A new rigid biomaterial is developed and tested as a candidate replacement tissue forvolumetric loss of bone. To evaluate biomechanics, the biomaterial is stretched in the vertical direction inan unconfined configuration. However, you are unsure whether the biomaterial shows isotropic oranisotropic material properties.Write expressions for normal strains €11, 22, and 833 for orthotropic material symmetry. Next, write expressions also for normal strains E11, E22, and E33 for isotropy, stating your assumptions that allow you to simplify the moduli of elasticity and Poisson's ratios.To evaluate the importance of anisotropy, you decide to evaluate error in 833 measured in the orthotropic case, compared against the isotropic case. If we know that Poisson's ratios for anisotropy change by 5%, i.e., U12 =U21= U13 = U31 = U23 = U32 = 1.05 u, determine further how E33 changes. Comment on whether the change in E33 is below 10%, considered "acceptable". For an incompressible, isotropic biomaterial, the loading shown in the figure is sometimes called "pure shear". Explain why the loading shown can be considered as pure shear.

In conclusion: Given the anisotropic character of the material, the elastic moduli (E11, E22, E33)…

Answered: A new rigid biomaterial is developed…

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A new rigid biomaterial is developed and tested as a candidate replacement tissue for

volumetric loss of bone. To evaluate biomechanics, the biomaterial is stretched in the vertical direction in

an unconfined configuration. However, you are unsure whether the biomaterial shows isotropic or

anisotropic material properties.

Write expressions for normal strains €11, 22, and 833 for orthotropic material symmetry. Next, write expressions also for normal strains E11, E22, and E33 for isotropy, stating your assumptions that allow you to simplify the moduli of elasticity and Poisson's ratios.
To evaluate the importance of anisotropy, you decide to evaluate error in 833 measured in the orthotropic case, compared against the isotropic case. If we know that Poisson's ratios for anisotropy change by 5%, i.e., U12 =U21= U13 = U31 = U23 = U32 = 1.05 u, determine further how E33 changes. Comment on whether the change in E33 is below 10%, considered "acceptable". For an incompressible, isotropic biomaterial, the loading shown in the figure is sometimes called "pure shear". Explain why the loading shown can be considered as pure shear.

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