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Type of thesis
From buckling springs to pneumatic artificial muscles: analytical and computational study of tubular braided meshes made of helical fibers
Scientific disciplinary sector
Istituto di Biorobotica - PHD IN BIOROBOTICA
relatore Prof. DE SIMONE, ANTONIO
- Braided meshes
- Differential geometry
- Computational mechanics
- Elastic rods
- Mckibben actuators
Exam session start date
Biology and engineering offer many examples of tubular assemblies of elastic helical fibers. The shape-shifting capabilities of such structures make them adaptable to dynamically-changing functional needs, and thus of great research interest in many technological applications. Historically, the highly non-linear mechanical behavior of helical assemblies has been studied either through simplified geometrical models or through complex numerical simulations. However, geometrical models are too simplistic, while numerical simulations have high computational cost and do not reveal the inner working principles (“black box” problem). In the perspective of developing novel biomedical and robotic applications, this thesis aims to overcome the limitations of the two mentioned approaches to model tubular braided meshes of helical fibers. According to the common use of braided meshes, we chose to study their force-displacement response under axial compression. To this aim, we developed a coarse-grained model that is accurate, and yet physically insightful and computationally efficient. Its speed does not rely on raw computational power nor it sacrifices accuracy: we carefully selected the essential degrees of freedom of the mesh to reproduce the target behavior. <br>To obtain this coarse-grained framework, we investigated what degrees of freedom could be neglected. Firstly, in order to understand the role of mutual interactions between helical fibers in the emergence of an ensemble response, we compared the mechanical response under axial compression of a single helical fiber with that of braided meshes, adopting a standard FEM approach (Chapter 3). We found that, whereas a single helix buckles, those forming a mesh deform coherently as stable helical shapes wound around a common axis, meaning that mutual interactions lead to a stable ensemble response without buckling. <br>Since fibers undergo the same deformation when compressed axially, their center-lines lie on a common revolution surface, called envelope surface. From this observation we developed a coarse-grained model based on a continuum theory that identifies tubular braided meshes with their envelope surface (Chapter 4). The key idea is to relate surface geometry and fiber kinematics, which allows us to follow large deformations of the fibers at a significantly lower computational cost than traditional FEM for Solid Mechanics. Moreover, the experimental validation revealed the emergence of a plateau with vanishing stiffness in the axial force-displacement curve; this feature could prove quite useful in applications where an applied compressive force has to be “forgiving” of small settlements of the compressed object.<br>Furthermore, we used a simplified version of the proposed model to study McKibben actuators, a well-known example of braided meshes in Soft Robotics, and validated it against experimental and numerical results found in the literature (Chapter 5). Our model shows higher accuracy than currently available geometric models, as well as good matching with complex FEM ones, while requiring a fraction of their computational cost. Additionally, our results indicate that the braided mesh sustains the major part of the load, whereas most of the external work is stored by the inner chamber as elastic energy, offering an explanation of why simplified formulas may be quite effective in predicting the force-pressure behavior of McKibben actuators.
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