A framework for coupled deformation–diffusion analysis with application to degradation/healing

Mudunuru, Maruti K.; Nakshatrala, K. B.

doi:10.1002/nme.3282

Cited by 17 publications

(14 citation statements)

References 58 publications

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“…It will also be shown that many popular models are special cases of the proposed mathematical model. For example, we will show that the small-strain moisture degradation model proposed in [Mudunuru and Nakshatrala, 2012] is a special case of the proposed model. (ii) We will calibrate the proposed degradation model with existing experimental data sets.…”

Section: Degradation Factormentioning

confidence: 99%

“…Status of the degradation model in [Mudunuru and Nakshatrala, 2012]. The small-strain chemo-mechano degradation model proposed in [Mudunuru and Nakshatrala, 2012] is a special case of the proposed chemo-thermo-mechano degradation, and can be obtained under a plethora of assumptions. These assumptions include steady-state response, small strains, and isothermal conditions with negative volumetric heat source in the entire degrading body.…”

Section: A General Constitutive Model For Chemo-thermo-mechano Degradmentioning

confidence: 99%

See 1 more Smart Citation

Material degradation due to moisture and temperature. Part 1: mathematical model, analysis, and analytical solutions

Mudunuru

Nakshatrala

2016

Continuum Mech. Thermodyn.

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Section: Degradation Factormentioning

confidence: 99%

Section: A General Constitutive Model For Chemo-thermo-mechano Degradmentioning

confidence: 99%

Material degradation due to moisture and temperature. Part 1: mathematical model, analysis, and analytical solutions

Mudunuru

Nakshatrala

2016

Continuum Mech. Thermodyn.

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“…Material degradation is a common phenomenon and affects its mechanical parameters [55,56]. Before node failure, the damage variable remains zero and Young's modulus stays constant.…”

Section: Relationship Between Damage and Permeabilitymentioning

confidence: 99%

Numerical Study of Fracture Network Evolution during Nitrogen Fracturing Processes in Shale Reservoirs

et al. 2018

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This paper develops a numerical model to study fracture network evolution during the nitrogen fracturing process in shale reservoirs. This model considers the differences of incompressible and compressible fluids, shear and tensile failure modes, shale heterogeneity, and the strength and permeability of both shale matrix and bedding planes through the coupling of mechanical-seepage-damage during fracturing fluid injection. The results show that nitrogen fracturing has a lower breakdown pressure and larger seepage zone than hydraulic fracturing under the same injection pressure. Tensile failure was identified as the major reason for the initiation and propagation of fractures. Ignoring the effect of bedding planes, the fracture initiation pressure, breakdown pressure, and fracturing effectiveness reached their maxima when the stress ratio is 1. Under the same strength ratio, the propagation path of the fractures was controlled by the stronger effect that was casused by the bedding angle and stress ratio. With increasing the strength ratio, the fracture number and shearing of the bedding plane increased significantly and the failure pattern changed from tensile-only mode to tensile-shear mode. These analyses indicated that the fracture network of bedding shale was typically induced by the combined impacts of stress ratio, bedding angle and strength ratio.Energies 2018, 11, 2503 2 of 22 more effective if N 2 is applied for the hydraulic fracturing [22,23]. Different fracturing fluids lead to the different pore pressure distributions during fluid flow due to the various properties such as viscosity and compressibility. According to the principle of effective stress, the difference in pore pressure distribution induces the difference in the stress distribution in rocks, which plays an important role in fracturing behavior during the fracturing process [24][25][26][27]. Lower breakdown pressure, larger seepage zone and more complex fracture network were observed during nitrogen fracturing [24][25][26][27]. However, these studies were performed on simple rock samples and the influence of other factors during nitrogen fracturing has not been well evaluated. It is essential to investigate fracture network evolution during the nitrogen fracturing process.Several numerical models have been developed to investigate fracture behaviors during the hydraulic fracturing process. These models include the boundary element method [28], finite element method [29][30][31], and discrete element method [32,33]. Wang et al. [29] applied a new mathematical model to investigate fracture network evolution of multi-stranded fractures with pre-existing natural fractures. Shalev and Lyakhovsky [31] studied the damage evolution and seismicity phenomenon in hydraulic fracturing using an improved damage model based on the finite element method. However, there are still only a few studies on a numerical model for nitrogen fracturing and the comparison between water fracturing and nitrogen fracturing. On the other hand, shale reservoirs occur at di...

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“…The current computing power available has allowed for complex fracture models to be applied to a wide range of length scales [31,32]. Of these, many continuum (or macro-scale) and phase-field modeling approaches [33][34][35][36][37][38][39] have been developed to address crack evolution and the overall material response in large samples (cm-scale and larger) including finite element methods [40][41][42] and boundary element methods [43,44]. Continuum-based approaches [45] assume that the computational domain can be treated as one continuous body.…”

Section: Introductionmentioning

confidence: 99%

Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials

et al. 2019

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In brittle fracture applications, failure paths, regions where the failure occurs and damage statistics, are some of the key quantities of interest (QoI). High-fidelity models for brittle failure that accurately predict these QoI exist but are highly computationally intensive, making them infeasible to incorporate in upscaling and uncertainty quantification frameworks. The goal of this paper is to provide a fast heuristic to reasonably estimate quantities such as failure path and damage in the process of brittle failure. Towards this goal, we first present a method to predict failure paths under tensile loading conditions and low-strain rates. The method uses a k-nearest neighbors algorithm built on fracture process zone theory, and identifies the set of all possible pre-existing cracks that are likely to join early to form a large crack. The method then identifies zone of failure and failure paths using weighted graphs algorithms. We compare these failure paths to those computed with a high-fidelity fracture mechanics model called the Hybrid Optimization Software Simulation Suite (HOSS). A probabilistic evolution model for average damage in a system is also developed that is trained using 150 HOSS simulations and tested on 40 simulations. A non-parametric approach based on confidence intervals is used to determine the damage evolution over time along the dominant failure path. For upscaling, damage is the key QoI needed as an input by the continuum models. This needs to be informed accurately by the surrogate models for calculating effective moduli at continuum-scale. We show that for the proposed average damage evolution model, the prediction accuracy on the test data is more than 90%. In terms of the computational time, the proposed models are ≈ O ( 10 6 ) times faster compared to high-fidelity fracture simulations by HOSS. These aspects make the proposed surrogate model attractive for upscaling damage from micro-scale models to continuum models. We would like to emphasize that the surrogate models are not a replacement of physical understanding of fracture propagation. The proposed method in this paper is limited to tensile loading conditions at low-strain rates. This loading condition corresponds to a dominant fracture perpendicular to tensile direction. The proposed method is not applicable for in-plane shear, out-of-plane shear, and higher strain rate loading conditions.

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A framework for coupled deformation–diffusion analysis with application to degradation/healing

Cited by 17 publications

References 58 publications

Material degradation due to moisture and temperature. Part 1: mathematical model, analysis, and analytical solutions

Material degradation due to moisture and temperature. Part 1: mathematical model, analysis, and analytical solutions

Numerical Study of Fracture Network Evolution during Nitrogen Fracturing Processes in Shale Reservoirs

Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials

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