Inverse analysis procedure for identifying hardening function in elasto-plastic problem by two-stage finite element scheme

This paper focuses on the inverse analysis method for identifying a nonlinear hardening function, which governs a plastic yielding of soil and rock materials in the framework of the elasto-plasticity theory. A concept of the two-stage finite element method is introduced, employing the independent finite element discretizations of both the state variables and the hardening function to be identified. This approach enables unknown material functions to be identified without providing their explicit forms, thus, it marks a significant departure from the traditional treatments of the characterization problems, in which only identification of the parameters present in the explicit forms of the material functions is attempted. The proposed inverse analysis method can be classified as the output least-squares method, since the discrepancy between material responses, measured and calculated by means of the finite element method is expressed in the form of the least-squares function to be minimized. In the presented work this minimization is made up of a variety of the Levenberg-Marquard optimization methods, based on the so called trust region approach. In this paper we give a numerical example of the hardening function identification in case of a simple-compression triaxial test performed on a soft rock material, whose plastic behavior is governed by the modified Drucker-Prager yield criterion. This example is supplemented by the analysis of the obtained results.