Identification Of Fractional Viscoelastic Constitutive Parameters

Viscoelasticity is a behavior of many materials used in practical engineering. A key issue to describe such a behavior is the description of the constitutive relationship and the determination of related parameters, and is significantly valuable practically and theoretically. Compared with the interger-order constitutive models, the fractional one is able to describe the viscoelastic behavior with fewer parameters accurately and to take a wider frequency range into account. The thesis mainly aims at the determination of parameters for fractional viscoelastic models from an angle of solving inverse problems of fractional viscoelastic field, the major works includes:1. For2-D direct fractional viscoelastic problems, an FE based semi-analytical model for homogeneous field and an FD-FE based model for regionally inhomogeneous field are developed in time domain. Utilizing these two models, a numerical model is presented for the inverse problem of constitutive parameters, and the single/combined identification of the parameters is fulfilled via an ACO based algorithm.2. For2-D direct static fractional viscoelastic problems with interval uncertainty, a numerical model is presented to estimate the upper and lower of bounds of displacement via the Taylor expansion and the interval analysis technique; For2-D inverse static fractional viscoelastic problems with interval uncertainty, two numerical models are proposed for the single/combined identification of the upper and lower bounds of constitutive parameters, and the ACO and the Gauss-Newton algorithms are employed in the solution process.3. For2-D direct dynamical fractional viscoelastic problems, a FE model is presented for homogeneous/regionally inhomogeneous fields in Laplace domain. Using this model, a numerical model is developed for the single/combined identification of constitutive parameters. The identification process is fulfilled via the Gauss-Newton algorithm.Another improtant part of this thesis is the investigation on the numerical techniques concerned with time dependent nonlinear problems by solving nonlinear transient convection-diffusion problems and shallow water equations. A temperally piecewise adaptive algorithm and FEM are combined for modelling2-D nonlinear transient convection-diffusion problems and1D shallow water equations without any appro xiemation in tackling nonlinear terms. The numerical results indicate that the proposed approaches can provide more stable computation accuracy in whole time domain in comparison with the modified Euler method, the Heun's method, the4-order classic Runge-Kutta method, and Crank-Nicolson method.The work presented in this thesis is pretty valuable for modeling fractional viscoelastic materials/structures and the further investgation on numerical solutions for time dependent nonlinear problems, and is hopefully used in some engineering areas with further improvement.