Generation of a Quadrilateral Mesh based on NURBS for Gyroids of Variable Thickness and Porosity

The Gyroid is a periodic minimal surface explored in different applications, such as architecture and nanotechnology. The general topology is suitable for the construction of porous structures. This paper presents a non-iterative, novel methodology for the generation of a NURBS-based Gyroid volume. The Gyroid fundamental patch is defined with the Weierstrass parameterization. Furthermore, the geometry is manipulated to generate a structured mesh, allowing better element quality for FEM and IGA simulations. The re-parametrization is carried out by a Least-Squares approximation with a parametric NURBS surface, enabling a better definition of the mid-surface normals for the generation of the complete Gyroid volume. Different cases of variational thickness and porosity are presented to validate the versatility of our method.