Energetic formulation of large‐deformation poroelasticity

Mina Karimi,1, ∗ Mehrdad Massoudi,2 Noel Walkington,3 Matteo Pozzi,1 and Kaushik Dayal1, 3, 4, † 1Department of Civil and Environmental Engineering, Carnegie Mellon University 2National Energy Technology Laboratory, Pittsburgh PA 15236-0940 3Center for Nonlinear Analysis, Department of Mathematical Sciences, Carnegie Mellon University 4Department of Materials Science and Engineering, Carnegie Mellon University (Dated: January 3, 2022)

[1]  Satish Karra,et al.  Model reduction for fractured porous media: a machine learning approach for identifying main flow pathways , 2019, Computational Geosciences.

[2]  R. M. Bowen,et al.  Incompressible porous media models by use of the theory of mixtures , 1980 .

[3]  M. Gurtin,et al.  The Mechanics and Thermodynamics of Continua , 2010 .

[4]  John H. Cushman,et al.  Multiscale, hybrid mixture theory for swelling systems—I: balance laws , 1996 .

[5]  K. Dayal,et al.  Dependence of equilibrium Griffith surface energy on crack speed in phase-field models for fracture coupled to elastodynamics , 2017, International Journal of Fracture.

[6]  Richard A. Regueiro,et al.  Dynamics of porous media at finite strain , 2004 .

[7]  J. Oden,et al.  Variational Methods in Theoretical Mechanics , 1976 .

[8]  Alejandro Mota,et al.  A variational constitutive model for porous metal plasticity , 2006 .

[9]  Maruti Kumar Mudunuru,et al.  A framework for coupled deformation–diffusion analysis with application to degradation/healing , 2011, ArXiv.

[10]  Sophia Blau,et al.  Analysis Of The Finite Element Method , 2016 .

[11]  M. Ortiz,et al.  A variational Cam-clay theory of plasticity , 2004 .

[12]  R. Borja,et al.  A mathematical framework for finite strain elastoplastic consolidation Part 1: Balance laws, variational formulation, and linearization , 1995 .

[13]  Kaushik Dayal,et al.  A dynamic phase-field model for structural transformations and twinning: Regularized interfaces with transparent prescription of complex kinetics and nucleation. Part II: Two-dimensional characterization and boundary kinetics , 2015 .

[14]  Ruben Juanes,et al.  Coupled multiphase flow and poromechanics: A computational model of pore pressure effects on fault slip and earthquake triggering , 2014 .

[15]  Sabine Himmel Mechanics Of Poroelastic Media , 2016 .

[16]  C. Arson,et al.  Fluid-driven transition from damage to fracture in anisotropic porous media: a multi-scale XFEM approach , 2020, Acta Geotechnica.

[17]  Kes Heffer,et al.  Theory of linear poroelasticity with applications to geomechanics and hydrogeology , 2004 .

[18]  E. Dufresne,et al.  Large deformations of a soft porous material , 2015, 1510.03455.

[19]  J. Rudnicki Coupled deformation-diffusion effects in the mechanics of faulting and failure of geomaterials , 2001 .

[20]  Paul C. Fife,et al.  Thermodynamically consistent models of phase-field type for the kinetics of phase transitions , 1990 .

[21]  Nicola Castelletto,et al.  A Scalable Multigrid Reduction Framework for Multiphase Poromechanics of Heterogeneous Media , 2019, SIAM J. Sci. Comput..

[22]  Massimiliano Zingales,et al.  Laminar flow through fractal porous materials: the fractional-order transport equation , 2015, Commun. Nonlinear Sci. Numer. Simul..

[23]  G. Buscarnera,et al.  Spatially distributed landslide triggering analyses accounting for coupled infiltration and volume change , 2020, Landslides.

[24]  Sally M. Benson,et al.  Relative permeability and trapping of CO2 and water in sandstone rocks at reservoir conditions , 2012 .

[25]  WaiChing Sun,et al.  A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain , 2013 .

[26]  Andreas Bielinski,et al.  Numerical simulation of CO2 sequestration in geological formations , 2007 .

