Modeling and Simulation of Stochastic Inverse Problems in Viscoplasticity

In this paper, we have proposed an approach for parameter identification of random field for rigid viscoplastic material. It is assumed that the random field is stationary and Gaussian with known autocovariance function. Karhunen–Loève decomposition has been used to quantify the effects of random inputs. A method is presented that takes into account only the first two statistical moments of the analyzed displacement field, and only two values of searched process are identified—mean value and coefficient of variation in autocovariation function. It has been shown that this approach is desirable when complicated systems are analyzed. The discretization of the governing equations has been described by the finite element method. The sparse grid stochastic collocation method has been used to solve the stochastic direct problem. It is shown that for the described nonlinear equations, the response function due to searched parameters with wide bounds and with reduced number of measurement points has many local extrema and global optimization technique is required. Genetic algorithm has been adopted to compute the functional cost. Numerical example shows the identification problem for compressed cylindrical sample. It is revealed that the key factor determining the convergence of the method is the degree of reduction in the height of the tested sample.