A generic energy‐conserving discrete element modeling strategy for concave particles represented by surface triangular meshes

A generic energy-conserving linear normal contact model for concave particles in the discrete element method (DEM) is presented in the current paper. It is derived based on a recently enhanced general energy-conserving contact theory for arbitrarily shaped particles. A set of more effective evaluation schemes required in the model are also given, which shows that only the intersection boundary between two contact shapes, instead of their contact region or surfaces, is required to be explicitly obtained, thereby substantially improving both efficiency and applicability of the proposed contact model over the previous version. A surface triangular mesh is used to represent any 3D concave particle. The computational issues associated with the contact of two surface triangulated 3D shapes, including the contact detection, the determination of intersection boundary segments, the computation of contact features and parallelisation, critical time step, and friction and damping treatment for multiple contacts are described in detail. Two sets of numerical examples involving various concave 3D shapes with a large number of surface triangles are presented to demonstrate either the superb energy-conserving property of the proposed model model, or its effectiveness, robustness and universal nature for wider and more complex problems

An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Contact volume based model and computational issues

The contact volume based energy-conserving contact model is presented in the current paper as a specialised version of the general energy-conserving contact model established in the first paper of this series (Feng, 2020). It is based on the assumption that the contact energy potential is taken to be a function of the contact volume between two contacting bodies with arbitrary (convex and concave) shapes in both 2D and 3D cases. By choosing such a contact energy function, the full normal contact features can be determined without the need to introduce any additional assumptions/parameters. By further exploiting the geometric properties of the contact surfaces concerned, more effective integration schemes are developed to reduce the evaluation costs involved. When a linear contact energy function of the contact volume is adopted, a linear contact model is derived in which only the intersection between two contact shapes is needed, thereby substantially improving both efficiency and applicability of the proposed contact model. A comparison of this linear energy-conserving contact model with some existing models for discs and spheres further reveals the nature of the proposed model, and provides insights into how to appropriately choose the stiffness parameter included in the energy function. For general non-spherical shapes, mesh representations are required. The corresponding computational aspects are described when shapes are discretised into volumetric meshes, while new developments are presented and recommended for shapes that are represented by surface triangular meshes. Owing to its additive property of the contact geometric features involved, the proposed contact model can be conducted locally in parallel using GPU or GPGPU computing without occurring much communication overhead for shapes represented as either a volumetric or surface triangular mesh. A set of examples considering the elastic impact of two shapes are presented to verify the energy-conserving property of the proposed model for a wide range of concave shapes and contact scenarios, followed by examples involving large numbers of arbitrarily shaped particles to demonstrate the robustness and applicability for more complex and realistic problems

An enthalpy based discrete thermal modelling framework for particulate systems with phase change materials

The latent thermal energy storage of phase change materials (PCM) is an attractive technique to use renewable energy. Systems with PCM capsules can be found in a wide variety of applications, but PCMs are usually approximated as a continuous phase in previous studies. The current work investigates this problem from the discontinuous point of view. The main objective is to develop an enthalpy based discrete thermal formulation that can take both heat conduction and phase change transition into consideration. The computational aspect of the formulation is fully discussed. The resulting algorithm is simple and effective. Its validity is demonstrated by solving a discrete/particle version of the one-phase Stenfan problem. In addition, the equivalent thermal properties of bulk particle materials with phase change are also derived based on a simple multi-scale modelling scheme. Numerical simulations are conducted to illustrate the effectiveness of the proposed enthalpy based discrete thermal modelling (DTEM) framework

An adaptive granular representative volume element model with an evolutionary periodic boundary for hierarchical multiscale analysis

The hierarchical multiscale analysis normally utilises a microscopic representative volume element (RVE) model to capture path/history‐dependent macroscopic responses instead of using phenomenological constitutive models. However, for problems involving large deformation, the current RVE model used in geomechanics may lose representative properties due to the progressive distortion of the RVE box, unless a proper reinitialization is applied. This work develops an adaptive RVE model in conjunction with an evolutionary periodic boundary (EPB) algorithm for hierarchical multiscale analysis of granular materials undergoing large deformation based on a recent RVE model proposed for coupling molecular dynamics and the material point method. The proposed adaptive RVE model avoids the reinitialization of the RVE box that even undergoes extremely large shear deformation; meanwhile, it accounts for the deformation history of the RVE model and treats the interaction between boundary particles and other image particles in a more efficient way. Numerical examples with extremely large deformation are used to illustrate the adaptive granular RVE model enhanced by the proposed EPB algorithm. Furthermore, some key features of this new methodology are further discussed for clarification

A coupled 3D discrete elements/isogeometric method for particle/structure interaction problems

To utilize the geometry smoothness of isogeometric analysis for solid media and the effectiveness of the discrete element method for particulate matters, a coupled three-dimensional isogeometric/discrete element method is developed to model the contact interaction between structures and particles. The coupling procedure for handling interactions between isogeometric elements and discrete elements includes global search, local search/resolution and interaction force calculation. Since interaction models for contacting particles and isogeometric elements have significant effects on the contact forces in simulations, several commonly used contact models, including linear, Hertz and quadratic models, are investigated. For a small ball impacting a thick plate example, it is found that the Hertz contact model exhibits the best behavior as the interaction law between a sphere and an isogeometric element in the elastic regime, and no additional correction factor is needed. In addition, an assembly of randomly arranged granular particles impacting a tailor rolled blank is also simulated to further illustrate the applicability of the proposed method

