OxDEM: Discrete element method based on strain energy formulation

Energy based topology optimization method has been used in the design of compliant mechanisms for many years. Although many successful examples from the energy based topology optimization have been presented, optimized configurations of these designs are often very similar to their rigid linkage counterparts except using compliant joints in place of rigid links. It is obvious that these complaint joints will endure large deformations under the applied forces in order to perform the specified motions and the large deformation will produce high stress which is very undesirable in compliant mechanism design. In this paper, a strain based topology optimization method is proposed to avoid localized high deformation design which is one of the drawbacks using strain energy formulation. Therefore, instead of minimizing the strain energy for structural rigidity, a global effective strain functional is minimized in order to distribute the deformation within the entire mechanism while maximizing the structural rigidity. Furthermore, the physical programming method is adopted to accommodate both flexibility and rigidity design objectives. Comparisons of design examples from both the strain energy based topology optimization and the strain based method are presented and discussed.

and Ogden [ll]material models. sion ratio based strain energy formulations include the Valanis-Landel [g] or Mooney-Rivlin formulation [5]. Examples of the latter principle extenfunction are the Rivlin formulation [lo] and the reduced Rivlin polynomial principal extension ratios. Examples of the former type of strain energy is taken where either the equation is based on the strain invariants or the plications a phenomenological approach to the strain energy formulation are many types of material model, but generally for most numerical apthe partial derivative of the strain energy with respect to strain [l].There methods the constitutive relationship between stress and strain is based on incompressibility. Consequently for both the finite and boundary element lems fail when Poisson’s ratio approaches 0.5 corresponding to near or total It is well known that standard displacement formulations of elastic prob-

This paper describes the development of a closed-form model and a finite element model for studying viscoelastic damping in woven fabric-reinforced polymer matrix composites. The closed-form model was obtained by first deriving an elastic solution based on the mechanics of materials theory, then applying the Elastic-Viscoelastic Correspondence Principle to the elastic solution. The damping loss factors were determined from the complex moduli. Three-dimensional finite element models with various mesh densities were constructed based on the actual geometry of a plain weave fabric-reinforced composite unit cell. Three different loading cases were designed to simulate extensional, shear and bending deformations of the unit cell. The strain energies stored in the fiber and matrix elements for each loading case were conveniently determined from the finite element analysis. A strain energy formulation was used to calculate the damping loss factors for each loading case. Experiments were conducted using an impulse-frequency response technique to measure damping in beam samples made of plain weave E-glass fabric-reinforced vinyl ester resin matrix composite. The predictions from both analytical models show reasonably good agreement with experimental data.

Numerical algorithm of concave polygon elements in solid mechanics: Theoretical analysis and performance evaluation of S-FEM and VEM

The proposed article provides a brief overview of publications devoted to solving problems of granular media mechanics using the discrete element method. These publications discuss the conditions for the successful application of algorithms and software developed for the effective functioning of computing systems implementing the discrete element method. It is noted that the most labor-intensive aspect of modeling deformation processes using the discrete element method are calculations associated with determining contact forces. The key problem is the evolutionary nature of contacts: during deformation of the medium under study, discrete elements can come into contact, which can subsequently be interrupted depending on the loading conditions. In this regard, it is necessary to carefully study the organization and management of memory associated with computer modeling of contacts. The main attention in the article is paid to algorithms for searching for discrete elements coming into contact. These algorithms should be robust (i.e. reliable), easy to implement; effective in terms of speed and use of RAM. Two variants of the algorithm based on the use of auxiliary (screening) grids are compared: the screening contact detection algorithm and the Munjiza-NBS contact detection algorithm. A brief description of these algorithms and their software implementation is given. The results of verification of the algorithms on test problems and a comparative analysis of their performance are presented. It is shown that the selected algorithms provide reliable information about discrete elements contacting during motion and can be successfully used in the software implementation of the discrete element method as applied to problems of granular media dynamics.

An optimized tumbling process can significantly improve the oxygen dissolving capacity of composting and fertilizer quality: by increasing the fluffiness of the lower layer of the pile, localized anaerobic fermentation can be avoided, thereby enhancing compost quality. This paper presents a method for improving the oxygen dissolving capacity of rotary drum food waste composting through a combination of simulation optimization and experimental validation. First, the discrete element method was used to optimize the key parameters of the tumbling process. The response surface method was then employed to analyze the composting test results and determine the optimal conditions. To ensure the reliability of the equipment under this method, failure risk analysis was conducted using the finite element method. The simulation optimization results showed that with a rotary drum reactor speed of 3.5 r/min, a horizontal angle of inclination of 2.5°, a mixing blade angle of inclination of 43°, and a blade pitch of 580 mm, the fluffiness of the lower layer of the pile increased by 8.515%, achieving the best tumbling and indirectly enhancing oxygen dissolving capacity. The maximum deformation of the load-bearing components was only 0.0548 mm, and the minimum safety factor was 4.408 (≥1 is considered safe). A 14-day composting experiment was conducted to validate the optimized parameters. The results showed that the maximum temperature of the compost pile reached 68.34 °C (lasting 7 days), with the pH, moisture content, C/N ratio, humus substances, humic acid, and fulvic acid contents of the fertilizer all meeting or exceeding the levels recommended by Chinese national standards. These findings indicate that the optimized tumbling device effectively improved the stability and dissolved oxygen efficiency of food waste composting, providing valuable practical insights and a research foundation for enhancing oxygen efficiency in the composting of other organic wastes.

