Urban Shorelines Protection

Triply Periodic Minimal Surface (TPMS)

Minimal Surface (MS) & Triply Periodic Minimal Surface (TPMS)

In nature, minimal surface can be formed effortlessly through the surface tension. For example, a soap film at equilibrium will have a constant thickness, and minimal surface area. MS can be modeled by math expressions. There are many types of minimal surfaces and some of them can form 3D periodic structures. These 3D MS structures are called TPMS (Triply Periodic Minimal Surface). We will study the properties of TPMS and how to transform them and how to create variations. Here are some resources you can start with:

Tools for Creating MSs/TPMSs

The Grapher (a default tool in Mac) is a convenient tool for visualizing the MS. It can create beautiful MS geometry, however, the result can only be exported as an image (not a 3D model). The MathMod (running on all platforms) can be used to create the MS and TPMS, manipulate their math equations, and export them as 3D surface files (wavefront .OBJ file format). The Blender (running on all platforms) can import the 3D surface files and "thicken" them into 3D models. Blender can further modify the 3D models, render them, and create 3D-printable files (.STL file format). The MSs & TPMSs created by this method will have uniform thicknesses since they were "thicken" uniformly through Blender. Another convenient way to create MSs & TPMSs is to use a software called MSLattice. The MSLattice can create 3D MS models directly by specifying their equations. It can generate both rectangular, cylindrical and spherical MSs/TPMSs. The user can also specify the density of the MS/TPMS. It can even create graded TPMSs (TPMSs with changing cell size or density along certain axis). The MSs & TPMSs created by this method will have uniform thicknesses since they were "thicken" uniformly through Blender. The MSs & TPMSs created by MSLattice will not have uniform thicknesses since they were created through two MSs & TPMSs of different values of parameters. Here are the links for downloading these tools.

MathMod (formally called K3DSurf): MathMod is a portable interactive plotting and graphing program for Windows, Linux, MacOSX and many other platforms. MathMod allows to plot 3D mathematical surfaces, described by implicit or parametric equations, and offers a very large database of model samples that can be generated with it.
Blender: Blender is a free and open-source 3D computer graphics software tool set used for creating animated films, visual effects, art, 3D-printed models, motion graphics, interactive 3D applications, virtual reality, and, formerly, video games. The Blender can run on Windows, Linux and MacOSX.
MSLattice: MSLattice is a software that can be used to generate the geometries of various types of lattices that are known as periodic cellular materials or architected materials. In particular, lattices based on the triply periodic minimal surfaces (TPMS). The user can generate the TPMS-based STL files needed for fabricating the lattices using additive manufacturing. MSLattice is running on Windows or Linux.

Computational Fluid Dynamics (CFD) Simulation for Waves

Waves & Model the Waves: Here are the links for basic concepts of waves and ocean waves.

Amplitude, period, frequency and wavelength of periodic waves [skip this video if you have taken Physics] (14:26)
Ocean Waves Basics (15:47)

The simplest wave model is called Linear Wave Theory. The wave can be described by the following equation:

The equation of a wave (14:43)
Linear wave theory (11:35)

Computational Fluid Dynamics (CFD):

Computational Fluid Dynamics (CFD) is an effective tool in studying many aspects of coastal simulation such as waves, coastal erosion, sediment transportation, loading of shoreline protection structure, scouring, coastal morphology, etc. However, CFD is a complex, interdisciplinary field that involves math, physics, and computer science.

There is an online electronic book called "An Introduction to Computational Fluid Dynamics" by H K Versteeg and W Malalasekera. It provides a brief introduction about CFD in Chapter 1: Introduction. The following videos can also serve as CFD tutorials.

CFD Software: Three major CFD software tools we are using last year are Ansys Discovery, Ansys Fluent & OpenFOAM. Both Ansys Discovery & Fluent are part of the Ansys Student Version. They can be both downloaded for free.

Tools for Generating & Simulating TPMS Structures

MALattice: Here are the links for tutorials and the paper of MSLattice which provide the practical and theoretical insights into the tool for generating TPMS 3D models.

MSLattice Uniform & Graded (10:00)
MSLattice Implicit Tab (7:19)
MSLattice - A free software for generating uniform and graded lattices based on triply periodic minimal surfaces by Oraib Al-Ketan1 & Rashid K. Abu Al-Rub [2020]

TPMS & TPMS Breakwaters: The following are two important, recent papers related to our research. The first paper is a comprehensive overview of the design, manufacturing, and applications TPMSs. It's a long read (32 pages) and you can first focus only on the part(s) relevant to your current needs. The second one details a research similar to want we are doing now. They performed Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) simulation on Gyroid TPMSs, and compared its performance to the traditional breakwater structure. It will be very beneficial to read through the paper in detail, learn from its approach and procedure to conduct their research, and compare our results with theirs.

Triply periodic minimal surface (TPMS) porous structures: from multi-scale design, precise additive manufacturing to multidisciplinary applications by Jiawei Feng, Jianzhong Fu, Xinhua Yao, and Yong He [2022]
Mechanical and hydrodynamic characteristics of emerged porous Gyroid breakwaters based on triply periodic minimal surfaces by Bao-Loi Dang, Vuong Nguyen-Van, Phuong Tran, Magd Abdel Wahab, Jaehong Lee, Klaus Hackle, H. Nguyen-Xuan [2022]

Ansys Discovery:

Computational Fluid Dynamics (CFD) is a powerful yet complex technology. We are going to explore this technology through a pretty new CFD tool - Ansys Discovery. Ansys Discovery is a simulation-driven 3D design software tool that combines interactive modeling and multiple simulation capabilities. The goal is to interactively adjust the 3D model design while visualizing its simulation results in real-time. Though Ansys Discovery can not perform the complex simulation such as wave-and--breakwater interaction in our project, it can help us get familiar with the major steps and capabilities of CFD simulation tools.

The following videos form the 3D Design with Ansys Discovery playlist can serve as the introductory tutorials.

Ansys Fluent 2D Wave Tank Simulation

Ansys Fluent: Here are the links for tutorials and the paper of MSLattice which provide the practical and theoretical insights into the tool for generating TPMS 3D models.

Getting started with Ansys Fluent by Ansys Virtual Academy
Session II: Seawall Design - Computer Simulation by Alex Yang

Ansys Discovery:

Computational Fluid Dynamics (CFD) is a powerful yet complex technology. We are going to explore this technology through a pretty new CFD tool - Ansys Discovery. Ansys Discovery is a simulation-driven 3D design software tool that combines interactive modeling and multiple simulation capabilities. The goal is to interactively adjust the 3D model design while visualizing its simulation results in real-time. Though Ansys Discovery can not perform the complex simulation such as wave-and--breakwater interaction in our project, it can help us get familiar with the major steps and capabilities of CFD simulation tools.

The following videos form the 3D Design with Ansys Discovery playlist can serve as the introductory tutorials.