SFB 1313 Publication "Mixed variational formulation and finite-element implementation of second-order poro-elasticity"

October 22, 2024 /

Authors: Hamza Khurshid, Elten Polukhov, Marc-André Keip | Scientific Journal: International Journal of Solids and Structures

New SFB 1313 publication, published in International Journal of Solids and Structures. The work has been developed in the context of SFB 1313 research project B01.

"Mixed variational formulation and finite-element implementation of second-order poro-elasticity"

Authors
Abstract

We present a variational formulation of second-order poro-elasticity that can be readily implemented into finite-element codes by using standard Lagrangian interpolation functions. Point of departure is a two-field minimization principle in terms of the displacement and the fluid flux as independent variables. That principle is taken as a basis for the derivation of continuous and incremental saddle-point formulations in terms of an extended set of independent variables. By static condensation this formulation is then reduced to a minimization principle in terms of the displacement and fluid flux as well as associated higher-order fields. Once implemented into a finite-element code, the resulting formulation can be applied to the numerical simulation of porous media in consideration of second-order effects. Here, we analyze the model response by means of several example problems including two standard tests in poro-elasticity, namely the consolidation problems of Terzaghi and Mandel, and compare the results with those of a corresponding first-order model. As becomes clear, the second-order formulation can unleash its full potential when applied to the study of porous media having spatial dimensions comparable to the size of their microstructure. In particular, it is capable to regularize steep field gradients at external as well as internal surfaces and to describe material dilatation effects known from experiments.

To the top of the page