This is an update to PII: S2665963820300178.We present an updated version v2.0 of our minimal surface generator MiniSurf v1.0, that creates triply periodic minimal surface (TPMS) computer-aided design (CAD) files for both finite element modeling and additive manufacturing. Besides making the GUI more user-friendly, in this new version we significantly improve the mesh quality of the generated CAD files by incorporating a mesh smoothing feature. With this new smoothing feature, MiniSurf v2.0 can now produce high quality CAD files for more accurate finite element modeling and more precise additive manufacturing

Hsieh, Meng-Ting

Valdevit, Lorenzo

eScholarship - University of California

UC IrvineUC Irvine Previously Published WorksTitleUpdate (2.0) to MiniSurf—A minimal surface generator for finite element modeling and additive manufacturingPermalinkhttps://escholarship.org/uc/item/8f82m0t5AuthorsHsieh, Meng-TingValdevit, LorenzoPublication Date2020-11-01DOI10.1016/j.simpa.2020.100035Data AvailabilityThe data associated with this publication are within the manuscript. Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaSoftware Impacts 6 (2020) 100035abContents lists available at ScienceDirectSoftware Impactsjournal homepage: www.journals.elsevier.com/software-impactsSoftware updateUpdate (2.0) toMiniSurf—A minimal surface generator for finite elementmodeling and additive manufacturingMeng-Ting Hsieh a,∗, Lorenzo Valdevit a,bMechanical and Aerospace Engineering Department, University of California, Irvine, CA 92697, USAMaterials Science and Engineering Department, University of California, Irvine, CA 92697, USAA R T I C L E I N F OKeywords:Triply periodic minimal surfaces (TPMSs)Finite element modeling (FEM)Additive manufacturing (AM)Computer-aided design (CAD) files3D printingArchitected materialsA B S T R A C TThis is an update to PII: S2665963820300178.We present an updated version v2.0 of our minimal surface generator MiniSurf v1.0, that creates triplyperiodic minimal surface (TPMS) computer-aided design (CAD) files for both finite element modeling andadditive manufacturing. Besides making the GUI more user-friendly, in this new version we significantlyimprove the mesh quality of the generated CAD files by incorporating a mesh smoothing feature. With thisnew smoothing feature, MiniSurf v2.0 can now produce high quality CAD files for more accurate finite elementmodeling and more precise additive manufacturing.Code metadataCurrent Code version v2.0Permanent link to code/repository used for this code version https://github.com/SoftwareImpacts/SIMPAC-2020-40Permanent link to Reproducible Capsule https://codeocean.com/capsule/1851964/tree/v2Legal Software License MITCode versioning system used NoneSoftware code languages, tools, and services used MatlabCompilation requirements, operat-ing environments, & dependenciesIf available Link to developer docu-mentation/manualSupport email for questions mengtinh@uci.edu and Valdevit@uci.eduSoftware metadataCurrent software version v2.0Permanent link to executables of this version https://github.com/mengtinh/MiniSurf_v2.0Permanent link to Reproducible Capsule https://codeocean.com/capsule/1851964/tree/v2Legal Software License MITComputing platform / Operating System Microsoft WindowsInstallation requirements & dependencies Matlab RuntimeIf available Link to user manual - if formally published include a reference to thepublication in the reference listhttps://github.com/mengtinh/MiniSurf_v2.0/blob/master/User%20Manual.pdfSupport email for questions mengtinh@uci.edu and Valdevit@uci.eduDOI of original article: https://doi.org/10.1016/j.simpa.2020.100026.The code (and data) in this article has been certified as Reproducible by Code Ocean: (https://codeocean.com/). More information on the ReproducibilityBadge Initiative is available at https://www.elsevier.com/physical-sciences-and-engineering/computer-science/journals.∗ Corresponding author.E-mail address: mengtinh@uci.edu (M.-T. Hsieh).https://doi.org/10.1016/j.simpa.2020.100035Received 13 September 2020; Received in revised form 16 September 2020; Accepted 18 September 20202665-9638/© 2020 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license(http://creativecommons.org/licenses/by/4.0/).M.-T. Hsieh and L. Valdevit Software Impacts 6 (2020) 1000351gtbrewtsfms2d𝑥tarcbpGi(tTtsottCaFig. 1. Display of MiniSurf v2.0 GUI with the smoothing feature highlighted in red.. IntroductionOne of the major limitations we discussed in MiniSurf v1.0 is theeneration of CAD files with suboptimal meshes (long and narrowriangular facets resulting from the meshing of very complex topologiesased on the 3D uniform grid points) [1]. The low-quality mesh oftenesults in the inaccurate prediction of the local stress field (undesirablespecially when the peak stress in an implant is estimated [2] orhen a local failure criterion is used such as in the case of the frac-ure toughness modeling of cellular materials [3]) in a finite elementimulation and the poor manufacturing of 3D printed parts (missingaces and geometric imprecision). To address this issue, we added theesh smoothing feature that was previously used to obtain the smoothpinodal shell-based structures [4–7].. Smoothing algorithm and