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Biosolid Mechanics Term Project1

Biosolid Mechanics Term Project1 - BIOSOLID MECHANICS TERM...

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B IOSOLID M ECHANICS T T ERM ERM P P ROJECT Part A – Manufacture and Characterization of Transverse Isotropic Material for Investigation of Mechanotransduction Introduction . A transverse isotropic membrane provides a crude model of vascular smooth muscle tissue in the body. By using an isotropic membrane, we would not achieve desirable results because the behavior of the isotropic membrane would not mimic the behavior of vascular smooth muscle tissue. Isotropic membranes will behave in the same manner in all directions, which is obviously not the behavior for this type of tissue. A transverse isotropic membrane will behave different when loads are applied from orthogonal directions, which is very close to the behavior of smooth muscle tissue in the vasculature of the body. Even though it is not a direct mimic of the vasculature, it provides an important model in understanding behavior of vascular smooth muscle tissue. Methods. In order to develop a model for a transverse isotropic membrane, suture was first laid down in parallel rows on a plate. The suture was then covered with Sylgard elastomer, forming a flexible plastic membrane with suture fibers running through it. The ends of the suture on both sides of the membrane in the fiber direction were then cut off. The membrane was subjected to a uniaxial strain in the cross-fiber and fiber direction. Four different loads were applied to the membrane and the results were recorded for each orthogonal direction. The loads applied to the membrane in each direction are listed below: Test Load 1 0N 2 9.8N 3 19.6N 4 29.4N Data for the Fiber Direction Test Length 1 0.0460m 2 0.0464m 3 0.0469m 4 0.0473m Data for the Cross-Fiber Direction Test Length 1 0.0260m 2 0.0287m 3 0.0314m

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4 0.0349m
Results. Table 1.1: Results for the Fiber Direction Test Load (N) Width Fiber (m) Thickness Fiber (m) Fiber direction initial (m) Fiber direction current (m) σ Fiber (N/ m 2 ) Ε Fiber λ Fiber G Fiber 1 0 0.032 0.003 0.0460 0.0460 0.00 0.0000 1.0000 N/A 2 9.8 0.032 0.003 0.0460 0.0464 102083.33 0.0087 1.1322 11688763 3 19.6 0.032 0.003 0.0460 0.0469 204166.67 0.0198 1.1988 9260807 4 29.4 0.032 0.003 0.0460 0.0473 306250.00 0.0287 1.2394 11465410 Table 1.2: Results for the Cross-Fiber Direction Te st Load (N) Width Cross- Fiber (m) Thickness Cross-Fiber (m) Cross-Fiber direction initial (m) Cross- Fiber direction current (m) σ Cross-Fiber (N/m 2 ) Ε Cross- Fiber λ Cross- Fiber G Cross-Fiber 1 0 0.052 0.003 0.0260 0.0260 0.00 0.0000 1.0000 N/A 2 9.8 0.052 0.003 0.0260 0.0287 62820.51 0.1092 1.4674 575078.4 3 19.6 0.052 0.003 0.0260 0.0314 125641.03 0.2293 1.6771 523407.5 4 29.4 0.052 0.003 0.0260 0.0349 188461.54 0.4009 1.8954 366013.1 Material Parameters: o Fiber direction: d /dE = 10 σ 7 (constant) o Cross-fiber direction: d /dE = -23510802*E σ 2 + 79950*E + 580066 Discussion. From our results, we see that the material used is behaving as it should—a transverse isotropic material. We know this by looking at Figure 1.3 from APPENDIX: PART A. The cross-fiber direction curve is seen to be much more compliant to a load than is seen with the fiber direction curve. This indicates that the material is transverse isotropic because it behaves differently in two orthogonal directions. The only implication of this uniaxial test is that it does not account for any other movement other than the direction the load is put on. A more accurate test would be a biaxial test because unlike the uniaxial test, if there is any simultaneous

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Biosolid Mechanics Term Project1 - BIOSOLID MECHANICS TERM...

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