The liner is a wear-prone component in ball mills, subject to continuous impacts, squeezing, and abrasion from the grinding media during operation. Its service performance directly affects the working efficiency of the ball mill. The service life of mining ball mill liners is about 8 months, and frequent downtimes occur due to liner wear and loss of effectiveness, with liner replacement accounting for about 6% of the total cost, resulting in huge economic losses. This paper focuses on a Φ305 mm × 150 mm experimental ball mill, using the discrete element software Rocky Discrete Element Method (DEM) (software version number Rocky 2022 R2) for simulation modeling analysis. With Φ10 mm and Φ20 mm mono-size particle simulations serving as reference groups, this study investigates the motion states and liner abrasion patterns under different liner heights for both sizes of grinding media in Equilibrium Quality Manufacturer (EQM) and Original Equipment Manufacturer (OEM) gradations. The results indicate that the impact of liner height on the wear of the ball mill liners is related to the size and gradation of the grinding media. The degree of liner wear from highest to lowest is as follows: EQM > Φ20 mm > OEM > Φ10 mm. Due to the effect of the cylinder end cap, the wear at the axial center of the ball mill liner is more severe than at both ends, and the wear on the facing side of the liner is more severe than on the backside. A thorough study of the influence of ball mill grinding media gradation on the wear pattern of liners is of great theoretical significance for optimizing liner structures, improving grinding efficiency, and promoting energy saving and cost reduction in ball mills. This study provides theoretical guidance for understanding the mechanisms behind liner wear in ball mills and predicting the liner lifespan.

The discusser was pleased and interested to see the application by Jiang et al. of discrete element method (DEM) technology to rough particles. In particular, the discusser was interested to see the claim by Jiang et al. that in the DEM, with a usual point-contact model, the couple/moment is neither available at the contact nor able to be transferred from one particle to the other. It would be for others more expert in DEM applications to judge the correctness of that claim; the discusser is happy to accept the claim at face value in relationship to the DEM methodology. However, it may be of interest to Jiang et al., and possibly the readership in general, to learn that a numerical model incorporating the couple/moment with the associated rotational mode of deformation was developed and published a very long time ago (Burman 1972). This development occurred as part of a doctoral research program by Burman at James Cook University of North Queensland in Australia under the guidance of well-known discontinuum instigator and long-term proponent, Professor Hugh Trollope. It so happened that at the time when Dr. Cundall was completing his initial work that lead ultimately to the DEM theory (Cundall 1971), Burman was engaged in a similarly directed effort to investigate the mechanics of blocky media, albeit by a different approach and for somewhat different ends. Dr. Cundall, working in the Royal School of Mines at Imperial College, was principally interested in miningrelated activities including dynamic phenomena, such as blasting and mass movements of blocky materials. Meanwhile, with a civil engineering bias, Burman was principally interested in the maintenance of structural integrity within blocky materials, including slopes and tunnels in jointed rock masses. This difference in emphasis was expressed in the greater attention by Burman to modeling rough contacts, whereas Dr. Cundall’s attention was directed to capturing the more spectacular and large block movements. Burman has always felt that the basic point-contact model used by Dr. Cundall was remarkably successful, in spite of its formational simplicity. In Burman’s view, this success demonstrated the power fundamentally involved in having specifically recognized the discrete nature of particles in a discontinuum regardless of the sophistication or otherwise of the micromodel used. The Burman model was developed for a system of rigid blocks interacting through a series of Goodman joint type finite elements (Goodman et al. 1968). The assumption of rigid blocks was necessitated at the time because of the severely restricted capacity of computers to deal with large sets of simultaneous equations. That restriction is no longer relevant, but it is still convenient to assume rigidity, as the writers have done, and to adopt the linearizing assumption of small incremental rotations. The Burman model, which is finite element based, employed the condition of static equilibrium together with the transformation of joint nodal displacements and nodal forces to associated block centroids yielding the basic matrix equation for equilibrium of an individual block (b) as

The conductivity of the proppant-pack plays a critical role in the productivity of a hydraulically fractured well. Here we combine the Discrete Element Method (DEM) and the Lattice Boltzmann Model (LBM) to investigate the conductivity of proppant-packs under variable confining stress. Three different proppant-packs including well graded, uniformly graded and poorly graded proppants are used to generate loose packing of spherical rigid particles with no initial contact. We then use a DEM algorithm, with specified confining stress, to compact the proppant-packs. A representative elementary volume of the pack is subsequently used for fluid flow simulations. LBM is used to calculate a detailed flow field at the pore scale and the Darcy-scale permeability is then calculated from the average pore-scale velocity and pressure information. The results show, as expected, that the porosity and permeability of the proppant-pack decreases with increasing confining pressure. The permeability of well graded proppant-packs is more sensitive to the stress while uniformly graded packs are more permeable than poorly graded proppant-packs. The calculated permabilities are in good agreement with available experimental data for a range of confining pressures. In addition, the permeability estimated from the Kozeny-Carman equation based on calculated porosities compares well with calculated permeabilities.

