Parametric linear finite element stress and stability analysis of isotropic and orthotropic self-supporting Miura-ori structures

References

• B. Castanie, C. Bouvet, and M. Ginot, Review of composite sandwich structure in aeronautic applications, Compos. Part C, vol. 1, pp. 100004, 2020. DOI: 10.1016/j.jcomc.2020.100004.
   Google Scholar
• S. Pantelakis and K. Tserpes, Revolutionizing Aircraft Materials and Processes, Springer Nature Switzerland AG, 2020. DOI: 10.1007/978-3-030-35346-9.
   Google Scholar
• M. Palmu, Folded and unfolded - Using tessellation patterns for foldable packaging, M.Sc. thesis, Aalto University, Espoo, 2019.
   Google Scholar
• M. Schenk, Folded shell structures, D.Sc. thesis, University of Cambridge, Cambridge, UK, 2011.
   Google Scholar
• N. Turner, B. Goodwine, and M. Sen, A review of origami applications in mechanical engineering, Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci., vol. 230, no. 14, pp. 2345–2362, 2016. DOI: 10.1177/0954406215597713.
   Web of Science ®Google Scholar
• X. M. Xiang, G. Lu, and Z. You, Energy absorption of origami inspired structures and materials, Thin-Walled Struct., vol. 157, pp. 107130, 2020. DOI: 10.1016/j.tws.2020.107130.
   Web of Science ®Google Scholar
• E. Baranger, C. Cluzel, and P.-A. Guidault, Modelling of the behaviour of aramid folded cores up to global crushing, Strain Int. J. Exp. Mech., vol. 47, pp. 170–178, 2011. DOI: 10.1111/j.1475-1305.2010.00753.x.
   Web of Science ®Google Scholar
• B. B. Basily and E. A. Elsayed, Dynamic axial crushing of multilayer core structures of folded Chevron patterns, IJMPT, vol. 21, no. 1/2/3, pp. 169–185, 2004. DOI: 10.1504/IJMPT.2004.004750.
   Web of Science ®Google Scholar
• B. B. Basily and E. A. Elsayed, Design and Development of Lightweight Sandwich Structures with Thin Sheet Folded Cores, Working papers, Department of Industrial and Systems Engineering, Rutgers University, New Brunswick, NJ, USA, 2005.
   Google Scholar
• B. Bender, S. Fischer, and K. Drechsler, Optimizing a foldcore concerning density specific stiffness properties, SAMPE Europe International Conference (SEICO-11), Paris, France, 2011.
   Google Scholar
• S. Fischer, Realistic Fe simulation of foldcore sandwich structures, Int. J. Mech. Mater. Eng., vol. 10, no. 1, pp. 1–11, 2015. DOI: 10.1186/s40712-015-0041-z.
   Web of Science ®Google Scholar
• J. M. Gattas, W. Lv, and Y. Chen, Rigid-foldable tubular arches, Eng. Struct., vol. 145, pp. 246–253, 2017. DOI: 10.1016/j.engstruct.2017.04.037.
   Web of Science ®Google Scholar
• S. Heimbs, P. Middendorf, and M. Maier, Numerical determination of the nonlinear effective mechanical properties of folded core structures for aircraft sandwich panels, 6th European LS-DYNA Users Conference, Gothenburg, Sweden, 2007.
   Google Scholar
• S. Heimbs, P. Middendorf, C. Hampf, F. Hähnel, and K. Wolf, Aircraft sandwich structures with folded core under impact load, Ferreira AJM, 8th International Conference on Sandwich Structures, Porto, Portugal, 2008.
   Google Scholar
• S. Heimbs, E. Baranger, M. Klaus, S. Kilchert, and S. Fischer, Sandwich structures with folded core: Mechanical modeling and impact simulations, SEICO 09 SAMPE Europe 30th International Jubilee Conference and Forum, Paris, France, 2009.
   Google Scholar
• S. Heimbs, Foldcore sandwich structures and their impact behaviour: An overview. In: S. Abrate, B. Castanié, and Y. Rajapakse (eds.), Dynamic Failure of Composite and Sandwich Structures. Solid Mechanics and Its Applications, Vol. 192, Springer, Dordrecht, 491–544, 2013. DOI: 10.1007/978-94-007-5329-7_11.
   Google Scholar
• S. Kilchert, Nonlinear finite element modelling of degradation and failure in folded core composite sandwich structures, D.Sc Thesis, University of Stuttgart, Germany, 2013.
   Google Scholar
• X. Zhou, H. Wanga, and Z. Youb, Mechanical properties of Miura-based folded cores under quasi-static loads, Thin-Walled Struct., vol. 82, pp. 296–310, 2014. DOI: 10.1016/j.tws.2014.05.001.
