Homogenization of the equations of state for a heterogeneous layered medium consisting of two creep materials

Шамаев, А. С.; Шумилова, В. В.

doi:10.1134/s0081543816080149

Cited by 14 publications

(5 citation statements)

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“…The above techniques are generally applicable to isotropic composites made up of ellipsoidal inclusions within a matrix, while homogenization‐based anisotropic viscoplasticity has received little attention in the literature 68–71 . Chatzigeorgiou et al 68 applied asymptotic expansion techniques to composites with generalized standard material laws and demonstrated their application to multilayered media.…”

Section: Introductionmentioning

confidence: 99%

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An anisotropic viscoplasticity model for shale based on layered microstructure homogenization

Choo

Semnani

White

2020

Num Anal Meth Geomechanics

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Viscoplastic deformation of shale is frequently observed in many subsurface applications. Many studies have suggested that this viscoplastic behavior is anisotropic—specifically, transversely isotropic—and closely linked to the layered composite structure at the microscale. In this work, we develop a two‐scale constitutive model for shale in which anisotropic viscoplastic behavior naturally emerges from semianalytical homogenization of a bilayer microstructure. The microstructure is modeled as a composite of soft layers, representing a ductile matrix formed by clay and organics, and hard layers, corresponding to a brittle matrix composed of stiff minerals. This layered microstructure renders the macroscopic behavior anisotropic, even when the individual layers are modeled with isotropic constitutive laws. Using a common correlation between clay and organic content and magnitude of creep, we apply a viscoplastic modified Cam‐Clay plasticity model to the soft layers, while treating the hard layers as a linear elastic material to minimize the number of calibration parameters. We then describe the implementation of the proposed model in a standard material update subroutine. The model is validated with laboratory creep data on samples from three gas shale formations. We also demonstrate the computational behavior of the proposed model through simulation of time‐dependent borehole closure in a shale formation with different bedding plane directions.

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Section: Introductionmentioning

confidence: 99%

“…Chatzigeorgiou et al 68 applied asymptotic expansion techniques to composites with generalized standard material laws and demonstrated their application to multilayered media. Mathematical approaches have also been adopted for perfectly bonded isotropic creep materials 70 and fiber‐reinforced laminates 69 …”

Section: Introductionmentioning

confidence: 99%

An anisotropic viscoplasticity model for shale based on layered microstructure homogenization

Choo

Semnani

White

2020

Num Anal Meth Geomechanics

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“…The above techniques are generally applicable to isotropic composites made of ellipsoidal inclusions within a matrix, while homogenization-based anisotropic viscoplasticity has received little attention in the literature [67][68][69][70]. Chatzigeorgiou et al [67] applied asymptotic expansion techniques to composites with generalized standard material laws and demonstrated their application to multi-layered media.…”

Section: Introductionmentioning

confidence: 99%

“…Chatzigeorgiou et al [67] applied asymptotic expansion techniques to composites with generalized standard material laws and demonstrated their application to multi-layered media. Mathematical approaches have also been adopted for perfectly bonded isotropic creep materials [69] and fiber-reinforced laminates [68].…”

Section: Introductionmentioning

confidence: 99%

An anisotropic viscoplasticity model for shale based on layered microstructure homogenization

Choo,

Semnani,

White

2020

Preprint

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Viscoplastic deformation of shale is frequently observed in many subsurface applications. Many studies have suggested that this viscoplastic behavior is anisotropic and closely linked to the layered composite structure at the microscale. In this work, we develop a two-scale constitutive model for shale in which anisotropic viscoplastic behavior naturally emerges from semi-analytical homogenization of a bi-layer microstructure. The microstructure is modeled as a composite of soft layers, representing a ductile matrix formed by clay and organics, and hard layers, corresponding to a brittle matrix composed of stiff minerals. This layered microstructure renders the macroscopic behavior anisotropic, even when the individual layers are modeled with isotropic constitutive laws. Using a common correlation between clay and organic content and magnitude of creep, we apply a viscoplastic Modified Cam-Clay plasticity model to the soft layers, while treating the hard layers as a linear elastic material to minimize the number of calibration parameters. We then describe the implementation of the proposed model in a standard material update subroutine. The model is validated with laboratory creep data on samples from three gas shale formations. We also demonstrate the computational behavior of the proposed model through simulation of time-dependent borehole closure in a shale formation with different bedding plane directions.

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“…In general, the obtained homogeneous medium is anisotropic, even if the original layers were isotropic. This method of averaging is developed in the works [1][2][3][4][5][6][7][8][9]. In this article the characteristics of the original array (elastic modulus, coefficients of creep kernels, specific weight) are the step functions, abruptly changing from layer to layer.…”

Section: Introductionmentioning

confidence: 99%

Method of Calculation of Stresses in the Layered Elastic-Creeping Arrays

Bobyleva

2016

MATEC Web Conf.

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Abstract. Stress calculation problem in an elastically creeping layered array is solved by the method of homogenization. Exponential function of time is taken as the kernel of creep of each layer. Experiments prove that such functions are the best way to describe the creep of mountain ranges over long periods of time. Integrals of convolution type with such exponential kernels are used to describe the creep process. The article contains formulas for calculating effective elastic-creep coefficients. These formulas contain exponential functions with both initial parameters and with new ones, which are also negative real numbers. As a computational example, kernel creep graph is shown for one of the average environment's effective modulus. Obtained solution can be used in underground construction.

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Homogenization of the equations of state for a heterogeneous layered medium consisting of two creep materials

Cited by 14 publications

References 1 publication

An anisotropic viscoplasticity model for shale based on layered microstructure homogenization

An anisotropic viscoplasticity model for shale based on layered microstructure homogenization

An anisotropic viscoplasticity model for shale based on layered microstructure homogenization

Method of Calculation of Stresses in the Layered Elastic-Creeping Arrays

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