Periodic boundary conditions of discrete element method-lattice Boltzmann method for fluid-particle coupling

This paper presents a periodic boundary condition for the coupled discrete element and lattice Boltzmann method for simulating fluid-particle systems. Detailed implementation of this special boundary condition is given. Besides, the detailed procedure of immersed moving boundary scheme for fluid–solid coupling is proposed. The accuracy and applicability of the proposed periodic boundary condition are well demonstrated by two benchmark tests, i.e. single particle transport and multiple particle migration in an infinite tube filled with water. It is found that the novel periodic boundary condition proposed for discrete element and lattice Boltzmann method can greatly improve the computational efficiency of the later which is computationally expensive when thousands of particles are involved

Numerical Assessment on Fatigue Failure of Castellated Steel Beams under Sinusoidal Vibration

Increase cost of material in the construction industry has led to the adoption of castellated steel beam as an alternative to substitute conventional steel rolled beam. However, the presence of web opening has resulted to various structural behaviour under static action and uncertainties under dynamic loading, especially fatigue failure. Therefore, this paper presents the numerical assessment on fatigue failure of castellated steel beams. The design of castellated steel beam was based on the parent steel beam of UKB 254 x 102 x 28. Meanwhile, various shapes of web opening (hexagonal, circular and rectangular) with size of 0.75D were considered. The finite-discrete element method program was used as a platform of numerical modelling. The stress range was analysed at 3 Hz of different load amplitudes of sinusoidal vibration. The fatigue life was compared among each shape of web opening at detail categories 90 and 160. At the initial load, the stress range reaches 65 MPa to 150 MPa. When the load increased, the stress range changes diminutively around 240 MPa to 280 MPa. The fatigue life attains at plateau value of 108 cycles, where circular castellated steel beams showed the best performance

Discrete element modelling of flexible membrane boundaries for triaxial tests

The discrete element modelling of triaxial tests plays a critical role in unveiling fundamental properties of particulate materials, but the numerical implementation of a flexible membrane boundary for the testing still imposes problems. In this study, a robust algorithm was proposed to reproduce a flexible membrane boundary in triaxial testing. The equivalence of strain energy enables the particle-scale parameters representing the flexible membrane to be directly determined from the real geometric and material parameters of the membrane. Then the proposed flexible membrane boundary was implemented in the context of discrete element simulation of triaxial testing and was validated with laboratory experiments. Furthermore, comparisons of triaxial tests with flexible and rigid boundaries were performed from macro-scale to meso-scale. The results show that the boundary condition has limited influences on the stress-strain behaviour but a relatively large impact on the volumetric change, the failure mode, the distribution of contact forces, and the fabric evolution of particles in the specimen during triaxial testing

An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Basic framework and general contact model

The first paper of this series establishes a unified theoretical framework that lays a solid foundation for developing energy-conserving normal contact models for arbitrarily shaped bodies in the discrete element method. It is derived based solely on the requirement that the potential energy must be conserved for an elastic impact of two shapes under any condition. The resulting general energy-conserving contact model states that the normal force as a vector must be the gradient of a contact potential field. When such a contact potential or energy function is specified, a complete normal contact model for a pair of arbitrarily shaped particles, including the contact normal direction, contact point/line and force magnitude, will be automatically followed without introducing any additional assumptions. In this framework, the contact geometry and contact force are indispensably related and are evaluated in a consistent manner. Due to the paramount role that the energy function plays in the current theory, its fundamental properties are discussed, which serve as general guidance for choosing a valid energy function. In addition, both single and multiple contacts and their evolution can be handled in a seamless way. Some symmetric properties of particle shapes can also be utilised to simplify the contact models.Within the proposed theoretical framework, different choices or combinations of geometric features as variables for the contact energy function can give rise to unique types of energy-conserving contact models with distinct characteristics and features. Two such functions using only one primary feature, which lead to two specialised energy-conserving contact models, will be presented in the subsequent papers of this series

Discrete Element Modelling of Dynamic Behaviour of Rockfills for Resisting High Speed Projectile Penetration

This paper presents a convex polyhedral based discrete element method for modelling the dynamic behaviour of rockfills for resisting high speed projectile penetration. The contact between two convex polyhedra is defined by the Minkowski overlap and determined by the GJK and EPA algorithm. The contact force is calculated by a Minkowski overlap based normal model. The rotational motion of polyhedral particles is solved by employing a quaternion based orientation representation scheme. The energy-conserving nature of the polyhedral DEM method ensures a robust and effective modelling of convex particle systems. The method is applied to simulate the dynamic behaviour of a rockfill system under impact of a high speed projectile. The rockfill sample is generated by a three-dimensional Voronoi meso method with a specific particle size distribution. The penetrating process of the projectile striking the rockfill target is simulated. Some physical quantities associated with the projectile such as the residual velocity, penetration resistance, and deflection angle are monitored which can reflect the influence of the characteristics of the rockfill target on its anti-penetration performance. It can be concluded that the developed polyhedral DEM method is a very promising numerical approach in analysing the dynamic behaviour of rockfill systems subject to high speed projectile impact