Treatment of anisotropic damage development within a scalar damage formulation

Chan, Kwai S.; Bodner, S. R.; Munson, D.E.

doi:10.1007/s004660050203

Cited by 9 publications

(6 citation statements)

References 8 publications

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“…7 (b) is63 MPa which is very close to the simulation peak stress of 60 MPa inFigure 4.6 (c) for low shape parameter. We chose our initial Young's modulus (E 0 ) like the experimental study by Lu et al[15].…”

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confidence: 77%

“…However, anisotropic rock mechanics have been pioneered by Amadei [60], particularly for the analysis of in situ subsurface stress measurements. Researchers [57][58][59][61][62][63][64][65] have recently proposed anisotropic damage models with different theoretical approaches. Pyroclastic behaviour of brittle rock material with anisotropic damage is discussed by Shao [66].…”

Section: Isotropic and Anisotropic Studiesmentioning

confidence: 99%

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Numerical modelling of damage evolution and fracture propagation in brittle materials

Mondal¹

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The understanding of damage evolution and fracture propagation in rocks as a brittle material is important for many industrial applications; for instance to investigate mine safety, to analyze material failure in manufacturing and construction and to understand the behaviour of pre-existing fractures on hydraulic fracturing in oil and gas extractions. Currently, numerical studies for fracture propagation in brittle rock specimens with pre-existing fractures show strong mesh dependence. To address the issue of mesh independence, further numerical investigation and improvement of damage models under a fully 3-D assumption is critical.In this thesis, we develop numerical tools to investigate the effect of model parameters, including the heterogeneity of rock by allowing Young's modulus to vary spatially, and of the geometry of a pre-existing fracture on the stress-strain response and damage evolution in rocks. The fracture propagation model uses continuum damage mechanics where the elastic modulus reduces with damage as the rock is weakened through the formation of fractures. Two failure conditions are presented, a micromechanical model [1,2] using the unified strength theory [3,4] and a strain-based form of a modified von-Mises condition [5]. Various damage evolution laws are considered which can simulate a range of behaviour from brittle to quasi-brittle. Four different damage evolution laws are analyzed for a 3-D rectangular single flaw specimen to deliver the most realistic results. The quasi-static equilibrium equation is solved for various cases of brittle failure and damage evolution for specimens under loading using the Finite Element Method (FEM) with tetrahedron elements on unstructured meshes. In contrast to previous implementations based on rectangular grids, the use of unstructured meshes provides higher geometrical flexibility and allows a more accurate way of including geological features, such as flaws, through locally adapted (FEM) meshes.An important factor affecting the mechanical behaviour during the failure process is the heterogeneity of the rock. Heterogeneity is simulated by sampling the initial local Young's modulus from a Weibull distribution over a cubic grid. The values are then interpolated to the computational (unstructured FEM) mesh. This approach introduces an additional length scale for rock heterogeneity represented by the cell size in the sampling grid that is independent of FEM mesh size. This approach is different from previous implementations of rock heterogeneity [6][7][8] where the length scale is determined by the mesh resolution.A well-known problem which arises in "local" damage models is that they suffer from mesh dependency [2] and strain localization [9]. In this work, we apply the non-local implicit gradient damage formulation of Peerlings et al.[5] to address the issue of mesh dependency. The basic concept of the non-local implicit gradient model is that the strain at a given point depends not only on the strain at that point but also on the nearby strain field. The lo...

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confidence: 77%

Section: Isotropic and Anisotropic Studiesmentioning

confidence: 99%

Numerical modelling of damage evolution and fracture propagation in brittle materials

Mondal¹

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“…Munson (1997) established the Munson-Dawson model for treating stress drops in salt under different temperatures and stresses according to dislocation gliding theory; Chan (1997) and Chan et al (1997) developed a creep-damage constitutive model of salt according to dislocation theory; Wu et al (2005) and Hou and Wu (2003) built the Hou/Lux constitutive model with consideration of creep rupture criterion and damage. Because the above functions are too complex to be widely applied in engineering, Weidinger et al (1997) and Hampel et al (1996) developed their steady-state creep rate constitutive model, respectively.…”

