Denture reinforcement via topology optimization

TL;DR

This study introduces a SIMP-based topology optimization framework to optimally place an E-glass reinforcement inside a 3D denture made of PMMA, aiming to increase stiffness and reduce displacement under high biting loads. The method solves a linear elastic PDE with a spatially variable stiffness C(θ) via FEM, minimizing compliance subject to a mass constraint ρ∫Ω θ dV ≤ M_0, where θ(x,y,z) indicates strong-material presence. The reinforcement design yields a skeleton of E-glass within the denture base, which is then filled with PMMA to produce a two-material reinforced denture; numerical results show significant reductions in displacement (e.g., about 44% in average displacement at 20% reinforcement) compared to non-reinforced dentures. A mesh convergence study confirms the numerical results are robust to mesh size, and the work lays a foundation for automated, manufacturable reinforcement placement, with future directions including experimental validation and exploration of stress constraints and manufacturability considerations.

Abstract

We present a computational design method that optimizes the reinforcement of dentures and increases the stiffness of dentures. Our approach optimally places reinforcement in the denture, which modern multi-material three-dimensional printers could implement. The study focuses on reducing denture displacement by identifying regions that require reinforcement (E-glass material) with the help of topology optimization. Our method is applied to a three-dimensional complete lower jaw denture. We compare the displacement results of a non-reinforced denture and a reinforced denture that has two materials. The comparison results indicate that there is a decrease in the displacement in the reinforced denture. Considering node-based displacement distribution, the reinforcement reduces the displacement magnitudes in the reinforced denture compared to the non-reinforced denture. The study guides dental technicians on where to automatically place reinforcement in the fabrication process, helping them save time and reduce material usage.

Figures (5)

• Figure 1: Steps of the proposed reinforcement method for the dental prosthesis.
• Figure 2: A depiction of the boundary condition and forces of the denture. The figure on the top left is the fixed boundary of the denture (Dirichlet boundary) (blue line). The figure on the top right is the fixed boundary of the denture in the mesh convergence study (blue region). Forces are applied vertically (Neumann boundary) $900$ N on posterior teeth (black region) $450$ N on premolars (turquoise region) and $150$ N on anterior teeth (green region) in the figure on the bottom left. The figure on the bottom right is the meshed denture.
• Figure 3: An illustration of the E-glass reinforcement (brown) distribution for the optimized prostheses with varying upper limits of reinforcement mass. Left top figure: the reinforcement distribution with 20% of the mass limit. Right top figure: the reinforcement distribution with 40% of the mass limit. Bottom figure: the reinforcement distribution with 57% of the mass limit. We use 20% of the reinforcement in the denture displacement investigation.
• Figure 4: A visualization of the displacements of the dentures. The left-hand side image shows the displacement of the non-reinforced denture, and the right-hand side image illustrates the displacement of the reinforced denture. The maximum displacement of the non-reinforced denture is 0.192 mm. The maximum displacement of the reinforced denture is 0.17 mm, which is for the optimized 20% of mass reinforcement. This comparison clearly shows the displacement of the non-reinforced (fully weak material) denture is higher than that of the reinforced denture.
• Figure 5: A presentation of the node-based displacement distributions of the non-reinforced and reinforced dentures. The reinforcement substantially reduces the high displacement magnitudes compared to the non-reinforced denture. This is evident in the node displacement distribution of the reinforced denture, which has a smaller variance and mean than the non-reinforced denture.