Hybrid porous materials describe a group of materials whose phase composition varies continuously between two or more solid materials, while incorporating graded porosity as a further property. The manufacturing possibilities for these materials have been opening up in recent years and are still a part of ongoing research. Optimizing components using these materials comes with a new set of challenges. Our approach is based on the Thermodynamic Topology Optimization [1,2] and further expands on it. Describing the optimization problem using energy functional allows for a seamless introduction of constraints and regularization. Using variational principles, we simultaneously obtain the balance of linear momentum as well as the governing equations for the evolution of the topology. The optimization of the relative density distribution is split into the optimization of the topology and into the optimization of the phase composition and porosity distribution, each corresponding to a separate design variable. The material model used is a extension of the SIMP model for each design variable. The developed method has been applied to various theoretical as well as practical problems, including passive-adaptive axial bearing rings. Here, the goal has been to optimize the material distribution within the bearing ring to reduce contact surface for small loads, while still maintaining the same maximal load capabilities. Thus, the rolling resistance of the bearing can be minimized.