Variational continuum multiphase poroelasticity : theory and applications

• Main Authors: Serpieri, Roberto (Author), Travascio, Francesco (Author)
• Format: Electronic eBook
• Language: English
• Published: Singapore : Springer, 2017.
• Series: Advanced structured materials ; 67.
• Subjects: Continuum mechanics.; Porous materials.; elektronické knihy; electronic books
• ISBN: 9789811034527; 9789811034510
• ISSN: 1869-8433 ;
• Physical Description: 1 online resource

This book collects the theoretical derivation of a recently presented general variational macroscopic continuum theory of multiphase poroelasticity (VMTPM), together with its applications to consolidation and stress partitioning problems of interest in several applicative engineering contexts, such...

Table of Contents:

• Foreword; Preface; Contents; 1 Variational Multi-phase Continuum Theories of Poroelasticity: A Short Retrospective; 1.1 Introduction; 1.2 Variational Theories from the 70s to the 80s; 1.2.1 Cowin's Theory; 1.2.2 Mindlin's Variational Single-Phase Theory; 1.2.3 The Variational Theory of Immiscible and Structured Mixtures by Bedford and Drumheller; 1.3 Most Recent Theories; 1.3.1 Variational Theories by Lopatnikov and Co-workers; 1.3.2 Variational Higher Gradient Theories by dell'Isola and Co-workers; 1.4 Conclusions; References.
• 2 Variational Macroscopic Two-Phase Poroelasticity. Derivation of General Medium-Independent Equations and Stress Partitioning Laws2.1 Introduction; 2.2 Variational Formulation; 2.2.1 Basic Configuration Descriptors; 2.2.2 Variational Formulation; 2.2.3 Integral Equations; 2.2.4 Strong Form Equations; 2.2.5 Additional Solid-Fluid Interaction; 2.2.6 The Kinematically-Linear Medium-Independent Problem; 2.2.7 Equations for Static and Quasi-static Problems; 2.3 Discussion and Conclusions; References; 3 The Linear Isotropic Variational Theory and the Recovery of Biot's Equations; 3.1 Introduction.
• 3.2 Two-Phase Medium-Independent Variational Equations for Infinitesimal Perturbations; 3.3 Linear Elastic Isotropic Constitutive Theory with Volumetric-Deviatoric Uncoupling; 3.4 Governing PDEs for the Isotropic Linear Problem; 3.4.1 baru(s)-baru(f) Hyperbolic PDEs with Inertial Terms; 3.4.2 Analysis of Wave Propagation; 3.4.3 PDE for Static and Quasi-static Interaction; 3.5 Bounds and Estimates of Elastic Moduli; 3.5.1 Basic Application of CSA; 3.5.2 Application of CSA to the Extrinsic/Intrinsic Description; 3.6 The Limit of Vanishing Porosity; 3.7 Comparison with Biot's Theory and Concluding Remarks; References.
• 4 Stress Partitioning in Two-Phase Media: Experiments and Remarks on Terzaghi's Principle4.1 Introduction; 4.2 Boundary Conditions with Unilateral Contact; 4.3 Kinematic and Static Characterization of Undrained Flow Conditions; 4.3.1 Static Characterization of Undrained Flow; 4.4 Stress Partitioning in Ideal Compression Tests; 4.4.1 Ideal Jacketed Drained Test; 4.4.2 Ideal Unjacketed Test; 4.4.3 Ideal Jacketed Undrained Test; 4.4.4 Creep Test with Controlled Pressure; 4.5 Analysis of Nur and Byerlee Experiments; 4.5.1 Determination of bare(s); 4.5.2 Estimates of (s).
• 4.6 Domain of Validity of Terzaghi's Principle According to VMTPM4.6.1 Recovery of Terzaghi's Law for Cohesionless Frictional Granular Materials; 4.6.2 Extensibility of Terzaghi's Effective Stress and Terzaghi's Principle Beyond Cohesionless Granular Materials; 4.7 Discussions and Conclusions; References; 5 Analysis of the Quasi-static Consolidation Problem of a Compressible Porous Medium; 5.1 Introduction; 5.2 Theoretical Background; 5.2.1 Dimensionless Analysis; 5.2.2 Semi-analytical Solution of the Stress-Relaxation Problem; 5.2.3 Numerical Solutions; 5.3 Discussion and Conclusions.