Numerical Analysis of Deformation under Compression of Structures Based on Triply Periodic Minimal Surfaces

M. P. Varygina

doi:10.17804/2410-9908.2024.4.047-056

M. P. Varygina

NUMERICAL ANALYSIS OF DEFORMATION UNDER COMPRESSION OF STRUCTURES BASED ON TRIPLY PERIODIC MINIMAL SURFACES

DOI: 10.17804/2410-9908.2024.4.047-056

Complex porous structures based on triply periodic minimal surfaces with high values of specific physical and mechanical characteristics are increasingly used in many industries. Numerical analysis is of great importance in evaluating the load-carrying capacity and mechanical behavior of such structures. The paper presents the results of finite element analysis of the stress-strained state of structures composed of triply periodic minimal surfaces and affected by compressive loading. The complexity of simulating the response of such structures to mechanical effects lies in the large dimension of the problem due to the need for fine discretization required for an adequate representation of the complex geometry of the model. The stages of constructing facet geometry for the construction of numerical models are shown. The effect of the type and parameters of these structures on their mechanical behavior under compression is exemplified by Schoen IWP surfaces and Schwarz primitives. Stiffness efficiency depending on the structure topology is analyzed.

Keywords: triply periodic minimal surfaces, finite element model, Schwarz primitive, Schoen IWP, stress-strain state

References:

Feng, J., Fu, J., Yao, X., and He, Y. Triply periodic minimal surface (TPMS) porous structures from multi-scale design, precise additive manufacturing to multidisciplinary applications. International Journal of Extreme Manufacturing, 2022, 4, 022001. DOI: 10.1088/2631-7990/ac5be6.
Gado, M.G., Al-Ketan, O., Aziz, M., Al-Rub, R.A., and Ookawara, S. Triply periodic minimal surface structures: design, fabrication, 3D printing techniques, state-of-the-art studies, and prospective thermal applications for efficient energy utilization. Energy Technology, 2024, 2301287. DOI: 10.1002/ente.202301287.
Schwarz, H.A. Gesammelte Mathematische Abhandlungen, Springer, Berlin, Heidelberg, 1890, 358 p.
Schoen, A.H. Infinite Periodic Minimal Surfaces Without Self-Intersections, DC NASA, Washington, 1970, 92 р.
Jones, A., Leary, M., Bateman, S., and Easton, M. Investigating mechanical properties of additively manufactured multimaterial gyroids: the effect of proportion, scale and shape. Additive Manufacturing, 2023, 76, 103784. DOI: 10.1016/j.addma.2023.103784.
Ramírez, E.A., Béraud, N., Pourroy, F., Villeneuve, F., and Museau, M. Design parameters effects on relative density of triply periodic minimal surfaces for additive manufacturing. Procedia CIRP, 2021, 100, 13–18. DOI: 10.1016/j.procir.2021.05.002.
Jones, A., Leary, M., Bateman, S., and Easton, M. Parametric design and evaluation of TPMS-like cellular solids. Materials & Design, 2022, 221, 110908. DOI: 10.1016/j.matdes.2022.110908.
Jones, A., Leary, M., Bateman, S., and Easton, M. A review of recent investigations on flow and heat transfer enhancement in cooling channels embedded with triply periodic minimal surfaces (TPMS). Software Impacts, 2021, 10, 100167. DOI: 10.3390/en15238994.
Eremin, A.V., Zinina, S.A., and Johnson, О.О. Investigation of heat transfer in a porous material. Vestnik Yugorskogo Gosudarstvennogo Universiteta, 2023, 1 (68), 60–66. (In Russian). DOI: 10.18822/byusu20230160-66.
Wang, E., Yao, R., Li, Q., Hu, X., and Sun, G. Lightweight metallic cellular. materials: a systematic review on mechanical characteristics and engineering applications. International Journal of Mechanical Sciences, 2024, 270, 108795. DOI: 10.1016/j.ijmecsci.2023.108795.
Dadashi, A. and Rahimi, G. A comprehensive investigation of the lattice structure mechanical properties based on Schwarz primitive triply periodic minimal surface: elastic modulus, yield strength, and maximum bearing force in the elastic region. International Journal of Solids and Structures, 2024, 295, 112776. DOI: 10.1016/j.ijsolstr.2024.112776.
Hsieh, M.-T. and Valdevit, L. Minisurf – a minimal surface generator for finite element modeling and additive manufacturing. Software Impacts, 2020, 6, 100026. DOI: 10.1016/j.simpa.2020.100026.
Jones, A., Leary, M., Bateman, S., and Easton, M. TPMS Designer: a tool for generating and analyzing triply periodic minimal surfaces. Software Impacts, 2021, 10, 100167. DOI: 10.1016/j.simpa.2021.100167.
Alketan, O. and Al-Rub, R.A MSLattice: A free software for generating uniform and graded lattices based on triply periodic minimal surfaces. Material Design & Processing Communications, 2020, 3 (2). DOI: 10.1002/mdp2.205.
Raju, S.K.K. and Onkar, P.S. Lattice_Karak: Lattice structure generator for tissue engineering, lightweighting and heat exchanger applications. Software Impacts, 2022, 14, 100425. DOI: 10.1016/j.simpa.2022.100425.

