In recent times, soft matter has gained significant interest among researchers in the fields of biomechanics and biomedicine, especially in areas like soft robotics and biopolymers, due to its remarkable ability to undergo substantial deformations. Soft robotics often requires materials that can flexibly adapt to or mimic the movements of living organisms, requiring properties of flexibility and easy deformability. Biopolymers, naturally occurring in the human body, such as within brain tissue or blood clots, have gained attention due to their tendency to exhibit extensive deformation even under minimal loads. Consequently, there has been a growing emphasis on investigating stress-strain responses associated with these materials in recent years. This research particularly centers on a specific deformation phenomenon known as the Poynting effect.

The Poynting effect is related to the transverse stress or strain response when subjected to simple shear, revealing that the application of simple shear strain does not solely result in simple shear stress. This intriguing phenomenon captures our attention, primarily because it challenges intuitive expectations.

Within the scope of this thesis, we employ two distinct deformation gradient tensors to analyze stress-strain responses under two separate boundary conditions: constant gap and constant normal stress boundary conditions. We also introduce a methodology for predicting the sign of the Poynting effect under conditions of small yet finite strain. Finally, we validate our analysis through simulation experiments.

We have modified Meng's original network-theory-based model, which is rooted in an energy density function derived from the force-extension relationship of a single chain. Our objective was to create a model with nearly incompressible properties in order to investigate the impact of compressibility. To determine the direction of the Poynting effect, we directly computed the stress and strain responses of a cube under shear forces. Later, we developed a method for predicting the direction of the Poynting effect without the need for precise stress and strain calculations. Our results demonstrate the successfulness of this prediction method.

The simulation outcomes reveal a closer alignment of the four-variable tensor, suggesting that our chosen boundary conditions more closely resemble those used in numerical solutions. Additionally, it is worth noting that the specific geometries we employed in our study, namely the cylinder and cube, did not have a discernible influence on determining the direction of the Poynting effect, especially within the context of the selected model and material parameters.

Emulsions, characterized as a metastable dispersion of one liquid into a second one in the presence of surface-active agents, have complex rheology that interests both physicists and industries. Depending on the volume fraction of the dispersed phase ($\phi$), emulsions can display both solid-like and liquid-like behavior. Rheometrical measurements of complex fluids usually yield several flow curves, each corresponding to a certain volume fraction. Scaling analysis assists in investigating the fundamental traits of those flow curves by rescaling the rheometrical data onto several master curves described by a few non-dimensional variables.

Whereas experiments successfully scaled the data onto master curves are usually of three-dimensional complex fluids, many numerical simulations are of low-cost two-dimensional flows, lacking direct referable experimental data. Additionally, scenarios involving droplets, bubbles, and particles trapped at the interface of two fluids inherently constitute a two-dimensional system. Motivated by these considerations, the project aims to measure the rheology of emulsion monolayers.

A cylindrical Couette ring configuration was built to facilitate the generation of monolayers and rheometrical measurements. The image processing method was developed to deal with three distinct scenarios, high $\phi$, medium $\phi$, and low $\phi$, depending on the concentration of droplets. The steady velocity profiles and the averaged packing fractions were acquired through image analysis. Subsequently, the local rheology was deduced and compared with the macroscopic rheological measurement at various packing fractions. While the densely packed emulsion monolayer is a shear-thinning yield stress material, the spatial cooperativity (non-local effect) and capillary force (wall effect) were found to have a profound influence on the rheology.

During the last years the demand for vegetarian products has increased. A subgroup of these vegetarian products consists of meat analogs, which are products that resemble meat in its functionality and are prepared in a similar fashion. One of the companies producing these meat analogs is Rival Foods. Rival Foods has been working on a production process based on a Couette cell, in which the dough is sheared in an annular region between two concentric cylinders. This allows them to create highly fibrous products with a thickness of roughly 3cm. Other production processes such as extrusion cooking are unable to achieve this combination of structure and thickness. In upscaling the production process, preferably a larger gap width between the cylindrical surfaces of the cell is preferred, because the thickness of the product is a unique selling point. Larger gap widths lead to greater temperature inhomogeneity and gradients, which negatively impacts product quality. It is currently not possible to accurately measure the temperature profile throughout the cell. Therefore, in this thesis a model has been developed in OpenFOAM which calculates the temperature profile with a small number of material parameters and process conditions as input. The model assumes the ingredient mixture behaves as a temperature dependent power law fluid. Rheological measurements have been performed to quantify these temperature dependent power law parameters. To study the influence of the viscous dissipation, preheat temperature, mixture density, and product thickness on the temperature field during processing, multiple simulations have been performed. The simulations used a time step of 0.0001s, for which the temperature, velocity, viscosity, and viscous dissipation were not yet fully converged. The principal flow in the Couette cell geometry was in the direction of rotation of the inner cylinder as expected and had a velocity with order of magnitude e-01 m/s. Besides the principal flow a secondary flow pattern has been found as well, consisting of vortices which had a velocity with order of magnitude e-03 m/s. These secondary velocity components were responsible for additional advection of heat in the simulation which resulted in a different temperature profile than expected. Since the Taylor number was well below the critical Taylor number, the existence of Taylor vortices could be excluded. After a further refinement of the time step the vortices disappeared. Running the full simulations with this time step would take months per simulation and was therefore not an option. It was concluded OpenFOAM had trouble simulating power law fluids with high viscosities.

