorithmic tangent moduli for the Minkowski sum completes the elements required for an efficient path-following nonlinear analysis. The proposed methodology is general and can be applied for the representation of any zonoid yield surface and the corresponding implicit stress integration to a variety of structural and plasticity models.