20 2 Linear Elastic Stress-Strain Relations Since aluminum is an isotropic material,the compliance matrix for aluminum is calculated using the MATLAB function IsotropicCompliance as follows: >S IsotropicCompliance(72.4,0.3) S= 0.0138 -0.0041 -0.0041 0 0 0 -0.0041 0.0138 -0.0041 0 0 0 -0.0041 -0.0041 0.0138 0 0 0 0 0 0 0.0359 0 0 0 0 0 0 0.0359 0 0 0 0 0 0 0.0359 Next,the strain vector is calculated using (2.2)as follows: >epsilon S*sigma epsilon 1.0e-003* -0.1151 0.3837 -0.11 0 0 0 Finally,the change in length in each direction is calculated by multiplying the strain by the dimension in each direction as follows: >d1 epsilon(1)*60 d1= -0.0069 >d2 epsilon(2)*60 d2= 0.0230 >d3 epsilon(3)*60 d3= -0.006920 2 Linear Elastic Stress-Strain Relations Since aluminum is an isotropic material, the compliance matrix for aluminum is calculated using the MATLAB function IsotropicCompliance as follows: >> S = IsotropicCompliance(72.4, 0.3) S = 0.0138 -0.0041 -0.0041 0 0 0 -0.0041 0.0138 -0.0041 0 0 0 -0.0041 -0.0041 0.0138 0 0 0 0 0 0 0.0359 0 0 0 0 0 0 0.0359 0 0 0 0 0 0 0.0359 Next, the strain vector is calculated using (2.2) as follows: >> epsilon = S*sigma epsilon = 1.0e-003 * -0.1151 0.3837 -0.1151 0 0 0 Finally, the change in length in each direction is calculated by multiplying the strain by the dimension in each direction as follows: >> d1 = epsilon(1)*60 d1 = -0.0069 >> d2 = epsilon(2)*60 d2 = 0.0230 >> d3 = epsilon(3)*60 d3 = -0.0069