Bridging the macro to mesoscale: Evaluating the fourth-order anisotropic damage tensor parameters from ultrasonic measurements of an isotropic solid under triaxial stress loading

Olsen-Kettle, Louise

doi:10.1177/1056789518757293

Cited by 20 publications

(11 citation statements)

References 42 publications

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“…Therefore, it is more complex to experimentally characterize the elastic properties of an anisotropic rock and determine the change of these anisotropic properties with damage [57][58][59]. Modelling anisotropic damage is not as straightforward as modelling isotropic damage.…”

Section: Isotropic and Anisotropic Studiesmentioning

confidence: 99%

“…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%

“…Pyroclastic behaviour of brittle rock material with anisotropic damage is discussed by Shao [66]. Recently, anisotropic damage models for transverse isotropic and orthotropic materials have been proposed by Olsen-Kettle [57][58][59]. Most rock mechanics analyzes have been conducted under the assumption of isotropic because anisotropic damage models are challenging to develop.…”

Section: Isotropic and Anisotropic Studiesmentioning

confidence: 99%

“…It is assumed that the damage that occurs is isotropic [2,97]. The implementation of this model is less complex because the damage variable is a scalar instead of a second or fourth order tensor [57].…”

Section: Damage Modelmentioning

confidence: 99%

“…In recent works, other researchers have included plasticity and anisotropy in their models of rock failure. Anisotropic damage models for transverse isotropic and orthotropic materials have been proposed by Olsen-Kettle [57][58][59]. A thermoplastic constitutive model [160] for transverse isotropic rocks assumed that the rocks remained transverse isotropic in both their elastic and plastic responses to predict strength and strain localization properties.…”

Section: Introductionmentioning

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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Section: Isotropic and Anisotropic Studiesmentioning

confidence: 99%

Section: Isotropic and Anisotropic Studiesmentioning

confidence: 99%

Section: Isotropic and Anisotropic Studiesmentioning

confidence: 99%

Section: Damage Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical modelling of damage evolution and fracture propagation in brittle materials

Mondal¹

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Simulating damage evolution and fracture propagation in sandstone containing a preexisting 3‐D surface flaw under uniaxial compression

Mondal

Olsen-Kettle

Gross

2019

Num Anal Meth Geomechanics

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Summary Preexisting flaws and rock heterogeneity have important ramifications on the process of rock fracturing and on rock stability in many applications. Therefore, there is great interest in numerical modelling of rock fracture and the underlying mechanisms. We simulated damage evolution and fracture propagation in sandstone specimens containing a preexisting 3‐D surface flaw under uniaxial compression. We applied the linear elastic damage model based on the unified strength theory following the rock failure process analysis code. However, in contrast to the rock failure process analysis code, we used the finite element method with tetrahedron elements on unstructured meshes. It provided higher geometrical flexibility and allowed for a more accurate representation of the disk‐shaped flaw with various flaw depths, angles, and lengths through locally adapted meshes. The rock heterogeneity was modelled by sampling the initial local Young's modulus from a Weibull distribution over a cubic grid. The values were then interpolated to the computational finite element method mesh. This method introduced an additional length scale for the rock heterogeneity represented by the cell size in the sampling grid. The generation of three typical surface cracking patterns, called wing cracks, anti‐wing cracks, and far‐field cracks, were identified in the simulation results. These depend on the geometry of the preexisting surface flaw. The simulated fracture propagation, coalescence types, and failure modes for the specimens with preexisting surface flaw show good agreement with recent experimental studies.

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Creep and Damage of Materials at Elevated Temperatures

Altenbach

2022

Advanced Theories for Deformation, Damage and Failure in Materials

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Bridging the macro to mesoscale: Evaluating the fourth-order anisotropic damage tensor parameters from ultrasonic measurements of an isotropic solid under triaxial stress loading

Cited by 20 publications

References 42 publications

Numerical modelling of damage evolution and fracture propagation in brittle materials

Numerical modelling of damage evolution and fracture propagation in brittle materials

Simulating damage evolution and fracture propagation in sandstone containing a preexisting 3‐D surface flaw under uniaxial compression

Creep and Damage of Materials at Elevated Temperatures

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