Models and finite element methods for porous media subjected to localized strains
Creators: name: ABATI, ANDREA
Publisher: name: Università degli Studi di Roma "Tor Vergata"
Year: 2008
Subjects: subject: multiphase porous continua; strong discontinuities; hyperelastic constitutive equations; macroscopic thermodynamic theory; symmetry and maxwell conditions; finite element formulation; unilateral boundary conditions; strain localization
subject: multiphase porous continua
subject: strong discontinuities
subject: hyperelastic constitutive equations
subject: macroscopic thermodynamic theory
subject: symmetry and maxwell conditions
subject: finite element formulation
subject: unilateral boundary conditions
subject: strain localization

description: 20. ciclo
description: Introduction - Motivations - Objectives - Dissertation overview. - 1 Hyperelastic constitutive equations - 1 1 Introduction - 1 2 Fluid mass balance - 1 3 Macroscopic thermodynamics of three-phase porous solids - 1 3 1 Energy balance - 1 3 2 Dissipation inequality - 1 3 3 Porous solid hyperelastic equations - 1 3 4 Rate form of hyperelastic relations - 1 4 Particular forms of hyperelastic relations - 1 4 1 Stress equation - 1 4 2 Fluid content equations - 1 4 3 Application of thermodynamic restrictions - 1 5 Infinitesimal deformations of flids. - 2 Finite element formulation and numerical simulations - 2 1 Introduction - 2 2 Governing equations - 2 3 Finite element formulation - 2 3 1 Time-integration consistent tangents - 2 3 2 Mass conservative scheme - 2 4 Representative numerical simulations - 2 4 1 Desaturation of a sand column - 2 4 2 Water-pressure driven infiltration problem - 2 4 3 Effects of rapid drawdown on a reservoir bank. - 3 Unilateral boundary conditions for unsaturated flow - 3 1 Introduction - 3 2 Interface between porous solid and atmosphere - 3 3 Seepage problem with unilateral constraints - 3 3 1 Poro-elastic model - 3 3 2 Unilateral boundary conditions - 3 4 A formally identical mechanical problem: the Signorini contact - 3 5 Numerical regularization techniques - 3 5 1 Penalty method - 3 5 2 Augmented Lagrangian - 3 6 Finite element - 3 6 1 Seepage problem - 3 6 2 Contact problem - 3 7 Representative numerical simulations - 3 7 1 One-dimensional mechanical and hydraulic examples - 3 7 2 Infiltration through a partially saturated layer - 3 7 3 Partial saturation of a concrete gravity dam. - 4 Strong discontinuities in multiphase solids - 4 1 Introduction - 4 2 Discontinuous solutions in multiphase porous continua - 4 2 1 Mechanical and fluid flow problems at the large scale - 4 2 2 Mechanical and fluid flow problems at the small scale - 4 2 3 Connection between large and small-scale problems - 4 3 Constitutive equations for strong discontinuities in multiphase media - 4 3 1 Continuum poro-elastoplastic model - 4 3 2 Formation of strong discontinuities in multiphase media - 4 3 3 Localized multiphase dissipative model - 4 4 Enhanced finite element formulation - 4 4 1 Finite element interpolations - 4 4 2 Finite element equations - 4 4 3 Solution of the finite element system - 4 5 Representative numerical simulations - 4 5 1 Plane strain compression test - Conclusions - Appendix A Relations between porosity and volumetric strains. - B Thermodynamic consistency of poro-elastic model. - B 1 Strain-independent retention laws. - B 2 Porosity-dependent retention laws. - C Convex Helmholtz free energy. - D Integrability conditions. - References