Abstract
Models to represent the interactions of liquid crystalline phases with vesicles membranes have been widely studied in recent times due to its connection with biological materials. In this work we propose a new model to represent a vesicle membrane with internal nematic order whose equilibrium states depend on the competition between the bending, elastic and anchoring energies. Moreover we present a new unconditionally energy stable numerical scheme to approximate the model. Additionally, we present several numerical simulations in order to illustrate the good performance of the proposed scheme and the influence of the nematic order in the dynamics of the system.