   Web of Science ®Google Scholar
• K. Lundin, The 9 biggest packaging design trends of 2020. Crowdspring homepage, 2020, Accessed March 23, 2020, Available from https://www.crowdspring.com/blog/packaging-design-trends-2020/
   Google Scholar
• M. J. Kirwan, Handbook of Paper and Paperboard Packaging Technology, John Wiley & Sons, Chichester, West Sussex, UK, 2012. DOI: 10.1002/9781118470930.
   Google Scholar
• L. Aktay, A. F. Johnson, and B.-H. Kröplin, Numerical modelling of honeycomb core crush behaviour, Eng. Fract. Mech., vol. 75, no. 9, pp. 2616–2630, 2008. DOI: 10.1016/j.engfracmech.2007.03.008.
   Web of Science ®Google Scholar
• S. Heimbs, P. Middendorf, S. Kilchert, A. F. Johnson, and M. Maier, Experimental and numerical analysis of composite folded sandwich core structures under compression, Appl. Compos. Mater., vol. 14, no. 5–6, pp. 363–377, 2007. DOI: 10.1007/s10443-008-9051-9.
   Web of Science ®Google Scholar
• S. Fischer, K. Drechsler, B. Kilchert, and A. Johnson, Mechanical tests for foldcore base material properties, Compos.: Part A, vol. 40, no. 12, pp. 1941–1952, 2009. DOI: 10.1016/j.compositesa.2009.03.005.
   Web of Science ®Google Scholar
• C. H. Yoo and S. C. Lee, Chpt 8. Buckling of Plate Elements, In: Stability of Structures - Principles and Applications, Elsevier, pp. 373–434, 2011. DOI: 10.1016/b978-0-12-385122-2.10008-9.
   Google Scholar
• G. A. Baum, D. C. Brennan, and C. C. Habeger, Orthotropic elastic constants of paper, Tappi, vol. 64, pp. 97–101, 1981.
   Google Scholar
• C. J. Biermann, Chapter 7 - Paper and its properties. In: Handbook of Pulping and Papermaking, 2nd ed., Elsevier, Cambridge, Massachusetts, USA, 1996, pp. 158–189. DOI: 10.1016/B978-0-12-097362-0.X5000-6.
   Google Scholar
• S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day Inc., San Francisco, California, USA, 1963.
   Google Scholar
• R. Szilard, Theory and Analysis of Plates. Classical and Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ, 1974.
   Google Scholar
• G. Lu and T. X. Yu, Energy Absorption of Structures and Materials, Woodhead Publishing, Cambridge, England, 2003.
   Google Scholar
• A. Lebée, L. Monasse, and H. Nassar, Fitting surfaces with the Miura tessellation, 7th International Meeting on Origami in Science, Mathematics and Education (7OSME), Oxford, UK, September 2018, p. 811.
   Google Scholar
• E. A. Elsayed and B. B. Basily, A continuous folding process for sheet materials, IJMPT, vol. 21, no. 1/2/3, pp. 217–238, 2004. DOI: 10.1504/IJMPT.2004.004753.
   Web of Science ®Google Scholar
• W. Szewczyk, Determination of Poisson's ratio in the plane of the paper, Fibres Textiles Eastern Europe, vol. 16, no. 4, pp. 117–120, 2008.
   Web of Science ®Google Scholar
• S. Fischer, S. Heimbs, S. Kilchert, M. Klaus, and C. Cluzel, Sandwich structures with folded core: Manufacturing and mechanical behavior, SAMPE Europe International Conference (SEICO-09), Paris, France, 2009.
   Google Scholar
• L. Göttsching and H. L. Baumgarten, Triaxial deformation of paper under tensile load. In: F. Bolam (ed.), The Fundamental Properties of Paper Related to Its Uses, Trans. Vth Fund. Res. Symp., Cambridge, 1973, pp. 227–249.
   Google Scholar
• M. W. Johnson and T. J. Urbanik, A nonlinear theory for elastic plates with application to characterizing paper properties, J Appl Mech., vol. 51, no. 1, pp. 146–152, 1984. DOI: 10.1115/1.3167559.
   Web of Science ®Google Scholar
• B. Thiria and M. Adda-Bedia, Relaxation mechanisms in the unfolding of thin sheets, Phys. Rev. Lett., vol. 107, no. 2, pp. 025506, 2011. DOI: 10.1103/PhysRevLett.107.025506.
   PubMed Web of Science ®Google Scholar
• F. Muhs, S. Thissen, and P. Middendorf, Virtual process chain for optimization of sandwich foldcores under flatwise compression, Thin-Walled Struct., vol. 157, pp. 107121, 2020. DOI: 10.1016/j.tws.2020.107121.
   Web of Science ®Google Scholar