a. Using the parameters and results from the example given in class in Lecture 5.2 in the "First Piola-Kirchoff (PK) Stress" section, and that the normal vector in the Reference State is (31,31,31) calculate the magnitude of the differential force, dFj, in terms of the differential area dA for the Nominal Stress, the 1st PK Stress, and the Cauchy Stress. [10 pts] b. Explain your results from part a. That is, if equal explain why and if not equal explain why. [10 pts] Example Given that the Deformation Gradient is equal to 0210.213131 and that the Cauchy stress is equal to 10205202535330 calculate the Nominal stress and the 1st PK stress in matrix form. We have Nominal Stress: N=JF1 =10205202535330 F=0210.213131 J=Det[F]=0(19)0.2(2+3)+1(61)=4 InI-I::Print"F1=",Inverse0210.213131//MatrixForm]F1=2.51.251.250.70.250.050.40.50.1 In[-J:Print"FT=",Transpose[Inverse0210.213131//MatrixForm].FT=2.50.70.41.250.250.51.250.050.1 In[II:=Print"N=",42.51.251.250.70.250.050.40.50.110205202535330//MatrixForm]N=36.20.44.125.269.93.889.682.36.4 In[JI:Print"T=",4102052025353302.50.70.41.250.250.51.250.050.1//Matrixform]T=36.125.289.620.69.82.44.93.836.4 Note the lack of symmetry of the Nominal Stress and 1st PK Stress