Application of Sensitivity analysis (SA) by means of statistical techniques in nonlinear elastic constitutive models including residual stress

Abstract

This thesis deals with applying the sensitivity analysis methods that consideration of different functions on the non-linear elastic constitutive models in particular a circular cylindrical tube with radial and circumferential residual stresses and in some different types of pressure-inflation relation in a pressurized and axially stretched tube.Considering the inflation of hyperelastic cylinders in the framework of non-linear elastic constitutive models imposed to an axial stretch and torsion in the presence of residual stress has been done in this work. The constitutive relation of the material depends on various parameters such as the cylinder geometry, the different loading parameters, the prescribed stretches, and the magnitude of the residual stresses. Applying sensitivity analysis methods with attention to a statistical approach determined how the variations of the input variables affect the output variables.After reviewing on applied sensitivity analysis and recapping on basic contents of the non-linear elastic constitutive models, through the implementation of Sobol and the Fourier Amplitude Sensitivity Test (FAST) methods, the most important parameters of the system under the applied pressure and axial force such as the thickness of the tube or axial and azimuthal stretch are gained in the first part of the thesis. Then, the complicated form of the mechanical problem is expressed which is the problem of mixed extension, inflation, and torsion of a circular cylindrical tube in the presence of residual stress which the input parameters in the material model are distributed according to three probability distribution methods, namely the uniform, the gamma, and the normal distribution. In other words, the relation between various parameters as they relate to the inflation pressure, the moment, and the reduced axial force is studied with the help of two sensitivity analysis methods, namely, the Sobol method and FAST method. Both methods found their application in relatively complex models, especially when these models show a non-linear and non-monotonic behaviour. After that, the pressure-inflation relation in a pressurized and axially stretched tube is studied in fiber-reinforcement materials with different natural configurations. The material consists of an isotropic ground substance that is reinforced by two families of fibers. The natural configuration of the fibers may differ from that of the ground substance and the fibers are taken to be dispersed. The sensitivity analysis is applied by means of statistical simulation in the "R" program to determine how the uncertainties of the cylinder stretch, the fiber dispersion, and the fiber natural configuration affect the required inflation pressure. The V implementation of the Sobol and FAST methods allows us to account for the interplay of different parameters and to identify the most influential parameters in the pressure-inflation relation.