Active drive towards elastic spinodals.

The paper starts by considering the broad framework of the industry, and in particular whether the current boom in production and the threatened shortages of certain strategic minerals are likely to lead to scarcities. The paper suggests that shortages are unlikely and that minerals will become even more widely available and at lower cost. That said, energy and maintaining the license to operate will drive the introduction of new technologies.Using copper as an example, we point out the inevitable lower grades that will be processed and for ever lower selling prices in real terms, as has happened for centuries. Technological innovation is the driver of these trends, and the paper highlights several areas where significant changes are poised to occur: in pre-conditioning and in minimizing grinding by removing gangue at coarser sizes earlier in the flowsheet; in recognition that the excessive energy used in comminution may be largely caused by the formation of force chains that bear the load and resist breakage events; and finally, two developments by Jameson (Can Metallurgical Quart 49(4), 324–330, 2010) for more energy efficient fine particle flotation and a significantly new concept for coarse particle flotation to 1400 micron.

The calculation of the impact pressure on obstacles in granular flows is a fundamental issue of practical relevance, e.g. for snow avalanches impacting obstacles. Previous research shows that the load on the obstacle builds up, due to the formation of force chains originating from the obstacle and extending into the granular material. This leads to the formation of a mobilized domain, wherein the flow is influenced by the presence of the obstacle. To identify the link between the physical mobilized domain properties and the pressure exerted on obstacles, we simulate subcritical cohesionless and cohesive avalanches of soft particles past obstacles with circular, rectangular or triangular cross-section using the Discrete Element Method. Our results show that the impact pressure decreases non-linearly with increasing obstacle width, regardless of the obstacle’s cross-section. While the mobilized domain size is proportional to the obstacle width, the pressure decrease with increasing width originates from the jammed material inside the mobilized domain. We provide evidence that the compression inside the mobilized domain governs the pressure build-up for cohesionless subcritical granular flows. In the cohesive case, the stress transmission in the compressed mobilized domain is further enhanced, causing a pressure increase compared with the cohesionless case. Considering a kinetic and a gravitational contribution, we are able to calculate the impact pressure based on the properties of the mobilized domain. The equations used for the pressure calculation in this article may be useful in future predictive pressure calculations based on mobilized domain properties.Graphic

Force chains (FCs) are a key determinant of the micromechanical properties and behaviour of heterogeneous materials, such as granular systems. However, less is known about FCs in fibrous materials, such as the networks composing the extracellular matrix (ECM) of biological systems. Using a finite-element computational model, we simulated the contraction of a single cell and two nearby cells embedded in two-dimensional fibrous elastic networks and analysed the tensile FCs that developed in the ECM. The role of ECM nonlinear elasticity on FC formation was evaluated by considering linear and nonlinear, i.e. exhibiting 'buckling' and/or 'strain-stiffening', stress-strain curves. The effect of the degree of cell contraction and network coordination value was assessed. We found that nonlinear elasticity of the ECM fibres influenced the structure of the FCs, facilitating the transition towards more distinct chains that were less branched and more radially oriented than the chains formed in linear elastic networks. When two neighbouring cells contract, a larger number of FCs bridged between the cells in nonlinear networks, and these chains had a larger effective rigidity than the chains that did not reach a neighbouring cell. These results suggest that FCs function as a route for mechanical communication between distant cells and highlight the contribution of ECM fibre nonlinear elasticity to the formation of FCs.

The elastic properties of the periodontal ligament (PDL) in eight multi-rooted teeth were examined in a combined experimental and numerical study in six minipigs. The initial tooth movement of the mandibular primary molars surrounded by the periodontium was registered three-dimensionally (3D) in an optomechanical measuring system. The dissections were then embedded in resin and cut in transverse sections. Based on these sections, 3D finite element (FE) models were constructed and numerically loaded with the same force systems as used in the experiment. The material behaviour of the PDL registered in the experiment was non-linear and could be approximated with a bilinear parameter set consisting of two Young's moduli, E1 and E2, and one ultimate strain, epsilon12, separating both elastic regimes. When a deficient congruence existed between the experimental and numerical force/deflection curves the material parameters were varied to obtain a satisfactory congruence. The material behaviour determined for these specimens delivered mean values of E1 = 0.05 MPa, E2 = 0.18 MPa and epsilon12 = 6.4 per cent for the elastic behaviour of the multi-rooted minipig teeth. There was no significant difference in the material parameters determined for specimens with two, four or six roots. The results were in close agreement with the material parameters of the PDL, determined in previous investigations of single-rooted human and pig teeth.

