On the Analysis, Simulation and Structural Design of Helical Constructions

The present thesis provides analytical and numerical modeling developments on the characterization and simulation of the mechanical response of helical constructions. Moreover, it presents a modeling framework for the assessment of the torsional response bounds of multilayer helical assemblies. Furthermore, it elaborates a methodology for the selection of the braiding pattern of layered helical constructions. Finally, it explicates a modeling scheme for the inference of the structural composition of tendon fascicles. On the characterization of the helix structural response, a modeling extension is presented, incorporating radial strain as an additional degree of freedom to the commonly favored axial and torsional ones. To that extent, the governing kinematic, constitutive and equilibrium equations are formulated with the use of a beam based model, providing closed-form stiffness term expressions. The extended structural response is further assessed by means of a dedicated planar finite element that not only allows for the simulation of the above broached loading patterns but also for the numerical modeling of thermal loading. Moreover, the present work provides a modeling scheme for the demarcation of the mechanical response bounds of multilayer helical constructions subject to structural kinematic constraints. In particular, the constructions’ torsional response bounds are analyzed considering a wide range of braiding patterns. The response of the kinematically constrained structures is related by means of scaling factors to the stiffness properties of the unconstrained one, which can be analytically calculated upon closed-form expressions. Furthermore, a quantitative framework guiding the mechanical design of layered helical assemblies is reported. More specifically, a methodology allowing for the optimization of the structural braiding patterns is presented. The favored structural arrangements are selected so that they maximize the resistance of the arising construction to axial loads and concurrently minimize its torsional propensity. The methodology is used to retrieve favorable structural patterns for helical assemblies comprised of up to five layers, providing a database that covers most practical applications. Finally, the present thesis explicates a numerical model for the inference of the structural composition of tendon fascicles. In particular, tendon experimental data are coupled to finite element and Bayesian uncertainty quantification modeling. The finite element models allow for the recreation of the available experimental set-ups in a computationally tractable way, while the Bayesian framework allows for a direct comparison amongst hundreds of different model classes. Thereupon, probabilistic bounds for the model parameters are provided, establishing a fundamental linkage between successive tendon hierarchi-