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. 2017 Aug 29;7:9750. doi: 10.1038/s41598-017-09649-5

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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FEA for the different morphotypes’ procuticle. (A) Simulated deformation of single cylinders used for model-creation of the different morphotypes (Side view); simulated deformation is visually amplified (factor 27). The graph shows the deformation of the single cylinders for the different morphotypes. Curve of best fit: f(x) = 93764x^−2.708 (R² = 1) (B) Simulated deformation of six calculated models with increasing thickness (one to six cylinders), representing morphotype i; simulated deformation is visually amplified (factor 27). The graph shows simulations of maximum deformation at the model’s bottom for all morphotypes. Curves of best fit: i: f(x) = 0.9679x^−2.822 (R^2 =0.9887); ii: f(x) = 0.5703x^−2.745 (R² = 0.9907); iii: f(x) = 0.3621x^−2.641 (R² = 0.993).