Toward engineering lattice structures with the Material Point Method (MPM)

Toward engineering lattice structures with the Material Point Method (MPM) | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Toward engineering lattice structures with the Material Point Method (MPM) Oliver Giraldo-Londoño, Rogelio A. Muñetón-López, Paul L. Barclay, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4189367/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 15 Jan, 2025 Read the published version in Engineering with Computers → Version 1 posted 9 You are reading this latest preprint version Abstract This study examins the potential of two variants of the material point method—the generalized interpolation material point (GIMP) and dual domain material point (DDMP) methods—in developing a robust computational framework for engineering lattice structures under different loading conditions. The study begins with assessing the ability of the two methods in predicting elastic buckling phenomena using column geometries with and without initial geometric imperfections. The results indicate that both methods effectively capture buckling phenomena when initial geometric imperfections are introduced. After this verification step, we create several models of tetrahedral lattice structures with varying strut diameter and orientation and subject them to quasi-static loading. We then validate the numerical results using laboratory test results. The results show that, while both methods accurately predict load-displacement curves in the pre-buckling regime, their predictive capabilities diminish in the post-buckling regime. Through visual comparison between the numerical and experimental deformed shapes, it appears that the discrepancies between model and experimental results are attributed to initial geometric imperfections in the lattices that occurred during 3D printing. We then establish a second set of lattice models where different types of initial geometric imperfections are considered. The results from these models show that imperfections have a negligible influence in the pre-buckling regime but affect the behavior considerably in the post-buckling regime. As a final step in this work, we subject the lattice models to impact loading and employ hyphotetical soft and stiff materials. These results show that the lattice stiffness, which depends on material stiffness, strut diameter, and orientation, significantly influences the ability of a lattice structure to resist impact. In particular, we find that a stiffer lattice (i.e., one made with a stiff material and thicker struts) is capable of absorbing more energy than a softer one during impact. Although material nonlinearities, inelasticity, and detailed contact formulations are not considered in this study, the findings obtained herein lay the groundwork for engineering lattice structures under extreme loading conditions through a simulation-driven framework based on particle-based methods. Material Point Method GIMP DDMP metamaterials lattices impact Full Text Additional Declarations No competing interests reported. Supplementary Files Supplementarymaterial.zip Cite Share Download PDF Status: Published Journal Publication published 15 Jan, 2025 Read the published version in Engineering with Computers → Version 1 posted Editorial decision: Revision requested 24 Aug, 2024 Reviews received at journal 28 May, 2024 Reviews received at journal 26 May, 2024 Reviewers agreed at journal 21 Apr, 2024 Reviewers agreed at journal 10 Apr, 2024 Reviewers invited by journal 09 Apr, 2024 Editor assigned by journal 01 Apr, 2024 Submission checks completed at journal 01 Apr, 2024 First submitted to journal 29 Mar, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4189367","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":286204056,"identity":"133c60f9-4c55-4b9f-be2d-257c410186fd","order_by":0,"name":"Oliver Giraldo-Londoño","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6klEQVRIiWNgGAWjYFACxgYGhgJmBn4wAwjYgFiCsBYDZgbJBuK1gABQi8EBJD5eLfz8i9s+/DCwljO+drj544+Kw/l8DMwHb/Pg0SI542HzzB6DdGOz24lt0jxnDlu2MbAlW+PTYnDjYDMDj8HhxG1ALcyMbYcN2Bh4zKQJaWH8A9SyeXZi88efYC383/BrOd/YzAyyZYN0YoMEL8QWNrxaJGcwNjPLAP0iAfFLugEbM5ux5Rw8Wvj5jz9mfFNhLcc/O/0xMMSsDeTbmx/eeINHC4NEAroIMz7lYGsOEFIxCkbBKBgFIx4AAD0CR5gs8E48AAAAAElFTkSuQmCC","orcid":"","institution":"University of Missouri","correspondingAuthor":true,"prefix":"","firstName":"Oliver","middleName":"","lastName":"Giraldo-Londoño","suffix":""},{"id":286204057,"identity":"7144fa2a-88dd-4b61-bb49-7b7ae4623cc6","order_by":1,"name":"Rogelio A. 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The study begins with assessing the ability of the two methods in predicting elastic buckling phenomena using column geometries with and without initial geometric imperfections. The results indicate that both methods effectively capture buckling phenomena when initial geometric imperfections are introduced. After this verification step, we create several models of tetrahedral lattice structures with varying strut diameter and orientation and subject them to quasi-static loading. We then validate the numerical results using laboratory test results. The results show that, while both methods accurately predict load-displacement curves in the pre-buckling regime, their predictive capabilities diminish in the post-buckling regime. Through visual comparison between the numerical and experimental deformed shapes, it appears that the discrepancies between model and experimental results are attributed to initial geometric imperfections in the lattices that occurred during 3D printing. We then establish a second set of lattice models where different types of initial geometric imperfections are considered. The results from these models show that imperfections have a negligible influence in the pre-buckling regime but affect the behavior considerably in the post-buckling regime. As a final step in this work, we subject the lattice models to impact loading and employ hyphotetical soft and stiff materials. These results show that the lattice stiffness, which depends on material stiffness, strut diameter, and orientation, significantly influences the ability of a lattice structure to resist impact. In particular, we find that a stiffer lattice (i.e., one made with a stiff material and thicker struts) is capable of absorbing more energy than a softer one during impact. 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