The main aim of our work is to explore the effect of particle shape heterogeneity on the dynamics of an intruder moving through a two-dimensional mixture of dumbbells and disks. In spite of similar physical conditions (the mass of the dumbbell is the same as that of the disk) and the same area fraction, we noticed a significant difference in the drag experienced by the intruder as the mixture concentration varies. The propagation of stress from the intruder to the granular grains manifests in the form of force chains, and interestingly these force chains can vary significantly depending on the shape of the grains. These differences, however, appear to be suppressed in the frictionless case where the force chains cannot extend very far from the initial point of contact. Apart from particle shape, the effect of the area fraction of the system and the size of the intruder have also been explored. As the area fraction increases, the drag force on the intruder increases owing to the increase in the contact forces. Finally, we present the velocity and stress fields at different dumbbell fractions and for various intruder diameters to show the effect of the moving intruder on its surrounding particles.

We present a comparative modelling study of fluid–structure interactions in microchannels. Through a mathematical analysis based on plate theory and the lubrication approximation for low-Reynolds-number flow, we derive models for the flow rate-pressure drop relation for long shallow microchannels with both thin and thick deformable top walls. These relations are tested against full three-dimensional two-way-coupled fluid–structure interaction simulations. Three types of microchannels, representing different elasticity regimes and having been experimentally characterized previously, are chosen as benchmarks for our theory and simulations. Good agreement is found in most cases for the predicted, simulated and measured flow rate-pressure drop relationships. The numerical simulations performed allow us to also carefully examine the deformation profile of the top wall of the microchannel in any cross section, showing good agreement with the theory. Specifically, the prediction that span-wise displacement in a long shallow microchannel decouples from the flow-wise deformation is confirmed, and the predicted scaling of the maximum displacement with the hydrodynamic pressure and the various material and geometric parameters is validated.

The composite varistor of epoxy resin and microvaristor has nonlinear voltage-current characteristics owing to microvaristor chains, which work as current paths, formed by applying an electric field during curing process. In this type of composite varistor, voltage-current characteristics and surge absorption capability are typical basic performance and strongly influenced by the chain formation and intrinsic characteristics of microvaristors. This paper reports the influence of gravity and electric field on the formation of microvaristor chains in epoxy resin and voltage-current characteristics and surge absorption capability of one microvaristor itself.

Porous ultra-high molecular weight polyethylene (UHMWPE) is a high-performance bioinert polymer used in cranio-facial reconstructive surgery in procedures where relatively low mechanical stresses arise. As an alternative to much stiffer and more costly polyether-ether-ketone (PEEK) polymer, UHMWPE is finding further wide applications in hierarchically structured hybrids for advanced implants mimicking cartilage, cortical and trabecular bone tissues within a single component. The mechanical behaviour of open-cell UHMWPE sponges obtained through sacrificial desalination of hot compression-moulded UHMWPE-NaCl powder mixtures shows a complex dependence on the fabrication parameters and microstructural features. In particular, similarly to other porous media, it displays significant inhomogeneity of strain that readily localises within deformation bands that govern the overall response. In this article, we report advances in the development of accurate experimental techniques for operando studies of the structure–performance relationship applied to the porous UHMWPE medium with pore sizes of about 250 µm that are most well-suited for live cell proliferation and fast vascularization of implants. Samples of UHMWPE sponges were subjected to in situ compression using a micromechanical testing device within Scanning Electron Microscope (SEM) chamber, allowing the acquisition of high-resolution image sequences for Digital Image Correlation (DIC) analysis. Special masking and image processing algorithms were developed and applied to reveal the evolution of pore size and aspect ratio. Key structural evolution and deformation localisation phenomena were identified at both macro- and micro-structural levels in the elastic and plastic regimes. The motion of pore walls was quantitatively described, and the presence and influence of strain localisation zones were revealed and analysed using DIC technique.

Powder compaction is the most fundamental and crucial process in powder forming. To elucidate the influence of multilevel force chains on powder compaction and forming, a new method for classifying force chains by force chain strength is proposed for the complexity of multilevel force chains in the actual iron powder compaction process. A discrete element model of iron powder compaction was developed and validated using the Heckle equation and experimental data. The results of the study indicate the following: Force chains shift from the compact's lower to upper regions post-compaction, with finer particle size distributions enhancing chain formation. 300 MPa serves as the critical threshold for force chain restructuring and accelerated densification. The average force chain transfer index for different levels of force chains increases with increasing compaction pressure. The particle compositions of force chains at all levels is concentrated in force chains of particle compositions number less than 6. The directionality of the force chain shows some anisotropy, and gradually concentrates on the Y-axis directions with the increase of the grade. This multilevel force chain analysis clarifies their role in compaction mechanics and provides theoretical insights for optimizing compaction quality. It has theoretical and guiding significance for the improvement of forming quality.

