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.
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.
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter2: Axially Loaded Members
Section: Chapter Questions
Problem 2.7.5P: Determine the strain energy per unit volume (units of psi) and the strain energy per unit weight...
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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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