On the dual effect of obstacles in preventing silo clogging in 2D

Placing an obstacle in front of a bottleneck has been proposed as a sound alternative to improve the flow of discrete materials in a wide variety of scenarios. Nevertheless, the physical reasons behind this behavior are not fully understood and the suitability of this practice has been recently challenged for pedestrian evacuations. In this work, we experimentally demonstrate that for the case of inert grains discharging from a silo, an obstacle above the exit leads to a reduction of clog formation via two different mechanisms: i) an alteration of the kinematic properties in the outlet proximities that prevents the stabilization of arches; and ii) an introduction of a clear anisotropy in the contact fabric tensor that becomes relevant when working at a quasi-static regime. Then, both mechanisms are encompassed using a single formulation that could be inspiring for other, more complex, systems.

Quantitative Description for Sand Void Fabric with the Principle of Stereology

Based on the principle of stereology to describe void fabric, the fabric tensor is redefined by the idea of normalization, and a novel quantitative description method for the orthotropic fabric of granular materials is presented. The scan line is described by two independent angles in the stereo space, and the projection of the scan line on three orthogonal planes is used to determine the plane tensor. The second-order plane tensor can be described equivalently by two invariants, which describe the degree and direction of anisotropy of the material, respectively. In the three-dimensional orthogonal space, there are three measurable amplitude parameters on the three orthogonal planes. Due to the normalized definition of tensor in this paper, there are only two independent variations of the three amplitude parameters, and any two amplitude parameters can be used to derive the three-dimensional orthotropic fabric tensor. Therefore, the same orthorhombic anisotropy structure can be described by three fabrics, which enriches the theoretical description of orthotropy greatly. As the geometric relationship of the stereoscopic space scan line changes, the three sets of orthotropic fabrics degenerate into different forms of transversely isotropic and isotropic fabrics naturally and have a clear physical meaning. The novel fabric tensor is quantitatively determined based on mathematical probability and statistics. The discrete distribution of voids in space is projected as a scalar measurable parameter on a plane. This parameter is related to the macroscopic constitutive relationship directly and can be used to describe the effect of microscopic voids on the macroscopic phenomenon of materials.

Micromechanical modelling of the anisotropic creep behaviour of granular medium as a fourth-order fabric tensor

The main objective of the present work is to develop a micromechanics approach to predict the macroscopic anisotropic creep behaviour of granular media. To this end, the linear viscoelastic behaviour of the inter-particle interaction at contact is adopted, and the contact distribution is characterized by a fourth-order fabric tensor in the local scale. Then, fourth-order tensor fabric-based micromechanical approaches based on Voigt and Reuss localization assumptions are applied to granular media in the Laplace–Carson space. With help of the inverse Laplace–Carson transformation of these obtained models, the macroscopic anisotropic creep behaviour of granular media submitted to a constant external loading is examined. Finally, the obtained results by specializing the Burgers model into the obtained models are compared with the numerical simulations in the particle flow code (PFC2D) to illustrate the validation and the accuracy of the analytical models for the macroscopic anisotropic creep behaviour of granular media.

On the dual effect of obstacles in preventing silo clogging

We experimentally demonstrate that an obstacle, when suitably placed above a bottleneck, leads to a reduction of clog formation in a silo via two different mechanisms. The first one, already suggested in previous works, is related to an alteration of the kinematic properties in the outlet proximities that prevents the stabilization of arches. The second, that is discovered when working at a quasi-static regime, appears because the obstacle induces a clear anisotropy in the contact fabric tensor. Then, both mechanisms are encompassed using a single equation in which two parameters -one related with the geometrical effects and the other to the kinematic ones- are enough to reproduce all the experimental results

MATHEMATICAL MODELING OF CANCELLOUS BONE TISSUE ADAPTATION APPLIED TO THE HUMAN MAXILLODENTAL SYSTEM

The bone tissue in different parts of the skeleton conforms to Wolff’s law: it aims to become optimal for the loading which acts on the corresponding bone; the bone is remodelling by means of osteosynthesis and resorption mechanisms. The modern problems of biomechanics demand research on the history of formation of bone structures in the course of time at both physiological and pathological loadings. Ever changing loadings of different nature have influence on development and functioning of the trabecular bone tissue. The mandible is one of the most liable to external and internal changes bones. Very often one has to deal with pathological changes caused by incorrect loading of different regions of bone tissue due to dysfunction of a dentition, a temporomandibular joint and so on. For example, the Popov-Godon’s syndrome which connects with tooth loss is accompanied by pathological remodelling of the surrounding bone tissue. Thus, the mathematical modeling of the cancellous bone tissue behavior in the human maxillodental system is one of the most topical problems of biomechanics and medicine. Trabecular bone tissue is a heterogeneous, porous, anisotropic material. Heterogeneity of spongy structure can be described by methods of quantitative stereology. At the same time, structural features of the trabecular bone can be described by means of the fabric tensor. This is possible to implement if there is both a constitutive relation which connects the stress tensor, the fabric tensor, and the strain tensor, and kinetic equations which describe the evolution of the fabric tensor and bone density. An initial boundary value problem on the trabecular bone tissue remodelling is stated. The effective numerical algorithm allowing to solve the problem is developed. This algorithm is implemented as a complex of problem-oriented programs. Verification of the model and identification of its parameters are carried out. All numerical calculations are performed using the ANSYS software. Trabecular bone tissue evolution is demonstrated on the set of model examples when the stress–strain state is changed. The results demonstrate different character of influence of changes of loading conditions on process of structure formation which follows from Wolff’s law.

Formulation of Anisotropic Strength Criterion for Geotechnical Materials

A new nonlinear unified strength (NUS) criterion is obtained based on the spatially mobilized plane (SMP) criterion and Mises criterion. New criterion is a series of smooth curves between SMP curved triangle and Mises circle in the π plane and thereby unifies the strength criteria. The new criterion can reflect the effect of the intermediate principal stress and consider the strength nonlinearity of a material. Based on the fabric tensor, the anisotropic parameter A is defined, and the anisotropic equation is proposed and introduced into the NUS criterion to form a nonlinear unified anisotropic strength criterion. The new criterion can be used to predict the strength variation of granular materials and cohesive materials under three-dimensional stress and can present the strength anisotropy of the geomaterials. The validity of the new criterion was checked using rock and soil materials. It is shown that the prediction results for the criterion agree well with the test data.