featureThe mesh smoothing algorithm is based on the Laplacian smoothingetailed in [8] and briefly described below:′𝑗 =1𝑁𝑁∑𝑖=1𝑥𝑖 (2.1)𝑦′𝑗 =1𝑁𝑁∑𝑖=1𝑦𝑖 (2.2)𝑧′𝑗 =1𝑁𝑁∑𝑖=1𝑧𝑖 (2.3)where N is the total number of the neighboring nodes i, each of whichconnects to a mesh node j by a single mesh edge; 𝑥′𝑗 , 𝑦′𝑗 , and 𝑧′𝑗 arehe new x, y, and z coordinates of the mesh node j found by taking theverage of 𝑥𝑖, 𝑦𝑖, and 𝑧𝑖, the current x, y, and z coordinates of nodes iespectively.To preserve the periodicity of the generated TPMS mesh, the Lapla-ian smoothing is only applied to the interior mesh nodes, so theoundary nodes remain unchanged. The smoothing algorithm is incor-orated in the smoothing push-button in the left control panel of theUI as shown in Fig. 1. Note that every time the button is pushed,t is equivalent to applying equation (2.1), (2.2) and (2.3) six timesthis has been found in general to produce an optimal balance betweenhe smoothness and shrinkage of a given mesh) as shown in Fig. 2.he mesh smoothing can be executed iteratively to the generatedriply periodic minimal surface (TPMS) mesh at user’s discretion. Themoothing algorithm is also parallelized (currently set to six processorsr less depending on its availability) for the efficient computation ofhe smoothed mesh. Furthermore, we decouple the visualization andhe CAD file generation in the GUI with the addition of the ‘‘ExportAD’’ button as shown in Fig. 1 providing a more convenient, intuitive,nd user-friendly experience.3. New advantages and impact overviewWe previously showed that MiniSurf v1.0 can efficiently create CAD(a mesh made of many triangular facets) files of 19 common TMPSs forfinite element modeling and additive manufacturing. These TPMSs havebeen studied extensively in multidisciplinary fields [9–17] due to theirlarge surface area with very uniform double curvatures (directly relatedto the quality of underlying mesh [18–20]); hence it is extremelyessential to ensure that the generated CAD files have high qualitymeshes consisting of triangular facets with aspect ratio close to one (notrealizable in MiniSurf v1.0).MiniSurf v2.0 is built to address this challenge by incorporatingthe Laplacian smoothing [18,21] feature detailed in Section 2. Weemphasize the advantages of MiniSurf v2.0 over v1.0 as follows: (1)Users can control the smoothness of the generated mesh and hencethe underlying mesh curvatures. (2) The mesh smoothing is highlyparallelized (up to six processors by default). A finely meshed surface(300 × 300 × 300 triangular facets) can be smoothed under threeseconds. (3) Most importantly, the generated TPMS CAD files nowhave high quality mesh for more accurate finite element modelingand more precise additive manufacturing. MiniSurf v2.0 is currentlybeing used in the following ongoing projects: (a) Whipple shield design— SPH modeling of hypervelocity impact on sandwiched TPMSs. Wereplace the traditional whipple shield design (a front bumper anda back plate) with the sandwiched primitive TPMS (smoothed andgenerated by MiniSurf v2.0). We then model the hypervelocity impactof a space debris (represented by a sphere projectile traveling at thespeed of 6 km/s) using smoothed particle hydrodynamics (followingsimilar procedures in [22]). (b) Fracture toughness of 3D cellularmaterials — minimal surface-based versus strut-based topologies. Weinvestigate the mode-I fracture toughness of primitive TPMS (smoothedand created by MiniSurf v2.0), octet, and cubic lattices by performingfinite element calculations of the J-integral on a single-edge-notch-bend(SENB) specimen (the numerical approach is detailed in [3]).We expect MiniSurf v2.0 to be impactful in multidisciplinary fieldsjust as the MiniSurf v1.0 given the recent growing interest in buildingnew multifunctional materials with TPMS topologies. Furthermore,with high quality CAD files (smoothed and generated by MiniSurf v2.0)researchers can now make more accurate finite element predictions andmore precise prototyping to better design the materials.4. ConclusionIn this work, we added the mesh smoothing functionality based onthe Laplacian smoothing to our previously developed software MiniSurf.TPMS CAD files can now be efficiently created with a user-controlledsmooth mesh for more accurate finite element modeling and sound2M.-T. Hsieh and L. Valdevit Software Impacts 6 (2020) 100035Fig. 2. Illustration of (a) unsmoothed gyroid mesh and (b) smoothed gyroid mesh with the zoom-in region shown in the red rectangular box.additive manufacturing. In the future, we will continue to tackle theremaining limitations mentioned in MiniSurf v1.0 [1]. Furthermore, wewill regularly add new TPMS to our existing library.Declaration of competing interestThe authors declare that they have no known competing finan-cial interests or personal relationships that could have appeared toinfluence the work reported in this paper.References[1] M.-T. Hsieh, L. Valdevit, Minisurf – A minimal surface generator for finiteelement modeling and additive manufacturing, Softw. 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Update (2.0) to MiniSurf—A minimal surface generator for finite element modeling and additive manufacturing

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