A Unified Sensitivity Analysis Approach for Parameter Identification of Material Models in Fluid-Saturated Porous Media

摘要

A large body of references can be found in the literature on the issue of sensitivity analysis (see e.g. the survey in [1] with 148 references). The main consequences and guidelines with regard to linear and nonlinear (history dependent) single-phase problems can be summarized as follows. 1. The analytical approach yields a linear equation for the sensitivities, and thus no iterations are necessary. This also holds for history dependent problems of continuum mechanics, where the response is the result of an iterative procedure. 2. As noted in [7] "the sensitivity formulation must use the consistent tangent operator, whether or not it is used to accelerate the convergence of the equilibrium iterations". 3. Concerning history dependent problems the design sensitivity at a given time (or load) step also necessitates results for the sensitivity at the previous time step, and thus the sensitivity formulation essentially exhibits a recursion structure. Consequently, errors at previous time steps effect the sensitivity at the actual time step. 4. A derivative of (stiffness-)matrices as occasionally found in the literature is not necessary. 5. From a computational point of view, the sensitivity computations are relatively inexpensive, since no iterations are required. Basically it consists of three steps: (1) assembly of a " pseudo-load" (pre-processing), (2) solution of a linear system of equations (with consistent tangent matrix already factorized in the equilibrium iteration), (3) back-substitu-tion in order to obtain the design sensitivity of quantities such as forces, stresses, strains or history-variables (post-processing). 6. The sensitivities are obtained simultaneously to the incremental computation at each time (load) step, at the converged state of the equilibrium iteration. It is the aim of this paper to reconsider the above guidelines towards a unified approach for the sensitivity analysis of a coupled problem modeling fluid saturated porous media.