Influence of the elasticity variation of the 3D printed PMMA structure on the axial tooth vibration

Abstract

Recently, 3D printing with poly methyl methacrylate (PMMA) has been widely used in dentistry: 3D printing is a suitable method for producing any complex three-dimensional shape, and PMMA is a material that has suitable properties in the oral cavity environment. That is why 3D printing is very often used to make PMMA teeth. There is the impact between teeth during chewing that causes shape variation and tooth vibration. As cyclic vibrations adversely affect the durability of PMMA teeth, they must be eliminated. The object of this work is to study the axial vibrations of a 3D printed tooth, as well as to give recommendations for modifying the PMMA structure with the aim of vibration dampening. Tooth vibration is mathematically modeled and analytically solved. The obtained result provides a link between the vibrational properties and the elasticity variation of the PMMA material. The function that defines the change in elasticity of PMMA depends on the "slow time". (The term "slow time" implies a product of time and a parameter that is less than one). For a decreasing elasticity function, the vibration is of damped type: for higher is the elasticity reduction, the faster is the vibration decay. Based on the determined elasticity function, the modification of the PMMA structure can be realized. Authors propose the application of the obtained elasticity variation function for programming 4D printing with modified PMMA.