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http://hdl.handle.net/2108/523
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| DC Field | Value | Language |
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| contributor.advisor | Callari, Carlo | - |
| contributor.advisor | Nova, Roberto | - |
| contributor.advisor | Savioia, Marco | - |
| contributor.advisor | Schrefler, Bernhard | - |
| contributor.author | Abati, Andrea | - |
| date.accessioned | 2008-06-04T09:30:40Z | - |
| date.available | 2008-06-04T09:30:40Z | - |
| date.issued | 2008-06-04T09:30:40Z | - |
| identifier.uri | http://hdl.handle.net/2108/523 | - |
| description | 20. ciclo | en |
| description.abstract | In questa tesi si presenta una teoria termodinamica per continui porosi multi-fase
basata sul lavoro di Biot e la relativa formulazione numerica mediante elementi finiti non convenzionali che consentono di modellare fenomeni di localizzazione delle deformazioni. In una prima fase si ricava una forma generale per le relazioni iperelastiche incrementali. Si ottengono quindi espressioni particolari per gli operatori iperelastici tangenti utilizzando argomenti tipici della teoria delle miscele. Si verifica la compatibilità di tali operatori con la suddetta teoria termodinamica utilizzando le condizioni di simmetria e di Maxwell. Fra i principali risultati della trattazione considerata vi è una semplice espressione della dissipazione, che sarà utilizzata in un approccio multi-scala alla localizzazione delle deformazioni.
Si considera quindi una formulazione agli elementi finiti del modello costitutivo ot
tenuto, concentrando l'attenzione sulla linearizzazione del sistema risolvente. Tra le possibili fonti di non-linearità, si considerano anche quelle dovute a condizioni al contorno unilatere sul flusso fluido, introdotte per modellare e±cacemente l'interfaccia tra mezzo poroso e atmosfera. Si analizzano semplici esempi numerici monodimensionali, allo scopo di valutare le prestazioni numeriche delle tecniche di regolarizzazione di tipo penalty e Lagrangiano aumentato utilizzate. In tali esempi si evidenzia anche l'analogia formale e numerica tra problemi di filtrazione con vincoli unilateri e problemi di contatto in assenza di attrito. Si prendono inoltre in considerazione altre situazioni di interesse pratico, come la propagazione di un fronte di saturazione in uno strato di terreno e la parziale saturzione in una diga di calcestruzzo a gravità.
Per modellare meccanismi dissipativi localizzati, si analizza la presenza di discontinuità negli spostamenti e nei flussi fluidi nel caso di mezzi porosi multi-fase. Nel corrispondente metodo agli elementi finiti, l'insorgere di tali discontinuità è simulato mediante "enhancement" locale delle funzioni interpolanti. Infine, si presentano i risultati della simulazione numerica di una prova di compressione piana su un mezzo poroso parzialmente saturo. Tale simulazione consente di evidenziare tutte le caratteristiche delle formulazioni teoriche e numeriche presentate in questa tesi. | en |
| description.abstract | In this thesis we present a thermodynamic theory for multiphase porous continua based
on Biot work and the corresponding numerical formulation by non-standard finite element methods modelling strain localization phenomena. Firstly, a general form of
hyperelastic rate equations is provided. Particular expressions for hyperelastic tangent operators are then obtained by using arguments typically employed in the mixture
theory. The compatibility of such operators with the aforementioned thermodynamic
theory is then investigated by means of symmetry and Maxwell conditions. Among
the main results of the presented formulation there is a simple expression for dissipation, that will be used in a multi-scale approach to the localization of deformations in multiphase solids.
A finite element formulation of this constitutive model is then presented, focusing the attention on the linearization of the resulting solving system. Among the different sources of non-linearity, also the ones due to unilateral boundary conditions on the fluid flow are considered. Such boundary conditions are introduced to effectively model the interface between the porous solid and the atmosphere. In order to investigate numerical performance of penalty and augmented Lagrangian regularization techniques employed herein, simple one-dimensional numerical examples are considered. In these examples, both the numerical and formal analogies between seepage problems with unilateral constraints and frictionless contact problems are pointed out. Further situations of practical interest are considered, as the propagation of a saturation front in a soil sample and the partial saturation of a concrete gravity dam.
To model localized dissipative mechanisms, we analyze the presence of discontinuities
in displacements and fluid flows. In the corresponding finite element method, the
appearance of these discontinuities is simulated by local enhancement of interpolating functions. Finally, results of the numerical simulation of a plain strain compression test on a partially saturated porous solid are presented. This simulation allows us to point out all the features of theoretical and numerical formulations presented in this thesis. | en |
| description.tableofcontents | 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 | en |
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| language.iso | en | en |
| subject | multiphase porous continua | en |
| subject | hyperelastic constitutive equations | en |
| subject | macroscopic thermodynamic theory | en |
| subject | symmetry and maxwell conditions | en |
| subject | finite element formulation | en |
| subject | unilateral boundary conditions | en |
| subject | strain localization | en |
| subject | strong discontinuities | en |
| title | Models and finite element methods for porous media subjected to localized strains | en |
| type | Doctoral thesis | en |
| degree.name | Dottorato in ingegneria delle strutture e geotecnica | en |
| degree.level | Dottorato | en |
| degree.discipline | Facoltà di Ingegneria | en |
| degree.grantor | Università degli Studi di Roma Tor Vergata | en |
| date.dateofdefense | A.A. 2007/2008 | en |
| Appears in Collections: | Tesi di dottorato in ingegneria
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| tesi.pdf | | 4629Kb | Adobe PDF | View/Open |
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