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Nonlinear analysis of helical structures

Francesco Filotto

office: LEE N 219
phone: +41 44 632 25 43
email: filotto@imes.mavt.ethz.ch

Introduction

Recent studies have shown the presence of helical patterns within the structure of highly hierarchical tendons. The current research seeks to develop fundamental models of helical structures that can be used to understand the basis of their mechanical function in collagen tissues. This project focuses on tendon and ligament as model tissues that are composed of extremely highly ordered, multi-scale helical collagen structures. These structures deliver exceptional mechanical properties, and the recovery of appropriate helical collagen structures after injury is an essential feature of healthy tissue repair. Being able to compute local distribution of stresses and strains helps understanding which mechanical stimuli act to promote in-cell growth.

Finite Element Model

Since the interaction between these sub-units and the embedding material, or their sliding against each other, are volumetric problems, thin-wire helix theories, largely used in ropes and cables literature, cannot be used. A complete 3D finite element model would be required. The current model is a constrained continuum model where, thanks to the kinematic assumption that the deformed body remains an helix, invariance is obtained in the deformation gradient and strain/stress measures. This allows to focus on any section of the helix, reducing the number of elements needed to get strain-stress distribution.

Fig.1 Deformed planar section and corresponding resulting axial force vs. applied axial stretch.

Multiscale Approach

The current research assumes that most hierarchical levels composing a tendon can be modeled as helical constructions. This allows us to create a single planar model that could be used (with different material and geometrical properties) at the various length scales. While in the first scale, both constituent elements might be considered isotropic, from the second scale on, a new material definition needs to be introduced to translate the structural response into the current scale. Helical structures offer a peculiar response: a torsion will also appear when axially stretched. In order to translate this phenomenon into material properties, chiral-cosserat materials will be considered.

Fig.2 Conceptual model for multi-scale approach.



 

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09/05/18 | Francesco Filotto | ZfM | ETH