Spring combination model in two-dimensional atomic systems

Hooke’s law establishes a direct relationship between the applied force and deformation triggered on an object, with the elastic constant being the proportionality factor. Introductory Physics courses usually address Hooke’s law in the context of real springs. This paper proposes a complementary didactic approach to the topic “elasticity of materials”, considering a microscopic model in wich the interatomic bonding behave like springs. Thus, the elastic constant of these structures can be predicted by an extremely simple closed formula in the case of periodic systems. Particularly, monolayer hexagonal boron nitride structures were modeled from a series-parallel combination of identical springs. The model was developed within the linear approach of elasticity to ensure theoretical simplicity. A study was conducted to establish an optimal value corresponding to this regime, and 1.8% was determined as the maximum strain. The model was tested via atomistic computational simulations, being able to accurately predict the values of the elastic constants of the structures. Finally, the proposed approach proved to be didactically simple and interesting in introductory Physics or Engineering courses, mainly for the confirmation of the validity of the usual rules of spring combination in the microscopic domain.

Keywords:
Hooke’s law; linear elasticity model; Young’s modulus; hexagonal boron nitride