Constitutive model building Elastic constitutive models represent the simplest material models as the stress merely depends on the current state of deformation. Based on stress-stress measurement data, a mathematical model can be fitted using least-squares regression. Different materials may show different linear or non-linear stress-strain behaviours TASK 2: Based on the equations above, write an Octave script to fit curves using linear, quadratic and cubic regression on a given stress-strain measurement data file of any n where nm>1. Use your script to determine best fit linear, quadratic and cubic polynomials for material A,B and C whose measurement data are given in files materialA . csv, materialB . csv and materialC. csv (see Appendix A1,A2 and A3 ). The Octave script should fulfill the following criteria: - The regression procedure must be implemented yourself. Use of any regression toolbox or higher level functions (eg. polyfit(), polyval()) is not allowed in your script, although may be helpful to check your own implementation. - To solve arising constructed system of equations, you are allowed to use available linear solvers directly (eg. mldivide(), linsolve()). However, in the report, you need to recognise the properties of the arising system of equations when the regression procedures are applied to the three measurement data files, then discuss the suitability of the solution methods to solve system of linear equations that have been discussed during the course. - When running the script the required input and output are as follows - Input: * Read the stress-strain data for a single material from the given CSV data files, and should also be able to process similar data file of any n where nm>1. - Output: * Stress-strain data information. * The system of equations (coefficient matrix and right-hand side vector) to be solved. * Solved polynomial coefficients, full equations, and standard errors for the fitted polynomials. * Stress-strain data and the fitted curves. Please enter data file name: materialA.csv Number of data points: 17 LINEAR REGRESSION Coefficient matrix: 17.00030.122 30.12277.213 RHS vector: 22.253 56.355 Coefficients of polynomials: a:.051095 a1:0.70992 The equation is: y=0.70992x+0.051095 Standard error: .11478 Figure 1: Example user prompt and output of the Octave script. Figure 2: Example regression plot. A1. Data file materialA.csv strain[-],2.4000E02,1.5860E01,2.9150E01,4.8580E01,7.4160E01,9.8210E01,1.2278E+00,1.4888E+00,1.7498E+00,1.9954E+00,2.2564E+00,2.4917E+00,2.7475E+00,3.0135E+00,3.2334E+00,3.4840E+00,3.7499E+00,stress[Mpa]6.8551E031.4616E013.2120E015.1815E016.6243E018.5516E019.5880E011.0831E+001.1854E+001.3463E+001.5024E+001.6685E+001.9248E+002.1693E+002.3954E+002.5247E+002.9841E+00 A2. Data file materialB.csv strain[-],0.0000E+00,1.0000E03,2.0000E03,3.0000E03,4.0000E03,5.0000E03,6.0000E03,7.0000E03,8.0000E03,9.0000E03,1.0000E02,1.1000E02,1.2000E02,1.3000E02,1.4000E02,1.5000E02,1.6000E02,1.7000E02,1.8000E02,1.9000E02,2.0000E02,stress[Mpa]0.000E+006.459E+001.289E+011.925E+012.644E+013.330E+013.888E+014.690E+015.174E+015.992E+016.398E+017.174E+017.728E+018.408E+018.738E+019.897E+011.012E+021.146E+021.180E+021.194E+021.268E+02 A2. Data file materialC.csv strain[-],1.0444E01,2.5869E01,4.4283E01,6.6183E01,9.5548E01,1.1845E+00,1.4085E+00,2.0157E+00,2.5981E+00,3.0660E+00,3.7577E+00,4.3648E+00,4.7628E+00,5.1558E+00,5.4095E+00,5.6333E+00,5.9068E+00,6.0609E+00,6.1652E+00,6.3194E+00,6.4585E+00,6.5329E+00,stress[Mpa]1.5890E012.8000E013.7840E014.6180E015.9820E016.4380E017.0450E018.8660E011.0838E+001.2431E+001.6822E+002.0609E+002.4997E+002.9008E+003.2413E+003.6422E+004.0431E+004.3986E+004.7162E+004.9733E+005.4119E+005.7446E+00