Mechanics of tubular meshes formed by elastic helical fibers

Tubular structures made of elastic helical fibers are widely found in nature and in technology. The complex and highly nonlinear mechanical properties of such assemblies have been understood either through minimal models or through complex simulations describing each individual fiber and their interactions. Here, inspired by Chebyshev’s geometric model of nets, we propose and experimentally validate a modeling framework that treats tubular braided meshes as continuum surfaces corresponding to the virtual envelope defined by the fibers. The key idea is to relate surface geometry and fiber kinematics, enabling us to follow large deformations. This theory is amenable to efficient computations and, in axisymmetric cases, the problem reduces to finding two scalar fields defined over 1D segments. We validate our model against experiments of axial compression, revealing the existence of a plateau with vanishing stiffness in the axial force–displacement curve, a feature that could prove particularly useful in applications where an applied compressive force needs to be held constant even against settlements of the compressed object.