No Arabic abstract
Soft or weakly-consolidated sand refers to porous materials composed of particles (or grains) weakly held together to form a solid but that can be easily broken when subjected to stress. These materials do not behave as conventional brittle, linear elastic materials and the transition between these two regimes cannot usually be described using poro-elastic models. Furthermore, conventional geotechnical sampling techniques often result in the destruction of the cementation and recovery of sufficient intact core is, therefore, difficult. This paper studies a numerical model that allows us to introduce weak consolidation in granular packs. The model, based on the LIGGGHTS open source project, simply adds an attractive contribution to particles in contact. This simple model allow us to reproduce key elements of the behaviour of the stress observed in compacted sands and clay, as well as in poorly consolidated sandstones. The paper finishes by inspecting the effect of different consolidation levels in fluid-driven fracture behaviour. Numerical results are compared against experimental results on bio-cemented sandstones.
The orthorhombic boride crystal family XYB$_{14}$, where X and Y are metal atoms, plays a critical role in a unique class of superhard compounds, yet there have been no studies aimed at understanding the origin of the mechanical strength of this compound. We present here the results from a comprehensive investigation into the fracture strength of the archetypal AlLiB$_{14}$ crystal. First-principles, textit{ab initio}, methods are used to determine the ideal brittle cleavage strength for several high-symmetry orientations. The elastic tensor and the orientation-dependent Youngs modulus are calculated. From these results the lower bound fracture strength of AlLiB$_{14}$ is predicted to be between 29 and 31 GPa, which is near the measured hardness reported in the literature. These results indicate that the intrinsic strength of AlLiB$_{14}$ is limited by the interatomic B--B bonds that span between the B layers.
Quasi-brittle behavior where macroscopic failure is preceded by stable damaging and intensive cracking activity is a desired feature of materials because it makes fracture predictable. Based on a fiber bundle model with global load sharing we show that blending strength and stiffness disorder of material elements leads to the stabilization of fracture, i.e. samples which are brittle when one source of disorder is present, become quasi-brittle as a consequence of blending. We derive a condition of quasi-brittle behavior in terms of the joint distribution of the two sources of disorder. Breaking bursts have a power law size distribution of exponent 5/2 without any crossover to a lower exponent when the amount of disorder is gradually decreased. The results have practical relevance for the design of materials to increase the safety of constructions.
We present the Onsager--Stefan--Maxwell thermodiffusion equations, which account for the Soret and Dufour effects in multicomponent fluids by treating heat as a pseudo-component. Unlike transport laws derived from kinetic theory, this framework preserves the structure of the isothermal Stefan--Maxwell equations, separating the thermodynamic forces that drive diffusion from the force that drives heat flow. The Onsager--Stefan--Maxwell transport-coefficient matrix is symmetric, and the second law of thermodynamics imbues it with simple spectral characteristics. This new approach proves equivalent to both the intuitive extension of Ficks law and the generalized Stefan--Maxwell equations popularized by Bird, Stewart, and Lightfoot. A general inversion process allows the unique formulation of flux-explicit transport equations relative to any choice of convective reference velocity. Stefan--Maxwell diffusivities and thermal diffusion factors are tabulated for gaseous mixtures containing helium, argon, neon, krypton, and xenon. The framework is deployed to perform numerical simulations of steady three-dimensional thermodiffusion in a ternary gas.
We investigate how forces spread through frictionless granular packs at the jamming transition. Previous work has indicated that such packs are isostatic, and thus obey a null stress law which, independent of the packing history, causes rays of stress to propagate away from a point force at oblique angles. Prior verifications of the null stress law have used a sequential packing method which yields packs with anisotropic packing histories. We create packs without this anisotropy, and then later break the symmetry by adding a boundary. Our isotropic packs are very sensitive, and their responses to point forces diverge wildly, indicating that they cannot be described by any continuum stress model. We stabilize the packs by supplying an additional boundary, which makes the response much more regular. The response of the stabilized packs resembles what one would expect in a hyperstatic pack, despite the isostatic bulk. The expected stress rays characteristic of null stress behavior are not present. This suggests that isostatic packs do not need to obey a null stress condition. We argue that the rays may arise instead from more simple geometric considerations, such as preferred contact angles between beads.
We study experimentally the fracture mechanisms of a model cohesive granular medium consisting of glass beads held together by solidified polymer bridges. The elastic response of this material can be controlled by changing the cross-linking of the polymer phase, for example. Here we show that its fracture toughness can be tuned over an order of magnitude by adjusting the stiffness and size of the polymer bridges. We extract a well-defined fracture energy from fracture testing under a range of material preparations. This energy is found to scale linearly with the cross-sectional area of the bridges. Finally, X-ray microcomputed tomography shows that crack propagation is driven by adhesive failure of about one polymer bridge per bead located at the interface, along with microcracks in the vicinity of the failure plane. Our findings provide insight to the fracture mechanisms of this model material, and the mechanical properties of disordered cohesive granular media in general.