A two-scale method to include essential behaviour of bolted connections in structures including elevated temperatures

A two-scale method is proposed to simulate the essential behavior of bolted connections in structures including elevated temperatures. It is presented, verified, and validated for the structural behavior of two plates, connected by a bolt, under a variety of loads and elevated temperatures. The method consists of a global-scale model that simulates the structure (here the two plates) by volume finite elements, and in which the bolt is modelled by a spring. The spring properties are provided by a small-scale model, in which the bolt is modelled by volume elements, and for which the boundary conditions are retrieved from the global-scale model. To ensure the small-scale model to be as computationally efficient as possible, simplifications are discussed regarding the material model and the modelling of the threads. For the latter, this leads to the experimentally validated application of a non-threaded shank with its stress area. It is shown that a non-linear elastic spring is needed for the bolt in the global-scale model, so the post-peak behavior of the structure can be described efficiently. All types of bolted connection failure as given by design standards are simulated by the two-scale method, which is successfully validated (except for net section failure) by experiments, and verified by a detailed system model, which models the structure in full detail. The sensitivity to the size of the part of the plate used in the small-scale model is also studied. Finally, multi-directional load cases, also for elevated temperatures, are studied with the two-scale method and verified with the detailed system model. As a result, a computationally efficient finite element modelling approach is provided for all possible combined load actions (except for nut thread failure and net section failure) and temperatures. The two-scale method is shown to be insightful, for it contains a functional separation of scales, revealing their relationships, and consequently, local small-scale non-convergence can be handled. Not presented in this paper, but the two-scale method can be used in e.g. computationally expensive two-way coupled fire-structure simulations, where it is beneficial for distributed computing and densely packed bolt configurations with stiff plates, for which a single small-scale model may be representative for several connections.