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A consistent u‐p formulation for porous media with hysteresis
Author(s) -
Pedroso Dorival M.
Publication year - 2014
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4808
Subject(s) - discretization , porous medium , nonlinear system , finite element method , mathematics , quadratic equation , convergence (economics) , mathematical analysis , hysteresis , porosity , physics , geometry , engineering , geotechnical engineering , thermodynamics , quantum mechanics , economics , economic growth
Summary This paper presents a continuum formulation based on the theory of porous media for the mechanics of liquid unsaturated porous media. The hysteresis of the liquid retention model is carefully modelled, including the derivation of the corresponding consistent tangent moduli. The quadratic convergence of Newton's method for solving the highly nonlinear system with an implicit finite element code is demonstrated. A u‐p formulation is proposed where the time discretisation is carried out prior to the space discretisation. In this way, the derivation of all consistent moduli is fairly straightforward. Time integration is approximated with the Theta and Newmark's methods, and hence the fully coupled nonlinear dynamics of porous media is considered. It is shown that the liquid retention model requires also the consistent second‐order derivative for quadratic convergence. Some predictive simulations are presented illustrating the capabilities of the formulation, in particular to the modelling of complex porous media behaviour. Copyright © 2014 John Wiley & Sons, Ltd.