Non-localized contact between beams with circular and elliptical cross-sections

Numerous materials and structures are aggregates of slender bodies. We can, for
example, refer to struts in metal foams, yarns in textiles, fibers in muscles or steel
wires in wire ropes. To predict the mechanical performance of these materials and
structures, it is important to understand how the mechanical load is distributed between
the different bodies. If one can predict which slender body is the most likely
to fail, changes in the design could be made to enhance its performance. As the
aggregates of slender bodies are highly complex, simulations are required to numerically
compute their mechanical behaviour. The most widely employed computational
framework is the Finite Element Method in which each slender body is modeled as
a series of beam elements. On top of an accurate mechanical representation of the
individual slender bodies, the contact between the slender bodies must often be accurately
modeled. In the past couple of decades, contact between beam elements
has received wide-spread attention. However, the focus was mainly directed towards
beams with circular cross-sections, whereas elliptical cross-sections are also relevant
for numerous applications. Only two works have considered contact between beams
with elliptical cross-sections, but they are limited to point-wise contact, which restricts
their applicability. In this Ph.D. thesis, different frameworks for beams with
elliptical cross-sections are proposed in case a point-wise contact treatment is insufficient.
The thesis also reports a framework for contact scenarios where a beam is
embedded inside another beam, which is in contrast to conventional contact frameworks
for beams in which penetrating beams are actively repelled from each other.
Finally, two of the three contact frameworks are enhanced with frictional sliding,
where friction not only occurs due to sliding in the beams’ longitudinal directions
but also in the transversal directions.