М. П. Варыгина

ЧИСЛЕННЫЙ АНАЛИЗ ДЕФОРМИРОВАНИЯ ПРИ СЖАТИИ СТРУКТУР НА ОСНОВЕ ТРИЖДЫ ПЕРИОДИЧЕСКИХ МИНИМАЛЬНЫХ ПОВЕРХНОСТЕЙ

Сложные пористые структуры, основанные на трижды периодических минимальных поверхностях, обладающие высокими удельными показателями физико-механических характеристик, находят все более широкое применение во многих отраслях промышленности. Численный анализ имеет большое значение при оценке несущей способности и механического поведения таких структур. В работе представлены результаты конечно-элементного анализа напряженно-деформированного состояния структур, составленных из трижды периодических минимальных поверхностей, под действием сжимающей нагрузки. Сложность моделирования отклика таких структур на механическое воздействие заключается в большой размерности задачи, обусловленной необходимостью мелкой дискретизации, требуемой для адекватного представления сложной геометрии модели. Показаны этапы построения фасетной геометрии для формирования численных моделей. На примере поверхностей Шёна IWP и примитивов Шварца рассмотрено влияние типа и параметров данных структур на их механическое поведение при сжатии. Выполнен анализ жесткостной эффективности в зависимости от топологии структур.

Ключевые слова: трижды периодические минимальные поверхности, конечно-элементная модель, примитивы Шварца, поверхности Шёна, напряженно-деформированное состояние

Библиография:

Triply periodic minimal surface (TPMS) porous structures from multi-scale design, precise additive manufacturing to multidisciplinary applications / J. Feng, J. Fu, X. Yao, Y. He // International Journal of Extreme Manufacturing. – 2022. – Vol. 4. – P. 022001. – DOI: 10.1088/2631-7990/ac5be6.
Triply periodic minimal surface structures: design, fabrication, 3D printing techniques, state-of-the-art studies, and prospective thermal applications for efficient energy utilization / M. G. Gado, O. Al-Ketan, M. Aziz, R. A. Al-Rub, S. Ookawara // Energy Technology. – 2024. – 2301287. – DOI: 10.1002/ente.202301287.
Schwarz H. A. Gesammelte Mathematische Abhandlungen. – Berlin, Heidelberg : Springer, 1890. – 358 p.
Schoen A. H. Infinite Periodic Minimal Surfaces without Self-Intersections. – Washington : DC NASA, 1970. – 92 р.
Investigating mechanical properties of additively manufactured multimaterial gyroids: the effect of proportion, scale and shape / A. Jones, M. Leary, S. Bateman, M. Easton // Additive Manufacturing. – 2023. – Vol. 76. – P. 103784. – DOI: 10.1016/j.addma.2023.103784.
Design parameters effects on relative density of triply periodic minimal surfaces for additive manufacturing / E. A. Ramírez, N. Béraud, F. Pourroy, F. Villeneuve, M. Museau // Procedia CIRP. – 2021. – Vol. 100. – P. 13–18. – DOI: 10.1016/j.procir.2021.05.002.
Parametric design and evaluation of TPMS-like cellular solids / A. Jones, M. Leary, S. Bateman, M. Easton // Materials & Design. – 2022. – Vol. 221. – P. 110908. – DOI: 10.1016/j.matdes.2022.110908.
A review of recent investigations on flow and heat transfer enhancement in cooling channels embedded with triply periodic minimal surfaces (TPMS) / A. Jones, M. Leary, S. Bateman, M. Easton // Software Impacts. – 2021. – Vol. 10. – P. 100167. – DOI: 10.3390/en15238994.
Еремин А. В., Зинина С. А., Джонсон О. О. Исследование теплопереноса в пористом материале на основе трижды периодических поверхностей минимальной энергии // Вестник Югорского государственного университета. – 2023. – Т. 1 (68). – С. 60–66. – DOI: 10.18822/byusu20230160-66.
Lightweight metallic cellular materials: a systematic review on mechanical characteristics and engineering applications / E. Wang, R. Yao, Q. Li, X. Hu, G. Sun // International Journal of Mechanical Sciences. – 2024. – Vol. 270. – P. 108795. – DOI: 10.1016/j.ijmecsci.2023.108795.
Dadashi A., Rahimi G. A comprehensive investigation of the lattice structure mechanical properties based on Schwarz primitive triply periodic minimal surface: elastic modulus, yield strength, and maximum bearing force in the elastic region // International Journal of Solids and Structures. – 2024. – Vol. 295. – P. 112776. – DOI: 10.1016/j.ijsolstr.2024.112776.
Hsieh M.-T., Valdevit L. Minisurf – a minimal surface generator for finite element modeling and additive manufacturing // Software Impacts. – 2020. – Vol. 6. – P. 100026. – DOI: 10.1016/j.simpa.2020.100026.
TPMS Designer: a tool for generating and analyzing triply periodic minimal surfaces / A. Jones, M. Leary, S. Bateman, M. Easton // Software Impacts. – 2021. – Vol. 10. – P. 100167. – DOI: 10.1016/j.simpa.2021.100167.
Alketan O., Al-Rub R. A. MSLattice: a free software for generating uniform and graded lattices based on triply periodic minimal surfaces // Material Design & Processing Communications. – 2020. – Vol. 3 (2). – DOI: 10.1002/mdp2.205.
Raju S. K. K., Onkar P. S. Lattice_Karak: lattice structure generator for tissue engineering, lightweighting and heat exchanger applications // Software Impacts. – 2022. – Vol. 14. – P. 100425. – DOI: 10.1016/j.simpa.2022.100425.

Библиографическая ссылка на статью

Varygina M. P. Numerical Analysis of Deformation under Compression of Structures Based on Triply Periodic Minimal Surfaces // Diagnostics, Resource and Mechanics of materials and structures. - 2024. - Iss. 4. - P. 47-56. -
DOI: 10.17804/2410-9908.2024.4.047-056. -
URL: http://dream-journal.org/issues/content/article_455.html
(accessed: 21.12.2024).