An anti-interpenetration model and connections between interphase and interface models in particle-reinforced composites

Linear spring interface model and interphase model are often used to simulate the interface behaviour of particle-reinforced composite materials. However, the former may give rise to nonphysical interpenetration at the interface between a particle and the surrounding material. In this paper, first, a model is presented to prevent the interpenetration phenomenon at the interface. This model can be used together with a given linear or nonlinear interface model to calculate the stress field in particle-reinforced composites with imperfect interface bonding condition, or with debonding damage. Second, the connections between the thin interphase model and interface models are studied for spherical particle-reinforced composites. It is found that while a relatively thin and compliant interphase can be well approximated by the equivalent linear spring interface model, a relatively thin and stiff interphase can be well approximated by the equivalent interface stress model. For the latter, the relations between the equivalent interface moduli and the interphase stiffness and thickness are presented.