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Mechanical instabilities in melt spinning

Melt spinning is an industrial process used to produce a myriad of industrial components and has recently grown of importance due the ubiquitous presence of additive manufactured parts. During this process the material is extruded through a die and subjected to a state of deformation approximately uni-axial. However the non-uniformity of the temperature field in the radial direction induces non-uniform viscoelastic radial stresses, which are the reason for a non-uniform radial orientation of the molecules and a strong variation of the crystallinity in the material. The immediate consequence is that mechanical instabilities can rise leading to the catastrophic failure of the spinning process. These instabilities limit the rate of spinning of the polymer up to even totally preventing it. The melt spinning process can present different types of instability:

• Failure by capillarity: this instability, described by Ziabicki, Ide and White, is due to the surface tension of the fluid in the post-extrusion zone that can cause the rupture and subsequent dispersion in the form of drops of the filament. To prevent such an instability, a limit extrusion rate is usually enforced.

• Ductile filament rupture: due to high local stresses, a narrowing (neck) is formed in the filament. This type of instability, described by Ide & White, Chang & Lodge, typically manifests itself in the extension of thin polymers.

• Cohesive filament rupture: in this case, an instantaneous reduction or rupture of the filament cross section occurs. Such instability occurs mainly in cases of extension of dense polymers.

• Draw resonance: represents the most common and most important type of instability in polymer extension and modeling processes, since it gives a non-uniformity to the filament or film depending on the process.

This complex mechanical problem can be approached from different perspectives. The student can develop simple one-dimensional problem to capture the main feature of the spinning process by making some simplifying assumptions. This toy-problem have the advantages to be easily treatable and solvable numerically (in Matlab or Mathematica), yet they give a useful indication of the bifurcation patterns occurring in the real process. More complex scenarios, including the temperature variation along the filament, can be simulated by approaching the problem with numerical tool based on finite element, such as Comsol or Abaqus.

Keywords: fibre spinning, instabilities, additive manufacturing.

Sequential axisymmetric buckling in compressed cylinders

Collaborazione con M. Taffetani (University of Bristol)

Buckling events in compressed cylindrical structures lead to the emergence of variety of shapes, ranging from a Euler type of buckling (in very slender geometries) to localized necking or the appearance of the so-called Yoshimura diamond pattern (for thicker geometries). Recent experimental evidence reveals the possibility that, in scenarios where the presence of an internal pressurization is included, axisymmetric buckling can appear as a cascade of axisymmetric wrinkles: although overall one would obtain a axisymmetric peristaltic bulging, the wavemode of the final morphology is different from the scenario at the onset of the instability, because the bulges emerge sequentially.

The project has a numerical part where the system under consideration is implemented in the open-source partial differential equitation solver FEniCs (Abaqus could be another option to explore). The ad hoc numerical model will be used to investigate: (i) the sequential appearance of buckles; (ii) the imperfection localization of the individual buckle; (iii) the relation between pressure and end-shortening and the large amplitude stable modes. Beyond the numerical phase of the project, there is the possibility to proceed with a theoretical analysis to explain the physical mechanisms behind this phenomenon, using the tools of linear and weakly non-linear analysis also including the effect of the dynamical behaviour. Since the project contains different levels of complexity, it is suitable for different levels of expertise.

Findings from this project are of interest in the areas of structural engineering where thin-walled, non-slender, pressurized cylindrical structures are used.

Keywords: continuum mechanics, buckling, finite element.

Non-invasive testing for growing tissue in bioreactors

Collaborazione con M. Taffetani (University of Bristol)

Bioreactors are devices widely used in the field of tissue engineering to grow in vitro artificial biological tissues. In these devices, cells are seeded in a porous structure -called scaffold- and they can proliferate because the environment created in those devices is as much as possible similar to the physiological one, i.e. the conditions that the cells would find in vivo in the human body. For this reason, the bioreactor have, at the very least, to provide nutrients to the cells, to remove their waste products and to guarantee the necessary mechanical loads to the cells to grow. Since different types of cells (and the associated tissues to be produced) need different environmental conditions, different types of bioreactors have been proposed and specified to the specific cell cultures.

Ideally, from the moment when the cells are seeded to the moment when the tissue produced is implanted in the human host, one would like to keep the scaffold isolated from the external world in order to prevent contamination. On the other side, one would like to know exactly that the tissue produced has the desired mechanical properties and, thus, one would like to perform mechanical testing before implantation.

The aim of this project is to investigate the possibility to measure the mechanical properties of the tissue produced in an artificial bioreactor using non-invasive techniques. The specific setup to be considered is the bioreactor where the mechanical load is guaranteed via an oscillatory pressure field applied to the whole system. The project requires the modelling of the structure of the bioreactor system (i.e. bioreactor including the scaffold and the growing cells) and the investigation of the passive elastography technique to probe the mechanical properties of the tissue, starting from simplified reduced models. The growth behaviour of the tissue can be assumed known and taken from literature.

Finding from this research would be of interest for companies developing novel bioreactors and for clinicians/biologist to increase their confidence that the final tissue produced in the bioreactor has the expected mechanical properties.

Keywords: perfusion bioreactors, non-invasive testing, elastography.

Dynamics of weakly asymmetric spherical shells

The student will investigate the dynamic behaviour of spherical shells under forced and free vibrations. The symmetry of the shell make its dynamic behaviour particularly rich with multiple eigenmodes associated to the same eigenfrequency. The identification of this repeated modes is particularly cumbersome and requires ad-hoc numerical strategies, yet they can be exploited in structural health monitoring strategies to evaluate stiffness or mass variations along the shell. Experiments on prototype structures can be performed at Laboratorio Materiali e Strutture of the Department by using accelerometers and fast cameras (DIC) to capture the structural response when the prototype structures are excited through shakers.

Applications to real-world structures, such as Nervi's Palazzetto dello Sport are foreseen and can be also taken into consideration by reproducing their dynamic behaviour into finite element software.

Keywords: structural dynamic, damage detection, structural health monitoring.