Hydro-mechanical multiscale numerical manifold model of the three-dimensional heterogeneous poro-elasticity

Wu, Wenan; Yang, Yongtao; Shen, Yinbin; Zheng, Hong; Yuan, Chi; Zhang, Ning

doi:10.1016/j.apm.2022.06.014

Cited by 22 publications

(11 citation statements)

References 69 publications

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“…22 Should these conditions not be completely fulfilled, micro-dynamics are expected to affect the overall properties of fractured material. Proper computational homogenization procedures would therefore be necessary for solving the microscale boundary value problem (e.g., 33,34 ).…”

Section: Overall Viscoelastic Behaviormentioning

confidence: 99%

“…The stress and displacement fields (𝜎, 𝜉) solution to the original problem (32) are obtained from those associated with of the auxiliary problems (33) and (37). It follows therefore that:…”

Section: Second Elementary Problem: Residual Problem With Prescribed ...mentioning

confidence: 99%

“…In the general context of computational analyses, one should quote the contributions addressing the fracture propagation in the framework of numerical manifold method. [30][31][32][33][34] These analyses fall either within purely macroscopic modeling category [30][31][32] or multiscale approaches. 33,34 Propagation criteria for fractures in materials in the context of instantaneous response (elastic and plastic) have already been well studied in the literature.…”

Section: Introductionmentioning

confidence: 99%

“…[30][31][32][33][34] These analyses fall either within purely macroscopic modeling category [30][31][32] or multiscale approaches. 33,34 Propagation criteria for fractures in materials in the context of instantaneous response (elastic and plastic) have already been well studied in the literature. However, in many situations, delayed behavior reveals a fundamental component in the material deformation.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, the third difficulty corresponds to the development of a fracture propagation condition to the equivalent material on the macroscopic scale, keeping the micromechanical essential conditions. In the general context of computational analyses, one should quote the contributions addressing the fracture propagation in the framework of numerical manifold method 30–34 . These analyses fall either within purely macroscopic modeling category 30–32 or multiscale approaches 33,34 …”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A micromechanics‐based approach to damage propagation criterion in viscoelastic fractured materials regarded as homogenized media

Aguiar

Maghous

2023

Num Anal Meth Geomechanics

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This paper aims to formulate a damage propagation criterion in microfractured viscoelastic materials, relying upon a micromechanics reasoning together with thermodynamics concepts. The fracture density is regarded as damage parameter at macroscopic scale. The equivalent behavior of the heterogeneous material (solid matrix + fractures) is first formulated within the framework of viscoelastic homogenization theory. In this context, relevant relationships relating local fields to macroscopic fields are derived, thus allowing a clear micromechanical interpretation of quantities involved in the upscaling process, such as the residual or viscous strains. Based on thermodynamic concepts, the energy dissipation and the free energy of the homogenized viscoelastic material are deduced at the macroscopic scale. The formulation of an energetic-based criterion for damage propagation in viscoelastic fractured materials is then achieved by viewing the macroscopic energy release rate as the thermodynamic force responsible for propagation. Due to the delayed deformation component, the formulation is time-dependent. Since it is formulated directly at the homogenized material level, the main advantage of the approach developed in this work is the rigorous determination of the energy release rate expression, without neglecting any residual term. In the last part of the paper, several numerical applications are performed to illustrate the main features of the modeling and to provide comparison with available simplified formulations. Finally, the proposed damage propagation criterion is applied to give qualitative insights on fracturing process of sedimentary layered rocks at geological times scale viewed as a long-term mechanical damage problem, emphasizing the viscosity effects in preventing fracture propagation.

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Section: Overall Viscoelastic Behaviormentioning

confidence: 99%

Section: Second Elementary Problem: Residual Problem With Prescribed ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A micromechanics‐based approach to damage propagation criterion in viscoelastic fractured materials regarded as homogenized media

Aguiar

Maghous

2023

Num Anal Meth Geomechanics

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Multiscale formulation for saturated porous media preserving the representative volume element size objectivity

Reinaldo A.,

Javier L.,

Pablo J.

2023

Numerical Meth Engineering

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SummaryA multiscale model for saturated porous media is proposed, based on the concept of representative volume element (RVE). The physics between macro and micro‐scales is linked in terms of virtual power measures given by the general theory of poromechanics. Then, applying the so‐called Principle of Multiscale Virtual Power, together with suitable admissible constraints on micro‐scale displacement and pore pressure fields, a well‐established variational framework is obtained. This setting allows deriving the weak form of micro‐scale balance equations as well as the homogenization rules for the macro‐scale stress‐like variables and body forces. Whenever the micro‐scale mechanical constitutive functionals admit, as input arguments, the full‐order expansion of the micro‐scale pore pressure field, a size effect is inherited on the macro‐scale material response. The current literature attributes this issue to the so‐called “dynamical” or “second‐order” term of the homogenized flux velocity. It has been commonly suggested that the influence of this term is negligible by assuming infinitely small micro‐scale dimensions. However, such an idea compromises the fundamental notion of the existence of RVE for highly heterogeneous media. In this work, we show that the micro‐scale size dependence can be consistently eliminated by a simple constitutive‐like assumption. Accordingly, slight and selective redefinitions in the input arguments of micro‐scale material laws are proposed, leading to a constitutive formulation that allows the combination of micro‐scale variables with different orders of expansion. Just at this specific (constitutive) level, a reduced‐order expansion is selectively adopted for the micro‐scale pore pressure field. Thus, the RVE notion is restored while still retaining the major effects of the “dynamical” component of the homogenized flux velocity. The proposed formulation is implemented within a finite element squared (FE) environment. Some numerical experiments are presented showing the viability of the methodology, including comparisons against analytical, mono‐scale and DNS solutions.

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Coupled hydro-mechanical two-phase flow model in fractured porous medium with the combined finite-discrete element method

Sun,

Tang,

Aboayanah

et al. 2024

Engineering with Computers

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Hydro-mechanical multiscale numerical manifold model of the three-dimensional heterogeneous poro-elasticity

Cited by 22 publications

References 69 publications

A micromechanics‐based approach to damage propagation criterion in viscoelastic fractured materials regarded as homogenized media

A micromechanics‐based approach to damage propagation criterion in viscoelastic fractured materials regarded as homogenized media

Multiscale formulation for saturated porous media preserving the representative volume element size objectivity

Coupled hydro-mechanical two-phase flow model in fractured porous medium with the combined finite-discrete element method

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