A random periodic two-dimensional spring network us built using a Poisson disk distribution and computing the Delaunay triangulation of the centers of the disks. The edges of the network represent springs that obey Hooke’s law with an adjustment on the spring constant. The adjustment allows spring to soften and to break. The two-dimensional spring network can, in combination with the adjustment, be used to model fatigue. The network softens during a cyclic loading. During each cycle the normal strain is increased until the normal stress equals a specific cyclic stress σcycle. The loading is continued until the network is broken into two pieces, with a number of N completed cycles. For a range of cyclic stresses the number of cycles before failure N is calculated and fitted with an exponential relation. The fitting parameters for networks with #n = 32 are similar to those of a networks with #n = 64. Throughout the cyclic loading springs will break and as a result the coordination of ¨ the network decreases. The coordination of the network can drop below 4. These ¨ networks are hypostatic, while the initial network was hyperstatic. This claim is asserted by the stress-strain curve. The transition from hyperstatic to hypostatic leads to a conceptual question: ”Is the spring network broken if it has teared into two pieces or when it is hypostatic?”.

Surprisingly, liquid media of dispersed dry micron-sized particles can generate tremendous impact resistance, can grow solid protrusions when acoustically-vibrated and can cause a range of other peculiar phenomena to objects sinking in their interior, even though their appearance essentially remains ’liquid-like’. These heterogeneous mixtures of undissolved particles, referred to as suspensions, can be found all around us: e.g. in paints, blood, mudslides, landslides, etc. Moreover, due to some suspensions’ shear-thickening behaviour their use has been investigated for liquid-like body armor applications, new damper designs and many more. Yet, the core physical mechanism of their behaviour in its various regimes is still not completely understood. This thesis work employs the novel ultra-fast Magnetic Resonance Imaging methodology proposed by Alexander Penn, also a member of the ETH Zurich laboratory from which this work originates, to image non-intrusively into a shear-thickening suspension of cornstarch and water while a spherical intruder impacts and settles in its interior. First off, by fitting a rigid steel wire inside the settling object and imaging a marker on top of it with a high-speed camera, behaviours similar to those observed by von Kann et al. are evident: the intruder oscillates around a terminal velocity in the bulk of the suspension and experiences stop-and-go cycles near the container base. This act, however, inherently restricts motion by allowing the intruder to move only in the vertical direction. Therefore, we utilize 1D and 2D MR imaging to obtain information about the intruder’s horizontal and undisturbed vertical motion to draw conclusions that the object exhibits similar oscillations in amplitude and frequency also in the transverse component. In addition to those, we perform 2D velocity-encoded MRI scans to obtain the velocity and shear rate fields with sufficient time resolution to capture the suspension behaviour at the relevant phenomenological regimes. The data suggested that, on comparison with reference rheology experiments, the shear rates during the terminal velocity oscillations, resultant from the fluid inertia around the object as it settles, appear to be in close proximity to the critical shear rate for discontinuous shear thickening (DST, or an orders-of-magnitude jump in stress). To continue, 1D MRI measurements revealed a phenomenon new to us to be visible just after the impact: upon increasing mass, size, and drop height of intruders, the transient oscillations which transition to stable bulk oscillations were found to transform into several distinct stop-and-go cycles very much alike those that occur close to the container bottom. A qualitative physical mechanism was proposed based on the dependencies found in these behaviours. Last but not least, the effects of size while keeping the same buoyancy ratio were studied qualitatively. Direct evidence from all executed experiments confirmed secondary stable bulk oscillation regions for objects of larger size.

Emulsions and foams are commonly found in products made by industries ranging from those
associated with food and pharmaceuticals to those involved in selling personal care products.
This work is motivated by the need for accurate models of their mechanics, which can then be
used for efficient processing.

They can be thought of as soft repulsive spheres that can overlap with one another to a
certain extent, along with a weakly attractive potential between the spheres. We study such
systems in the context of the jamming transition - a transition seen in disordered systems
from a flowing state to one where they jam and develop rigidity. The canonical model for
the jamming transition is one of soft, repulsive and frictionless spheres which describe many
common physical systems. An attractive tail is added to the repulsive potential used in this
canonical model, in order to describe systems like emulsions and foams.

We compare the linear response of emulsions and foams with that of the canonical model.
Recent studies have shown for the canonical model that when we impose a quasi-static shear
strain at the boundaries of disordered systems, the linear elastic regime survives for a small
window close to the beginning of the straining action. It gives way to softening in the linear
elastic regime, associated with the beginning of a nonlinear response regime. We investigate
how this window leading to the non linear response changes for emulsions and foams. The
predictions obtained for softening, from ideas that derive from linear response in the jamming
transition and by imposing a quasi-static shear strain is compared for both emulsions and the
canonical model.