Derivation of a surrogate membrane element for ring-net structures

The thesis work involves a comprehensive review of truss and membrane elements, with a focus on the respective element derivation and the extension to geometric non-linear kinematics. The theoretical review concerns also the mathematical foundations of the constitutive law, particularly focusing on a multi linear constitutive law and a new methodology was developed in case of materials with enormous increase of stiffness depending on their current strain. The multi-linear material law known from literature suffers from convergence issues in case of the special material behaviour of the ring nets which show a sudden increase of stiffness in dependence on the ring deformation. Therefore, a new methodology which enhances the existing multi-linear material model and allows to solve the constitutive behaviour of these ring elements using an implicit solution scheme. In addition, the physical behaviour of the ring wire net was transferred to a membrane description deriving a correlation of membrane strain and the deformation of the ring combining it with the respective multi-linear material formulation. This approach allows to define the constitutive material behaviours of surrogate membrane models to describe the complex physical behaviour of the ring net wires which are a main component of highly flexible protective structures. The model's theoretical validity was systematically assessed through implementation and verification using open-source computational tools, ensuring alignment between numerical predictions and physical experiments.