[27]  Konstantina Trivisa,et al.  Analysis and Simulations on a Model for the Evolution of Tumors Under the Influence of Nutrient and Drug Application , 2018, SIAM J. Numer. Anal..

[28]  Joshua A. White,et al.  Thermoplasticity and strain localization in transversely isotropic materials based on anisotropic critical state plasticity , 2016 .

[29]  Ronaldo I. Borja,et al.  On the mechanical energy and effective stress in saturated and unsaturated porous continua , 2006 .

[30]  Kamy Sepehrnoori,et al.  Three-Phase Gas/Oil/Brine Relative Permeabilities Measured under CO2 Flooding Conditions , 1993 .

[31]  Kaushik Dayal,et al.  A dynamic phase-field model for structural transformations and twinning: Regularized interfaces with transparent prescription of complex kinetics and nucleation. Part I: Formulation and one-dimensional characterization , 2015 .

[32]  Ronaldo I. Borja,et al.  Cam-Clay plasticity. Part V: A mathematical framework for three-phase deformation and strain localization analyses of partially saturated porous media , 2004 .

[33]  K. Dayal,et al.  Atomistic-to-continuum multiscale modeling with long-range electrostatic interactions in ionic solids , 2013, 1310.2500.

[34]  Ronaldo I. Borja,et al.  Mathematical framework for unsaturated flow in the finite deformation range , 2014 .

[36]  M. Biot General Theory of Three‐Dimensional Consolidation , 1941 .

[38]  J. H. Cushman,et al.  Mixture theory and unsaturated flow in swelling soils , 2007 .

[39]  Lallit Anand,et al.  A coupled theory of fluid permeation and large deformations for elastomeric materials , 2010 .

[40]  Maurice A. Biot,et al.  Nonlinear and semilinear rheology of porous solids , 1973 .

[41]  James K. Knowles,et al.  Evolution of Phase Transitions: A Continuum Theory , 2006 .

[42]  A. D. Taleghani,et al.  Thermoporoelastic Analysis of Artificially Fractured Geothermal Reservoirs: A Multiphysics Problem , 2020 .

[43]  William G. Gray,et al.  General conservation equations for multi-phase systems: 1. Averaging procedure , 1979 .

[44]  P. Newell,et al.  Basement Fault Reactivation by Fluid Injection Into Sedimentary Reservoirs: Poroelastic Effects , 2017, Journal of Geophysical Research: Solid Earth.

[45]  J. Andrade,et al.  Modeling the static liquefaction of unsaturated sand containing gas bubbles , 2018 .

[46]  Z. Suo,et al.  A theory of coupled diffusion and large deformation in polymeric gels , 2008 .

[47]  R. Borja Conservation laws for three-phase partially saturated granular media , 2005 .

[48]  A. M. Sarem Three-Phase Relative Permeability Measurements by Unsteady-State Method , 1966 .

[49]  Ingo Müller,et al.  Fundamentals of Thermodynamics and Applications: With Historical Annotations and Many Citations from Avogadro to Zermelo , 2009 .

[50]  王东东,et al.  Computer Methods in Applied Mechanics and Engineering , 2004 .

[51]  Alfio Grillo,et al.  Elasticity and permeability of porous fibre-reinforced materials under large deformations , 2012 .

[52]  Wolfgang Ehlers,et al.  Challenges of porous media models in geo- and biomechanical engineering including electro-chemically active polymers and gels , 2009 .

[53]  J. Bassis,et al.  A non-local continuum poro-damage mechanics model for hydrofracturing of surface crevasses in grounded glaciers , 2020, Journal of Glaciology.

[54]  A. Gajo A general approach to isothermal hyperelastic modelling of saturated porous media at finite strains with compressible solid constituents , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[55]  Eliot Fried,et al.  A theory for species migration in a finitely strained solid with application to polymer network swelling , 2010 .

[56]  S. Cowin Bone poroelasticity. , 1999, Journal of biomechanics.

[57]  B. Simon,et al.  Multiphase Poroelastic Finite Element Models for Soft Tissue Structures , 1992 .