Optimization in the disturbed state concept: Constitutive modeling and application in finite element analysis

Abstract

In constitutive modeling, one of important tasks is to calibrate the model. To calibrate a model is to find out the values of the model parameters for a material whose stress-strain behavior is to be simulated by the model. Conventional approach is to find certain well-defined states ill certain tests where behavior of a material is controlled by those parameters and then the stress and strain and other history parameters at those states can be used to find them. However, as the model evolves more sophisticated, such as the Disturbed State Concept Model (DSC), in which a greater number of parameters are introduced to account for behavior of the material under various stress conditions, it is not possible to find an easy way to calibrate, mainly due to certain stress-strain states are difficult to be isolated out. In this study an optimization approach is proposed by using quasi-Newton method with BFGS up-dating scheme. Contrary to the conventional approach which determines parameter values by averaging values of laboratory tests or by simple data fitting of the assumed parameter relations, the optimization approach is to find the best agreement of the model simulation with the experimental observation, then gives a set of parameter values for the best agreement which is quantitatively measured by the least error residual. Weight is used in the optimization procedure to emphasize on better simulation agreement with the observation for certain stress path conditions. This weight can be decided based on the engineering judgment for certain practical problems. By using the DSC model to simulate stress-strain response of various laboratory tests of sands, and by using the DSC model in a finite element analysis to simulate dynamic soil-structure interaction response of a shaking table test for saturated soil, it is shown that the optimization approach yields closer agreement with the observation. Based on the proposed optimization approach, a computer program DSCOPT is developed for the DSC model. The program takes the laboratory test data as input and outputs the model parameter values by the conventional and optimized approaches, and graphics plots of the model simulation.