Numerical investigation of drag force on a spherical intruder by granular material

The geo-mechanical behavior of granular materials rigorously depends on their initial packing density, stress level and particle size distribution. Moreover, the behavior of binary granular soil is affected by the quality and quantity of their small particles named the fines content (FC). The contribution mechanism of the FC to the load-bearing structure of the soil at various particle sizes, stress levels and densities is still pending. The present study aimed to use a micromechanical approach to simulate the behavior of binary mixtures with particle size ratios (α) of 2.5 to 7.1 and study the effect of stress level and initial packing density on the stress–strain behavior using discrete element method (DEM). Accordingly, the effect of FC on the internal friction angle, anisotropy parameters, coordination number and coarse–fine (C–F) contacts have been studied. The results indicate that the variation in peak shear strength versus FC is bell-shaped with a minimum for FC of 30% to 40% and this is independent of initial packing density and stress level, but depending on the value of α. The greater particle size ratios (α = 7.1) increase the tendency of fines particles to rotate during biaxial testing, reduced the shear strength in comparison with samples with small particle size ratios (α = 2.5). Exceeding the threshold FC (30–40%) led to formation of stronger force chains among the fines and increased the role of FC on the peak shear strength.

Sand Penetration: A Near Nose Investigation of a Sand Penetration Event

The compression behavior of polytetrafluoroethylene (PTFE)–aluminum (Al) is studied by the means of the two-dimensional finite element analysis of mesoscale model containing a random dispersion of particles. The results show that for composite materials with a single particle size the strength of the material increases first and then decreases with the increase of the content of metal particles. When the particle content is high the strength of the material can be improved by a reasonable particle gradation. The influence of particle content and size on the strength of particle composites is obtained and theoretical analysis is carried out from the perspective of the formation and evolution of force chains.

Traumatic brain injury (TBI), resulting from blunt or blast impact to the head, affects approximately 1.6 million Americans per year. Brain biomechanics and injury models play a fundamental role in the TBI community as they can be used to evaluate protective equipment, refine safety standards, and improve individual treatment plans. To maximize clinical relevance, these models require accurate and precise mechanical input parameters relevant to expected injuries. Magnetic resonance elastography (MRE) offers a noninvasive method to quantify the viscoelastic properties of soft tissues by phase-encoding mechanical waves as they propagate through a tissue. While MRE has advanced our understanding of brain tissue mechanics, characterizing nonlinear behavior under large deformations remains a critical challenge for improving TBI models. Here, we coupled ex vivo MRE with incremental compression to characterize brain tissue mechanics beyond the linear elastic and linear viscoelastic regimes, which are more relevant for injury. Using a custom-made MR-compatible compression device, controlled axial pre-strain was applied to fresh brain tissue-agar phantoms. On average, the tissue storage modulus increased by 73.6% when approximately 6.4% of strain was applied. The resulting experimental data, namely storage modulus and applied pre-strain, were successfully fit to a phenomenological equation to output material parameters, including a nonlinearity metric. These findings provide novel, strain-dependent mechanical data for brain tissue that extend beyond small-strain assumptions. The results will improve computational models of TBI by supplying mechanical input parameters for predicting brain response under injury-relevant loading conditions.

Living systems adopt a diversity of curved and highly dynamic shapes. These diverse morphologies appear on many length scales, from cells to tissues and organismal scales. The common driving force for these dynamic shape changes are contractile stresses generated by myosin motors in the cell cytoskeleton, that converts chemical energy into mechanical work. A good understanding of how contractile stresses in the cytoskeleton arise into different three-dimensional (3D) shapes and what are the shape selection rules that determine their final configurations is still lacking. To obtain insight into the relevant physical mechanisms, we recreate the actomyosin cytoskeleton in vitro, with precisely controlled composition and initial geometry. A set of actomyosin gel discs, intrinsically identical but of variable initial geometry, dynamically self-organize into a family of 3D shapes, such as domes and wrinkled shapes, without the need for specific preprogramming or additional regulation. Shape deformation is driven by the spontaneous emergence of stress gradients driven by myosin and is encoded in the initial disc radius to thickness aspect ratio, which may indicate shaping scalability. Our results suggest that while the dynamical pathways may depend on the detailed interactions between the different microscopic components within the gel, the final selected shapes obey the general theory of elastic deformations of thin sheets. Altogether, our results emphasize the importance for the emergence of active stress gradients for buckling-driven shape deformations and provide insights on the mechanically induced spontaneous shape transitions in contractile active matter, revealing potential shared mechanisms with living systems across scales.