Controllable three-dimension auxetic structure design strategies based on triply periodic minimal surfaces and the application in hip implant

Abstract

Based on the triply periodic minimal surface (TPMS), 3D auxetic structures are successfully implemented using a dual-period function. A series of shape-controllable, dual-period deformation functions are obtained by summarising the characteristics of periodic deformation functions and applying Bezier curve fitting methods. Then, with the geometry originating from the Schwarz primitive (P) of TPMS, the periodic shape transformation of TPMS is achieved using the dual-period deformation functions. The property (negative Poisson’s ratio) of the auxetic structure is investigated based on the control parameters (the TPMS c value, periodic function η, and deformation index γ). The auxetic structures can exhibit excellent 3D negative Poisson’s ratio properties, and the Poisson’s ratio can be effectively adjusted. Moreover, a heterostructure with positive and negative Poisson’s ratio structures is obtained and applied to a stem in the hip joint. The simulation proves that the heterostructure can effectively prevent the failure of the bone implant.

Keywords

• negative poisson’s ratio
• triply periodic minimal surfaces
• auxetic structure
• bone implant
• hip joint