In order to systematically obtain the excavation characteristic parameters for ginger harvesting, experimental analysis was conducted on the discrete elemental parameters in a particle simulation model of the ginger-soil system. Through stacking tests, the surface energy of soil-ginger tuber JKR was determined to be 3.7 J/m2, the coefficient of static friction of soil-steel (65 Mn) was 0.56, the coefficient of rolling friction was 0.03, and the coefficient of restitution of collision was 0.40. Utilizing normal and lateral compression tests conducted on the soil body, the soil base parameters required for the Bonding model were determined. Subsequently, a three-dimensional model of ginger root and stem was constructed using these parameters. With the aid of 3D scanning technology, a discrete element parameter model was established for the ginger field during the harvesting period. On the basis of the measured parameters, a three-dimensional model of ginger rhizome was established and finally a discrete parameter model of ginger field was constructed in the harvesting period. The calibration parameters are highly reliable after the model’s tightness and field harvesting test, which provides reliable data support for the soil flow and the force of the soil-touching parts during the later simulation of ginger harvesting and digging operation. Keywords: ginger, soil, discrete element, simulation parameters, calibration DOI: 10.25165/j.ijabe.20241705.9102 Citation: Wang W L, Zhang P C, Wang X, Meng X J, Wang F Y. Construction of the particle simulation model for ginger-soil system using discrete element method. Int J Agric & Biol Eng, 2024; 17(5): 58-64.

Heat transfer by conduction using DEM–FEM coupling method

Discrete element modelling of a chevron patterned conveyor belt and a transfer chute

This paper presents a preliminary study on the effect of the clay content on the mechanical properties of the fault gouge materials using the discrete element method (DEM). It is also a feasibility study to examine how numerical modeling based on the DEM can be used to predict the hydro-mechanical properties of the fault. 2-dimensional (2D) models were used. The sand and the clay particles were explicitly mimicked using mixed two groups of elements with different sizes and different mechanical properties. Simulations of biaxial compression tests were performed, and the friction coefficients of the models with different clay contents were calculated from the simulation results. The modeling results were compared with some published laboratory experimental results. They agreed qualitatively. This study therefore demonstrates that a simple 2D DEM model can qualitatively capture the effect of the clay contents on the mechanical properties of the sand-clay mixtures. However, further studies are expected to be done in order to quantitatively predict the hydro-mechanical parameters of the fault gouge materials using DEM modeling.

The discrete element method considers the total aerodynamic drag on a rough surface to be the sum of shear drag on the flat part of the surface and the form drag on the individual roughness elements. The total heat transfer from a rough surface is the sum of convection through the fluid on the flat part of the surface and the convection from each of the roughness elements. The discrete element method has been widely used and validated for predicting heat transfer and skin friction for rough surfaces composed of sparse, ordered, and deterministic elements. Real gas turbine surface roughness is different from surfaces with sparse, ordered, and deterministic roughness elements. Modifications made to the discrete element roughness method to extend the validation to real gas turbine surface roughness are detailed. Two rough surfaces found on high-hour gas turbine blades were characterized using a Taylor-Hobson Form Talysurf Series 2 profilometer. Two rough surfaces and two elliptical-analog surfaces were generated for wind tunnel testing using a three-dimensional printer. The printed surfaces were scaled to maintain similar boundary layer thickness to roughness height ratio in the wind tunnel as found in gas turbine operation. The results of the wind tunnel skin friction and Stanton number measurements and the discrete element method predictions for each of the four surfaces are presented and discussed. The discrete element predictions made considering the gas turbine roughness modifications are within 7% of the experimentally measured skin friction coefficients and are within 16% of the experimentally measured Stanton numbers.

BACKGROUND: The traction characteristic of a wheel mover depends both on its type and rigidity properties, and on the physico-mechanical soil properties. The combined use of the discrete element method to describe the soil and the finite element method to model the wheel makes it possible to specify and expand the existing empirical models of the interaction of the mover with the ground. The application of this method will reduce the amount of full-scale testing required to verify the interaction model. AIMS: Development the traction characteristic of a metal wheel by varying its design parameters. METHODS: To develop a mathematical model of a metal wheel and determine traction characteristics, numerical methods of discrete and finite elements are used. RESULTS: In this paper, a metal wheel mathematical model with ability to vary the thickness of the elastic sidewall was developed. Radial stiffness characteristics were obtained for three wheel samples. The developed mathematical model of the interaction of a wheel mover with a ground is based on the application of discrete and finite element methods. In this paper, a proportional controller was used to application of forces to the wheel mover. The dependences of the longitudinal reaction coefficient on the slip coefficient were obtained and a comparative analysis of the radial stiffness influence on traction characteristics was carried out. CONCLUSIONS: The combined application of the discrete and finite element methods will make it possible to determine the traction characteristics of the movers of various designs when interacting with a deformable soil and to evaluate the influence of its design parameters on it.