Question

10 points)- A skin sample of 6 X 4 cm in size is placed on the flatbed of a material testing system with the four corner points located at (0, 0), (6, 0), (6, 4), and (0, 4). This sample is then attached to a test jig in preparation for testing. Upon completion of the specimen preparation, the four corner points have the coordinates of (5.000, 2.000), (10.196, 5.000), (8.196, 8.404), (1.536, 4.000). (a) Calculate the deformation gradient matrix in component form F, and (b) Calculate the Jacobian value.

Answer 1

The coordinates are A(0, 0) B*6, 0) C(6, 4) the new coordinates are A^T(5, 00, 2 - 000) B^1(10, 196, 5-000) c^1(8, 196, 8.404) D^1(1.0536, 4.000) now delta A = 5x + 2y {change in coordinates of A} delta B = 4.196 x + 5y delta C = 2.196 x + 4.404 y delta D = 1.536 hence, F = deformation gradient matrix = [partial differential A/partial differential x partial differential A/partial differential y partial differential B/partial differential x partial differential B/partial differential y partial differential c/partial differential x partial differential c/partial differential y partial differential d/partial differential x partial differential D/partial differential y] \r\n f = [5 2 4.196 5 2.196 4.404 1.536 0]