Macroscopic constitutive equations of thermo-poroviscoelasticity derived using eigenstrains

Suvorov, A. P.; Selvadurai, A. P. S.

doi:10.1016/j.jmps.2010.07.016

Cited by 15 publications

(8 citation statements)

References 30 publications

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“…Many efforts have been made to rederive and extend BG theory in a variety of ways. These include Brown and Korringa (1975), Burridge and Keller (1981), Pride et al (1992), Ciz and Shapiro (2007), Suvorov and Selvadurai (2010), and Anand (2015). For example, Brown and Korringa (1975) relax Gassmann's assumption of microscopic homogeneity and isotropy and subsequently extend the BG relationship to anisotropic materials with pore-scale heterogeneous/multiphase solids.…”

Section: Introductionmentioning

confidence: 99%

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Deriving Biot-Gassmann relationship by inclusion-based method

Song

Rudnicki

2016

GEOPHYSICS

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The quasi-static theory of poroelasticity presented by Biot and Gassmann provides a relationship between the drained and undrained elastic constants of an isotropic fluid-saturated porous material in terms of the porosity of the material, bulk modulus of the solid grains, and bulk modulus of the pore fluid. We have developed an alternative approach to derive the Biot-Gassmann (BG) relationship while including the effects of the pore microstructure. First, the Eshelby transformation is used to express the local inclusion/pore strain tensor in terms of the applied strain tensor and reference material elastic properties by the superposition of a void strain and a perturbation term due to induced inclusion stress. Second, the inclusion strain expression and Hill's average principles are combined with the Mori-Tanaka/Kuster-Toksöz scheme to obtain inclusion-stress-dependent effective elastic moduli of porous materials. For an isolated pore system, the effective modulus tensor corresponds to the original Mori-Tanaka/Kuster-Toksöz's expression. Although for communicating pore system, it is proven to satisfy the BG relation. In the second case, the deformation is assumed to occur so slowly that the infiltrating fluid mass has sufficient time to diffuse between material elements and, consequently, the pore fluid pressure is equilibrated within the whole pore system. It is noteworthy that we arrive at a BG relationship without applying reciprocity theorem and that the porous material effective strain is defined from Hill's principles instead of solid phase average strain. A potential application of the stress-independent effective modulus is to help develop a dynamical modulus model of rock physics for a specific pore microstructure.

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Section: Introductionmentioning

confidence: 99%

“…Their expressions of undrained moduli were also the same as the BG relation. Suvorov and Selvadurai (2010) develop macroscopic constitutive equations of thermoporoelasticity using the concept of eigenstrain. If the thermal effect was ignored, their constitutive equations would also be consistent with Biot's stressstrain relations.…”

Section: Introductionmentioning

confidence: 99%

Deriving Biot-Gassmann relationship by inclusion-based method

Song

Rudnicki

2016

GEOPHYSICS

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“…Luo [1996] presented Gurtin-type variational principles for coupled porous thermoelastodynamics. Suvorov and Selvadurai [2010] extended the classical equations of poroelasticity to thermo-poroviscoelastic materials by using the eigenstrain theory and derived macroscopic constitutive equations of thermo-poroviscoelasticity. Apostolakis and Dargush [2013] developed several new mixed variational statements for dynamical continuum problems of thermoelasticity and poroelasticity.…”

Section: Introductionmentioning

confidence: 99%

A Nonlinear Mathematical Model of Thermoelastic Thin Plates with Voids and Its Applications

Yuanlin

Zhong

Chang-jun

2015

Int. J. Appl. Mechanics

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Following the linear theory of thermoelastic materials with voids, a generalized Hamilton variational principle is extended to the thermoelastic plates with voids under the case of large deflection, and a 3D nonlinear mathematical model is presented. In this process, the balance equation of the entropy is converted to an equivalent form without the firstorder time-derivative by integral, and the concept of the moments for the volume fraction of voids and temperature field is introduced. As application, the nonlinear dynamic and aerodynamic characteristics of simply-supported rectangular thermoelastic plates with voids for four different materials are studied and compared by using a Galerkin approach. The effects of the initial deflections and material parameters are considered in detail. In addition to providing a generalized Hamilton variational principle and a 3D nonlinear mathematical model, it is also provided a valuable numerical method to solve the dynamic problem directly in the paper. The theory and the method can be applied to solving various problems of the thermoelastic plates with voids easily.

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“…In addition to these experimental procedures, computational approaches have recently been utilized to evaluate the effective properties of heterogeneous porous media [12,13]. Computational homogenisation principles have been employed to evaluate damage-induced permeability alterations [14].…”

Section: Introductionmentioning

confidence: 99%

Computational modelling of crack-induced permeability evolution in granite with dilatant cracks

Massart

Selvadurai

2014

International Journal of Rock Mechanics and Mining Sciences

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A computational homogenization technique is used to investigate the role of fine scale dilatancy on the stress-induced permeability evolution in a granitic material. A representative volume element incorporating the heterogeneous fabric of the material is combined with a fine-scale interfacial decohesion model to account for microcracking. A material model that incorporates dilatancy is used to assess the influence of dilatant processes at the fine scale on the averaged mechanical behaviour and on permeability evolution, based on the evolving opening of microcracks. The influence of the stress states on the evolution of the spatially averaged permeability obtained from simulations is examined and compared with experimental results available in the literature. It is shown that the dilatancy-dependent permeability evolution can be successfully modelled by the averaging approach.

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Macroscopic constitutive equations of thermo-poroviscoelasticity derived using eigenstrains

Cited by 15 publications

References 30 publications

Deriving Biot-Gassmann relationship by inclusion-based method

Deriving Biot-Gassmann relationship by inclusion-based method

A Nonlinear Mathematical Model of Thermoelastic Thin Plates with Voids and Its Applications

Computational modelling of crack-induced permeability evolution in granite with dilatant cracks

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