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Rock behaviour frequently does not fit the classical theory of continuum mechanics because of rock aggregated granular structure. Particularly, rock fracturing may be accompanied by zonal disintegration formation. The key to building the non-classic model of rock fracturing is the granulated structure. Deformations of solid bodies with microscopic...
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Rock behavior does not fit the classical theory of continuum mechanics at high level of stresses with respect to the tensile strength because of rock heterogeneous structure. Particularly, rock failure may be accompanied by initiation of zonal disintegration. The key to building the non–classical model of rock failure is the granulated structure. D...
In the paper the relationship between pure geometrical concepts of the theory of affine connections, physical concepts related with non-linear theory of distributed defects and concepts of non-linear continuum mechanics for bodies with variable material composition is discussed. Distinguishing feature of the bodies with variable material compositio...
ABSTRACT: Rock behavior frequently does not fit the classical theory of continuum mechanics because of rock heterogeneous
structure. Particularly, rock failure may be accompanied by zonal disintegration formation.
The key to building the non-classic model of rock failure is the structure with grain boundaries. Deformations of solid bodies with
micr...
Citations
... Relying on this theoretical assumption and the modern concept of zonal disintegration, we have come up with a new approach to chip size prediction based on characteristic scale within a scope of zonal disintegration theory.3. Numerical study of rock failure while cutting with a rigid massless tool In the publication[21], the weak formulation of the problem (18 -23), (26) followed by a numerical algorithm which uses the finite-element mixed method is given. In this paper, the simulator developed in[21] is applied for modelingof rock behavior in the vicinity of a rigid cutter and with no description of the numerical technique applied. ...
... Numerical study of rock failure while cutting with a rigid massless tool In the publication[21], the weak formulation of the problem (18 -23), (26) followed by a numerical algorithm which uses the finite-element mixed method is given. In this paper, the simulator developed in[21] is applied for modelingof rock behavior in the vicinity of a rigid cutter and with no description of the numerical technique applied. The computational domain is a step of height h(DOC) on a rectangle of 5 mm high and 24 mm long (Figure 4). ...
Rock behavior does not fit the classical theory of continuum mechanics at high level of stresses with respect to the tensile strength because of rock heterogeneous structure. Particularly, rock failure may be accompanied by initiation of zonal disintegration. The key to building the non–classical model of rock failure is the granulated structure. Deformations of solid bodies with microscopic flaws can be described within the scope of non–Euclidean geometry, and the non–trivial deformation incompatibility can be referred to as a failure parameter. The new dynamic model presented in this paper enables one to predict the failure zones to initialize and develop them as a periodic structure. The non–Euclidean description of this phenomenon initiates two unusual material constants that can be called “inelastic” moduli. The coupled model must include a fourthorder parabolic equation to find a disintegration thermodynamic parameter. The equation should be solved together with the classical hyperbolic system of equations for continuous medium dynamics. In the classical approach to the rock cutting problem, the fracture is caused by critical shear stresses when the failure criterion based on the Tresca (or more general Mohr) theory is applied. In this case, it is difficult to predict the chip size and optimal depth of cut because the criterion is beyond the model. Another flaw of the conventional approach is that it is hard to explain a dynamic hardening effect in the scope of local models of plasticity. In this paper, the developed dynamic theory of zonal disintegration (Dorovsky et al., 2015) is applied to the numerical analysis of rock cutting by polycrystalline diamond compact (PDC) bit cutter process. It has been shown that the initial shear stress at the cutter tip causes the disintegration (destruction) developing deep into the medium and along the cutting direction with contouring of the rock failure scale. The appearance of plasticity effects at the yield stress above tensile/shear strength allows us to come up with an adequate description of the dynamic hardening observed in recent laboratory experiments.
... Among these methods, gradient-damage (Peerlings et al. 1996;Pham et al. 2011;Alessi et al. 2015;Nedjar 2016) and phase-field methods (Bourdin et al. 2000;Miehe et al. 2010;Kuhn and Müller 2010;Borden et al. 2012;Wheeler et al. 2014;Ambati et al. 2015) are among the most prominent. They are sometimes referred to as weakly non-local, where strongly non-local models (Bazant and Jirasek 2002;He et al. 2015;Silani et al. 2016;Vtorushin 2016) are a third category of smeared models in which the material response at a given point is influenced by long-range interactions with neighbouring points falling into a given radius. These approaches offer the additional benefit of linking the classically separate theories strength of materials and fracture mechanics (Klinsmann et al. 2015;Tanné et al. 2018) and can be interpreted based on common physical origins such that they can be transferred into each other (Kuhl et al. 2000;de Borst and Verhoosel 2016a). ...
The numerical treatment of propagating fractures as embedded discontinuities is a challenging task for which an analyst has to select a suitable numerical method from a range of options. Since their inception in the mid-80s, smeared approaches for fracture simulation such as non-local damage, gradient damage or more lately phase-field modelling have steadily gained popularity. One of the appeals of a smeared implicit fracture representation, the ability to handle complex topologies with unknown crack paths in relatively coarse meshes as well as multiple-crack interaction and multiphysics, is a fundamental requirement for the numerical simulation of hydraulic fracturing in complex situations which is technically more difficult to achieve with many other methods. However, in hydraulic fracturing simulations, not only the prediction of the fracture path but also the computation of fracture width and propagation pressure (frac pressure) is crucial for reliable and meaningful applications of the simulation tool; how to determine some of these quantities in smeared representations is not immediately obvious. In this study, two of the most popular smeared approaches of recent, namely non-local damage and phase-field models, and an approach in which the solution space is locally enriched to capture a strong discontinuity combined with a cohesive-zone model are verified against fundamental hydraulic fracture propagation problems in the toughness-dominated regime. The individual theoretical foundations of each approach are discussed and differences in the treatment of physical and numerical properties of the methods when applied to the same physical problems are highlighted through examples.
... In this paper the rock medium' behavior in the vicinity of a rigid moving cutter is analyzed numerically in scope of the nonlocal model of inelastic deformations. The mixed finite element solver presented by E.V. Vtorushin in [5] is applied. The computational domain is a step of 1 cm in height on a rectangle of 5 cm in height and 24 cm in length (Fig. 1). ...
The major factor of well drilling with PDC bit is a dynamic interaction of cutting tool and rock. In this paper non-stationary nonlocal model of inelastic deformations is applied to rock cutting with cutting tool problem. The suggested numerical solution of 2-dimensional dynamic problem is based on mixed finite element method. The nonlocal model leads to the appearance of two non-classical material constants that by analogy with classic model, can be called ’inelastic’ moduli. Numerical modeling has proven that is possible to predict both chip size and depth of cut within the scope of the suggested model if only the non-classical moduli are defined
