Generative Design Of Geometric Microstructures Based On Triply Periodic Minimal Surface

In recent years,revolutionary advances in additive manufacturing(3D printing)technology have enabled precise digital manufacturing of complex geometric microstructures.Triply periodic minimal surface(TPMS)-based shell lattices have recently emerged as microstructures in heat dissipation,implants,energy absorption,lightweight design and architecture because of their superior geometric and mechanical properties.Compared with truss-lattices,TPMS-based shell lattices can significantly reduce the occurrence of stress concentration die to its smoothness,and can maintain excellent mechanical properties at low volume fraction.Compared with plate-lattices,TPMS-based shell lattices can be easily manufactured by 3D printing technology based on powder or liquid materials due to their natural double-connected open cell topology.At present,there are two main methods for generating TPMS.One is the implicit equation generation method based on mathematical expression,which can approximate the TPMS with some implicit equations composed of trigonometric functions.The level-set surface is extracted through the iso-surface extraction algorithm to obtain the three-dimensional data structure explicitly expressed for TPMS.However,the mathematical expression with TPMS is limited and the shape of TPMS is controlled only by adjusting the value of iso-surface,which limits the modeling space of geometric microstructures.The other method is an explicit generation method based on the boundary.This method explicitly generates the minimal surface satisfying the input boundary constraint by minimizing the area.However,this method requires specifying an initial structure that satisfies input boundary constraints in advance,which not only increases the complexity of the modeling process,but also limits the generation of minimal surfaces with complex topologies.This paper proposes a parametric modeling method for TPMS-like geometric microstructures with the key idea of constructing periodic boundaries explicitly and implicitly generating corresponding minimal surfaces.First,we introduce a parametric representation for boundaries by proposing a search algorithm over boundary topology and parameterizing them with spline curves.Then we solve for corresponding TPMS bordered with the given boundary implicitly by a formulation of geometric currents adapted with boundary periodicity and C1 continuity constraints,the purpose is to achieve a balance between minimizing the surface area and surface boundary smoothness after periodic tiling,so we call the generated geometric microstructures as TPMS-like geometric microstructures.Finally,this paper uses the homogenization method to analyze the mechanical properties of the generated structures,including Young’s modulus,Poisson’s ratio,isotropy and so on.The proposed modeling method has successfully generated a series of TPMS-like geometric microstructures with different topologies.Mechanical property analysis results show our TPMS-like shell lattices can extends the mechanical property space compared with traditional TPMS-based shell lattices.Moreover,we also introduce two applications,namely functionally graded structures design and inverse homogenization,using the proposed modeling framework:By designing boundary parameters elaborately,functional gradient structures with good connectivity can be generated;Combining the TPMS-like geometric microstructures library of our work and deep learning technology,we can perform inverse homogenization which obtain geometric microstructure parameters that meet the target mechanical properties and generate the TPMS-like geometric microstructures corresponding to the geometric parameters using the proposed modeling method to achieving the effect of generative design.