You are given a sheet of fibrous connective tissue to investigate. The tissue fibers run in...

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You are given a sheet of fibrous connective tissue to investigate. The tissue fibers run in a single direction. When subjected to biaxial testing of forces f and f2, the tissue 1 undergoes a deformation given by: x = \X, x2 = \2X2, X3 = 3X3. (a) Given that this material is incompressible, find 3 from X and 2. (b) It has been suggested that biaxial testing of this material can be described by the following strain energy function: W = Ce, where Q = bE + bE2 + b3E3. Find the S1 of the 2nd Piola Kirchhoff stress tensor S. (c) When testing this material, you notice that the tissue behaves differently during unloading compared to loading. What is this phenomenon called and under what conditions would it still be appropriate to use the constitutive law proposed in part b)? You are given a sheet of fibrous connective tissue to investigate. The tissue fibers run in a single direction. When subjected to biaxial testing of forces f and f2, the tissue 1 undergoes a deformation given by: x = \X, x2 = \2X2, X3 = 3X3. (a) Given that this material is incompressible, find 3 from X and 2. (b) It has been suggested that biaxial testing of this material can be described by the following strain energy function: W = Ce, where Q = bE + bE2 + b3E3. Find the S1 of the 2nd Piola Kirchhoff stress tensor S. (c) When testing this material, you notice that the tissue behaves differently during unloading compared to loading. What is this phenomenon called and under what conditions would it still be appropriate to use the constitutive law proposed in part b)?