Granular matter is widely present in nature and human production and life. It exhibits many mechanical properties that differ from those of conventional solids and liquids. Janssen effect is one of the important and well-known phenomena that demonstrates the unique static mechanical properties of granular matter. Researchers have conducted in-depth studies on this effect from various perspectives, including theoretical models and computer simulations. “Chopstick rice-lifting” is an interesting physical phenomenon closely related to the Janssen effect. However, existing research lacks a quantitative analysis of this phenomenon, particularly regarding the discussion of the critical depth. In this paper, the actual system involved in “chopstick rice-lifting” is simplified into a system composed of a silo, grains, and a lifting rod, and the Janssen continuum model is employed to conduct a static mechanical analysis of this system, leading to the theoretical derivation of a transcendental equation concerning the critical depth. Subsequently, by combining experimental data with the numerical solution of this transcendental equation, the authors explore how the Janssen coefficient and critical depth of the granular system in the experiment vary with relevant physical quantities. The results indicate that the Janssen coefficient under different experimental conditions fluctuates slightly around an average value 1.16; and that, when the diameter of the lifting rod is held constant, an increase in the diameter and mass of the silo results in a higher total mass of both the grains and the silo, thereby increasing the critical depth. Conversely, when the diameter of the silo is constant, an increase in the diameter of the lifting rod leads to a decrease in the total mass and an increase in the contact area between the lifting rod and the grains, resulting in a decrease in the critical depth. The theoretical calculation results are generally consistent with the experimental measurement results.

To clarify the interaction mechanism between asphalt components and waste wood oil (WWO) in waste sawdust-based bio-asphalts in a molecular scale, five molecular models including virgin asphalt and four kinds of bio-asphalts were established based on the SARA theory by using molecular dynamics (MD) method, and their validity was verified by using the radial distribution function (RDF), energy, density, and solubility parameters. The interaction behavior between WWO and asphalt components was tracked through the analysis of interaction energy, RDF, and snapshots of stable configurations. The results show that the interaction energies between WWO and asphalt components in different bio-asphalt systems are negative, indicating that they attract each other. The order of interaction energies is WWO-resin>WWO-aromatic>WWO-asphaltene>WWO-saturate, which suggests that WWO has the largest interaction force with the resin molecules and the smallest interaction force with the saturate. The intermolecular RDF curves between WWO and four asphalt components stabilize with increasing distance and eventually converge to 1.0, indicating that the molecules within the system show a disordered distribution over a long range. The RDF curves of WWO-resin, WWO-aromatic, and WWO-asphaltene are flat, and there are no significant peaks. However, the RDF curve of WWO-saturate has obvious fluctuations in the range of 0.5~1.5 nm, and the maximum peak intensity is only 1.24, indicating that there are molecular aggregation phenomena in some regions. In addition, similar conclusions to the interaction energy and RDF analyses were found by analyzing the MD snapshots of the stable configurations. The findings demonstrate at the molecular level that WWO is compatible with asphalt components.

Isogeometric analysis uses computer splines such as non-uniform rational B-splines as the basis functions. When the order of the basis function is 2 or greater, the control points do not coincide with the element nodes and the support domain of the basis function spans multiple elements, which makes it difficult to impose local fixed constraints precisely in isogeometric analysis. To solve this problem, this paper uses a step function to modify the displacement interpolation function of isogeometric analysis. The step function takes a value of 0 in the locally fixed constraint region and 1 in the other region, so that the displacement value in the fixed constraint region is forced to be 0, and the displacement interpolation function in other region is revert to the original form. In order to minimize the influence of step function on the analysis domain, the rising interval of the step function is set to be small. Meanwhile, the hierarchical spline is used to subdivide the elements in the rising interval locally, therefore, the Gaussian points of the subdivided elements fall into the rising interval of the step function as well as the step function has an effect on the stiffness matrix. In addition, the element subdivision also effectively improves the solution accuracy in the local constraint region where large strains are present. Finally, the method mentioned above is compared with analytical solution and the finite element method to verify its accuracy, flexibility and reliability, finding that the results of calculation coincide with the analytical solution. Finally, by considering the situations with different fixed constrains that vary in shape, area and location., the finite element method with coarse mesh and fine mesh are used to calculate the examples, finding that the displacement and stress obtained by the proposed method are closer to those obtained by the fine mesh finite element method, which illustrates that the solution accuracy can be achieved with fewer elements; and that the proposed method is of good accuracy, flexibility and reliability.