Aspects of shape an parameter sensitivity analysis in the theory of porous media

Abstract

This contribution is concerned with the application of variational shape sensitivity analysis and parameter sensitivity analysis to the theory of porous media. Both areas contribute to structural optimization and other inverse problems like parameter identification. The correct and efficient derivation, implementation and computation of the sensitivities, that are the gradient values of objectives and constraints with respect to different kind of design variables, have a significant influence on the overall performance of the nonlinear programming algorithms applied to the numerical treatment of inverse problems.The theory of porous media is built upon the mixture of several phases and their interaction using the concept of volume fractions. Thus, a complex continuum mechanical description for each single phase as well as for the whole mixture is used in this approach. This proposal formulates a general viewpoint using an intrinsic formulation in local coordinates which permit a rigorous split of continuum mechanical functions into parts being either geometry or deformation depending. The variational approach to sensitivity analysis is built not only upon this separation but also upon material parameters and yields some general insight into the structure of porous media. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)