Cyclic Yielding of Tubular Structures

In an effort to design according to the true behaviour of structures focus is on increasing the accuracy of the individual aspects of the structural models. The present thesis addresses cyclic plasticity models and is organised in five parts; the first four parts focus on different aspects of computational cyclic plasticity models. The fifth part focuses on the effects of using improved cyclic plasticity models. The sum of the parts will support the ability to design according to the true behaviour of a structure.
The first part addresses the development of a cyclic plasticity model. A cyclic plasticity model with parameter evolution is presented based on three potentials; a specific energy defining the constitutive relations, a yield function defining the size and shape of the elastic domain in the form of a yield surface, and a plastic flow potential defining the evolution of the plastic strains. The cyclic plasticity model exhibits kinematic hardening and the translation of the center of the yield surface is limited by a surface similar to the yield surface defining an ultimate capacity. The parameter evolution enables modelling of effects as cyclic hardening/softening.
The second part focuses on developing a generic first-order yield surface format usable for e.g. anisotropic materials and plastic hinges in beam members and joints. The format is defined as a sum of square roots of quadratic terms that individually would represent ellipsoids and the surface is thereby convex. The format will be homogeneous for most yield surfaces of interest resulting in improved algorithmic properties. It is shown to be possible to locally reduce the curvature of the yield surface while still having a single-equation format.
The third part describes how a frame element can include the four most important effects in analysis of tubular structures with cyclic plasticity: an elastic initially imperfect member, elastic local joint flexibility and plastic mechanisms at the member ends and in the joints. The frame element is based on an equilibrium format, splitting element displacements into a set of deformations and a set of rigid body motions. The deformations and thereby the flexibilities are additive. The element has an explicit stiffness matrix that only requires inversion of a matrix of maximum size 4 × 4. A standard full format element including rigid body motions is obtained by use of the equilibrium conditions.
In the fourth part a robust return algorithm is developed. The return algorithm is based on satisfying the generalized strain evolution equations in the final state in combination with ensuring the final stress state is located on the yield surface. The robustness is increased by making a second order approximation of the generalized stress increment leading to a two-step return algorithm. First a mid-step is made to obtain information and subsequently a full step is made with the information obtained at the mid-step.
In the final part the effects of cyclic plasticity are discussed including the effects of elasto-plastic buckling and plastic deformation for complex structures. The permanent change of the geometry reduces characteristic stiffness and capacities of the structure. The previously developed models have been used to update a recognized computer code making it more robust and increasing the ability to represent the true behaviour of frame structures.