Dealing with stress : elasticity and fracture of soft network materials

Fracture of materials is both undesirable and unavoidable; therefore, there is great interest in methods to either forecast or control the fracture process of a material. To develop these methods, a deep understanding of the microscopic fracture process is needed covering the entire process from the scission of the first atomic bond to catastrophic failure of the entire material. In this thesis we study the microscopic fracture processes in soft network materials, ranging from elastomers, like rubber, to biological fibre networks, like collagen. Due to their disordered network structure, these materials can undergo large deformations prior to the damage accumulation process, in contrast to stiff materials, like concrete, where deformation is negligible. Here we investigate the implications of these large deformations on the elastic response and the fracture process of soft network materials. Specifically, we investigate the role of the network structure on elasticity and fracture via highly coarse grained models, wherein the network structure plays a central role. To cover the whole range of soft network materials ranging from soft brittle to soft ductile, we model both single network materials and composite networks materials where two or more networks are combined.

In Chapter 2 we introduce the simplest model to study fracture in networks that can undergo large deformations: the athermal central-force elastic model. In this two-dimensional model the network structure is simplified to a graph consisting of linear springs and nodes and its equilibrium configuration is found by an energy minimization procedure. Although the elastic contributions in these networks only comes from the elements, rearrangements at the network level have a significant impact on the mechanical and fracture response. We also use our model to explain the role of network structure in the fracture response of disordered collagen networks, revealing that the athermal central-force elastic model can be a helpful tool in understanding the microscopic fracture response of real soft network materials.

In the athermal model, the effect of thermal fluctuations and other time related processes, such as relaxation, are neglected. However, many soft network materials are actually highly sensitive to thermal fluctuations. To study the effect of these fluctuations we embed our central-force elastic model in a Langevin dynamics environment in Chapter 3, introducing both thermal fluctuations and an implicit solvent. We find that temperature has two seemingly opposing effects on network fracture. Entropic effects homogenize stress with respect to the athermal simulation. However, the stochastic nature of the thermal fluctuations also allows rupture of bonds that are on average not overstretched, which can be understood as a destabilizing effect.

In Chapter 4 we shift our attention to composite networks, by investigating the linear and non-linear response of collagen networks embedded in a matrix of crosslinked hyaluronan polysaccharides, the two main component of the extracellular matrix, the network structure that supports the cells in our body. The presence of two networks results in an enhancement in the linear modulus due to a competition between their preferred modes of local deformation. Another intriguing experimental finding is that upon crosslinking the hyaluronan, a negative normal stress arises, indicative of a tendency to compress. We find that the hyaluronan network pulls on the collagen fibres, which causes a delay in the onset of strain-stiffening. We have been able to capture both the enhanced linear modulus and the delayed strain stiffening by expanding the central-force elastic model, describing the composite as a subisostatic network with bending interactions between neighbouring bonds, representing the collagen network, which is coupled to a homogeneous soft network, representing the hyaluronan matrix.

In Chapter 5 we shift our focus to the fracture response of double networks, inspired by the significantly enhanced fracture response found in double network elastomers, hydrogels, and macroscopic materials. All these materials show that the response of an initially brittle network, also called the sacrificial network, can be shifted to a seemingly ductile response by embedding it in a significantly softer matrix network. We explore this transition from brittle to ductile behaviour by expanding upon the idea that the location of the brittle-to-ductile transition is governed by a force balance between the two networks. We locate the transition from brittle to ductile in a two-spring model, a multi-spring model and a random spring network model (another variant of the central-force elastic model) and find that in all models the location of the brittle-to-ductile transition can be predicted even when disorder is included in the latter two models. A detailed study of the network model reveals that also the development of the microscopic fracture response can be understood with respect to this brittle-to-ductile transition.

In Chapter 6 we also study the fracture response of a double network via a coarse grained model, but now we use a three-dimensional model that specifically targets polymer double networks. We explicitly model the polymers as a string of particles, so that each bond represents a Kuhn length. We find that our networks behave similar to the experimental systems, and we can even rescale the initial mechanical response following a procedure proposed in literature for elastomers and hydrogels. We find that the damage response of our networks takes place in two steps. At first bond scission is governed by the first network, while after the yield strain interactions between the two networks dominate bond scission. This fracture mechanism, and the associated evolution of microscopic damage deviates significantly from the affine predictions for the damage response, where network structure is not considered. Overall, this research demonstrates that redistribution of stress over the network plays an important role in the damage response of polymer networks.

In the general discussion we reflect on our findings and present a microscopic picture of fracture in soft network materials. Furthermore, we discuss a strategy to explore fracture processes that span a range of time scales, such as delayed fracture. Finally, we discuss our findings in the context of continuum elasticity and provide an outlook for future research into fracture of soft network materials.