Section: Creep Testsmentioning

confidence: 99%

“…From the engineering perspective, salt formations are considered as suitable repository media since they are assumed to be impervious to fluids. Salt permeability can be lower than 10 -20 m 2 , and salt has excellent creep and damage self-healing behavior (Munson 1997;Chan 1997;Chan et al 1997;Weidinger et al 1997;Hampel et al 1996;Huang et al 2009), which can ensure the tightness of the storage caverns. Because salt rock has a self-healing capacity, it also can adapt well to variation of the storage pressure.…”

Section: Introductionmentioning

confidence: 96%

Geotechnical Feasibility Analysis of Compressed Air Energy Storage (CAES) in Bedded Salt Formations: a Case Study in Huai’an City, China

Zhang

Daemen

et al. 2014

Rock Mech Rock Eng

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The lower reaches of the Yangtze River is one of the most developed regions in China. It is desirable to build compressed air energy storage (CAES) power plants in this area to ensure the safety, stability, and economic operation of the power network. Geotechnical feasibility analysis was carried out for CAES in impure bedded salt formations in Huai'an City, China, located in this region. First, geological investigation revealed that the salt groups in the Zhangxing Block meet the basic geological conditions for CAES storage, even though the possible unfavorable characteristics of the salt formations include bedding and different percentages of impurities. Second, mechanical tests were carried out to determine the mechanical characteristics of the bedded salt formations. It is encouraging that the samples did not fail even when they had undergone large creep deformation. Finally, numerical simulation was performed to evaluate the stability and volume shrinkage of the CAES under the following conditions: the shape of a single cavern is that of a pear; the width of the pillar is adopted as two times the largest diameter; three regular operating patterns were adopted for two operating caverns (internal pressure 9-10.5 MPa, 10-11.5 MPa, and 11-12.5 MPa), while the other two were kept at high pressure (internal pressure 10.5, 11.5, and 12.5 MPa) as backups; an emergency operating pattern in which two operating caverns were kept at atmospheric pressure (0.1 MPa) for emergency while the backups were under operation (9-10.5 MPa), simulated for 12 months at the beginning of the 5th year. The results of the analysis for the plastic zone, displacement, and volume shrinkage support the feasibility of the construction of an underground CAES power station. KeywordsGeotechnical feasibility Á Compressed air energy storage (CAES) Á Bedded salt formations Á Mechanical experiments Á Numerical simulation Abbreviations V cavern Volume of cavern G eff Volume of working gas M air Molar mass of gas V mol Molar volume of gas at standard state V sediment Volume of sediment V sphere Volume of lower half-sphere h sediment Distance between sediment surface and the above cross-section v Withdrawal velocity t Withdrawal time N Mole number of gas R m Ideal gas constant, 8.314 J/(mol K) a Average insoluble content percentage at the location of the cavern b Expansion coefficient of sediment A max Cross-sectional area at the maximum diameter A 1 , A 2 Coefficients in virial equation A

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“…In addition, Chan et al 15,26 proposed applying the BC damage model to initially anisotropic materials using a scalar damage formulation. Furthermore, in the present study, the original anisotropic BC damage model can be rewritten in a loading directiondependent form as follows:…”

Section: Damage Model Including Microcrack Closure Effectmentioning

confidence: 99%

Anisotropic elasto-viscoplastic damage model for glass-fiber-reinforced polyurethane foam

Lee

2013

Journal of Composite Materials

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The aim of the present study was to propose a unified anisotropic elasto-viscoplastic damage model and computational analysis method for predicting the damage growth and material behavior of initially anisotropic glass-fiber-reinforced polyurethane foam (RPUF). A plasticity damage mechanism-based mechanical model with no yield surface is introduced. To consider the microcrack closure effect according to different loading directions, two types of elasto-viscoplastic damage models were developed. The developed models were transformed into the implicit form and implemented in an ABAQUS user-defined material subroutine for the application of finite elements. Finally, the simulation results were compared with a series of tensile and compressive test results on RPUF to validate the proposed model and computation.

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Treatment of anisotropic damage development within a scalar damage formulation

Cited by 9 publications

References 8 publications

Numerical modelling of damage evolution and fracture propagation in brittle materials

Numerical modelling of damage evolution and fracture propagation in brittle materials

Geotechnical Feasibility Analysis of Compressed Air Energy Storage (CAES) in Bedded Salt Formations: a Case Study in Huai’an City, China

Anisotropic elasto-viscoplastic damage model for glass-fiber-reinforced polyurethane foam

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