ADVANCES IN GEOMETRY INDEPENDENT APPROXIMATIONS

Scientific Conference (2019, April 11)

We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no ... [more ▼]

We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no-longer has to be identical to the approximation used to describe the geometry of the domain. As such, the geometry can be described using usual CAD representations, e.g. NURBS, which are the most common in the CAD area, whilst local refinement and meshes approximations can be used to describe the field variables, enabling local adaptivity. We show in which cases the approach passes the patch test and present applications to various mechanics, fracture and multi-physics problems. [less ▲]

Model I cohesive zone models of different rank coals

in International Journal of Rock Mechanics and Mining Sciences (2019), 115

The present work develops cohesive zone models (CZM), i.e. cohesion-separation laws, for mode I fractures in different rank coals, including weakly caking coals, gas coals, fat coals, meager-lean coals ... [more ▼]

The present work develops cohesive zone models (CZM), i.e. cohesion-separation laws, for mode I fractures in different rank coals, including weakly caking coals, gas coals, fat coals, meager-lean coals and anthracite, through disk-shaped compact tension tests. Firstly, the experiments show that with the coal rank rising, the critical crack separation displacements and the degrees of the nonlinearity of the softening function decline gradually. By fitting the experimental data with the four commonly used cohesive zone models including the power law, the exponential law, the bilinear law and the linear law, the best-fitted model for each rank of coals was identified and the corresponding parameters were found. Secondly, to arrive at a general CZM formulation for the different rank coals, Karihaloo’s polynomial law was employed, which also gave better fit to the experimental data compared with the aforementioned four CZMs. After obtaining the CZM for coals, fracture energy was evaluated which is equal to the area under the softening curve. With the increase of the coal rank, the fracture energy reduces but its coefficient of variation increases. Thirdly, the geometric characteristics of fractures in different rank coals are studied. The lower rank coals have more tortuous crack propagation paths and larger roughness coefficients, whereas the higher rank coals possess wider average fracture apertures. Lastly, in order to further test the applicability of the obtained cohesion-separation laws, we implemented the Karihaloo’s polynomial CZM and the bilinear CZM into the cohesive elements of ABAQUS® using the user-subroutine VUMAT, and thereby simulated the crack propagation in single-edge notched beams made of weakly caking coals, fat coals, and meager-lean coals, respectively. It is found that the numerical results based on Karihaloo’s polynomial CZM have a better agreement with the experimental data than the bilinear CZM [less ▲]

The influence of fracture geometry variation on non-Darcy flow in fractures under confining stresses

in International Journal of Rock Mechanics and Mining Sciences (2018), 113

To investigate the influence of geometric characteristics of deformable rough fractures under confining stresses on the behaviors of non-Darcy flow, four fractured sandstone specimens were used for ... [more ▼]

To investigate the influence of geometric characteristics of deformable rough fractures under confining stresses on the behaviors of non-Darcy flow, four fractured sandstone specimens were used for hydraulic tests in the experiments. According to the experimental results of the relationships between the hydraulic gradient and the flow rate, it is demonstrated that the Forchheimer's equation can offer a good description of the non-Darcy flow in rough fractures. In addition, the coefficients A and B in Forchheimer's equation are sensitive to the fracture geometric characteristics, and their values also increase as the confining stress rises, mainly owing to the reduction of the hydraulic aperture and the heterogeneous distribution of the interconnected void areas with the confining stress rising. Then, the surface and interior geometric properties of rough fractures were quantitatively characterized with the peak asperity height and the box-counting fractal dimension of the heterogeneous distribution of the interconnected void areas, respectively. Furthermore, an empirical relationship between the fractal dimension D and the fracture apertures was constructed according to the experimental results. Lastly, a quantitative model was proposed to represent the relationship between the fracture geometric characteristics and the non-Darcy coefficient . This model was further used to link the non-linear coefficient of Forchheimer's equation and the critical Reynold number with the fracture geometric characteristics. The proposed models were validated by the experimental data and would be helpful to characterize the non-Darcy flow behavior in rough fractures under various confining stresses. [less ▲]