Values should be derived and plotted with MATLAB with experimental data.
I am attaching the document with the relevant LE NOTES.
Project HW File name: 'RAT188_SUHXW8_ProjectBiaxData.txt' Columns in file: Axis 1 load [g] Axis 2 load [g] dudx dvdx dudy dvdy Where dudx, dvdx, dudy and dvdy are components of the displacement gradient tensor Tissue sample dimensions: Thickness: 2.2022 [mm] Length: 8.94 [mm] Width: 8.60 [mm] one important part of the data : the sampling frequency for the data is 200 Hz. You will need this value to complete your analysis. Q1. Given the planar biaxial data for the class project, based on the tissue dimensions and displacement gradient, a) Compute and plot the deformation gradient F as a function of time. b) Decompose F into R and U and plot each tensor as a function of time. c) Compute the Green strain tensor and plot as function of time. d) Plot E11 vs. E22. e) Compute and plot the 1st Piola-Kirchhoff stress tensor as a function of time. f) Plot the normal stress as a function of normal strain relations (1st PK stress and Green strain) You are welcome to plot the normal and shear components in two different graphs. Also, for each tensor you plot, write a few sentences describing what these graphs tell you about the tissue behavior and or the mechanical test. Q2. Draw free-body diagrams that include the forces that are acting on the biological sample. These diagrams can be done manually but need to be scanned and put in the document as a figure with legend and caption. Include the axes used to study the material. Here it is important to include dimensions with units of the sample. Q3. Address the assumptions made regarding planar biaxial testing (i.e., can you justify why planar biaxial testing can address the mechanical properties of this material vs. uniaxial or triaxial?). Q4. Describe the measured data. What is directly measured and what is calculated. Include how the data are collected from the motors and sensors and how they are transformed into digital data. Make sure to include all equations used in the code to generate the plots. Q5. Compute and plot the deformation gradient F, 1st and 2nd Piola-Kirchhoff stresses, and the Green strain tensors as function of time. Include the decomposition of F and describe what the components of R and U tells you about the mechanical test. Generate figures of stress and strain as function of time, as function of each other, and strain E11 vs. E22 for both axes and describe the tissue behavior. Use words like: isotropy, nonlinear, stiffness, etc. Q6. Propose a function that can relate your measured stress and strain. This should be based on work in the literature (make sure you cite it). 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