Modelling of damage of a liquid-core microcapsule in simple shear flow until rupture

Capsules, composed of a liquid core protected by a thin deformable membrane, offer high-potential applications in many fields of industry such as bioengineering. One of their limitations comes from the absence of models of capsule damage and/or rupture when they are subjected to an external flow. To assess when rupture is initiated, we develop a fluid-structure interaction (FSI) numerical model of a capsule in Stokes flow that accounts for potential damage of the capsule membrane. We consider the framework of Continuum Damage Mechanics and model the membrane with an isotropic brittle damage model, in which the membrane damage state depends on the history of loading. The FSI problem is solved by coupling the finite element method, to solve for the membrane deformation, with the boundary integral method, to solve for the inner and outer fluid flows. The model is applied to an initially spherical capsule subjected to a simple shear flow. Damage initiates at a critical value of the capillary number, ratio of the fluid viscous forces to the membrane elastic forces, and rupture at a higher capillary number, when it reaches a threshold value. The material parameters introduced in the damage model do not influence the mode of damage but only the values of the critical and threshold capillary numbers. When the capillary number is larger than the critical value, damage develops in the two symmetric central regions containing the vorticity axis. It is indeed in these regions that the internal tensions are the highest on the membrane.