**3. Discussion**

This study illustrates how the relationship between the microstructure and function of a product can be studied using a dedicated nonlinear multiphysics, multicomponent, finite element analysis. The type of analysis done in this study was made possible with commercial codes, because they lack the vital options needed. The feasibility of complex non-linear analyses combining large deformations and mesh-free multiple crack propagations through a swelling heterogeneous material has been demonstrated. Much more is needed for the robustness of the XFEM code in computations that resolve the microstructure, as deformations are very large, locally, and heterogeneities hamper the smoothness of the solutions. This investigation is mainly focused on the effects of intrinsic properties on the fracture behaviour. We studied two dissipative mechanisms here, where one is the propagation of existing cracks, and the other is the nucleation of cracks. From the results, it appears that the crack propagation and nucleation are largely affected by the intrinsic properties of the material, and particularly the properties of the cross-linked shell around the softer swelling hydrogel particle.

Generally, the higher the shear modulus of the shell, the earlier the initial crack propagates. Besides, a stiffer shell resists the particle's ability to deform, and helps to keep the shape of the particle. Less deformation comes with smaller effective stress in the middle part, which suppresses crack growth. However, a swelling media requires high swelling capacity. Therefore, there needs to be a balance between the swelling of the inner part and the elastic stiffness of the outer part. This numerical simulation can be used as a tool to optimize the material property of the gel in the microstructural design of the swelling hydrogel particle. By comparing the crack propagation with different ultimate strengths of the shell, we found that the ultimate strength only affects the rate of the propagation. Thehighertheultimatestrengthis,theslowerthecrackpropagates.

 From Figures 5–7, we conclude that:

• The higher the ultimate strength of the shell, the fewer the cracks which nucleate.

• The higher the shear modulus of the shell, the more cracks which nucleate.


Figure 8 presents a cascade of nucleations with different crack openings with material properties of Table 1. The events illustrate that the failure of the gel builds up in stages. It starts from fewer defects and weakens the material while the material is still functioning. When more and more defects appear and interact with each other, the material finally fails. The process of the defects is the same as the process of the nucleation. The opening of cracks not only depends on the stress state, but also on the neighbouring cracks. If the neighbouring crack is located close to the current crack with a relatively large opening, it will impede the opening of the current crack.

The software presented in this paper serves as a grea<sup>t</sup> numerical support for the design of a proper cross-linked shell, such as the special cross-link density required to achieve a specific stiffness and fracture resistance. The stiffness ratio between the inner part and the shell is a critical parameter that determines the performance of the product. A high ratio delays the swelling of the hydrogel, and too high a ratio disallows the failure of the hydrogel altogether.
