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This paper aims to present a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the representative volume element (RVE) of discrete particle assembly in the frame of the second-order computational homogenization methods for granular materials.

The proposed scheme is based on the generalized Hill’s lemma of gradient Cosserat continuum and the incremental non-linear constitutive relation condensed to the peripheral particles of the RVE of discrete particle assembly. The generalized Hill’s lemma conducts to downscale the macroscopic strain or stress measures and to impose the periodic boundary conditions on the RVE boundary so that the Hill-Mandel energy equivalence condition is ensured. Because of the incremental non-linear constitutive relation condensed to the peripheral particles of the RVE, the periodic boundary displacement and traction constraints together with the downscaled macroscopic strains and strain gradients, micro-rotations and curvatures are imposed in the point-wise sense without the need of introducing the Lagrange multipliers for enforcing the periodic boundary displacement and traction constraints in a weak sense.

Numerical results demonstrate that the applicability and effectiveness of the proposed scheme in imposing the periodic boundary conditions on the RVE. The results of the RVE subjected to the periodic boundary conditions together with the displacement boundary conditions in the second-order computational homogenization for granular materials provide the desired estimations, which lie between the upper and the lower bounds provided by the displacement and the traction boundary conditions imposed on the RVE respectively.

Each grain in the particulate system under consideration is assumed to be rigid and circular.

The proposed scheme for imposing periodic boundary conditions on the RVE can be adopted solely for estimating the effective mechanical properties of granular materials and/or integrated into the frame of the second-order computational homogenization method with a nested finite element method-discrete element method solution procedure for granular materials. It will tend to provide, at least theoretically, more reasonable results for effective material properties and solutions of a macroscopic boundary value problem simulated by the computational homogenization method.

This paper presents a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the RVE of discrete particle assembly for granular materials without need of introducing Lagrange multipliers for enforcing periodic boundary conditions in a weak (integration) sense.

The mixed assumed strain approach proposed by Simo and Rifai is used to derive three 8‐noded hexahedral mixed strain elements. The approach is also generalized to geometrically non‐linear problems. Based on the Galerkin form of Hu‐Washizu three field variational principle, the Green‐Lagrange strain tensor and the second Piola‐Kirchhoff stress tensor (symmetric) are employed to develop the geometrically non‐linear formulation for 2D and 3D mixed enhanced strain elements. Numerical results are presented to show that the resulting hexahedral mixed strain elements possess all the ideal qualities. They are able to pass the patch test, do not exhibit the false shear phenomena and do not lock for nearly incompressible materials. Also, they are less sensitive to distorted meshes than standard isoparametric elements and exhibit high accuracy for both linear and non‐linear problems, permitting coarse discretizations to be utilized. The elements developed in this paper have been implemented in the general purpose FE package LUSAS.

The purpose of this paper is to extend the bridge scale method (BSM) developed for granular materials with only the solid phase to that taking into account the effects of wetting process in porous continuum. The granular material is modeled as partially saturated porous Cosserat continuum and discrete particle assembly in the coarse and fine scales, respectively.

Based on the mass and momentum conservation laws for the three phases, i.e. the solid skeleton, the pore water and the pore air, the governing equations for the unsaturated porous Biot-Cosserat continuum model in the coarse scale are derived. In light of the passive air pressure assumption, a reduced finite element model for the model is proposed. According to the decoupling of the fine and coarse scale calculations in the BSM, the unsaturated porous Cosserat continuum model using the finite element method and the discrete element model using the discrete element method for granular media are combined.

The numerical results for a 2D example problem of slope stability subjected to increasing rainfall along with mechanical loading demonstrate the applicability and performance of the present BSM. The microscopic mechanisms of macroscopic shear band developed in the slope are demonstrated.

Do not account for yet the effects of unsaturated pore water in the fine scale.

The novel BSM that couples the Biot-Cosserat porous continuum modeling and the discrete particle assembly modeling in both coarse and fine scales, respectively, is proposed to provide a micro-macro discrete-continuum two-scale modeling approach for numerical simulations of the hydro-mechanical coupling problems in unsaturated granular materials.

The purpose of this paper is to investigate different baffles on mitigating liquid sloshing in a rectangular tank due to a horizontal excitation and to find out the optimal selection of sloshing mitigation for practical applications.

The numerical study is conducted by using a proven improved smoothed particle hydrodynamics (SPH), which is convenient in tracking free surfaces and capable of obtaining smooth and correct pressure field.

Liquid sloshing effects in a rectangular tank with vertical middle baffles, horizontal baffles, T-shape baffles and porous baffles are investigated together with those without any baffles. It is found that the existence of baffles can mitigate sloshing effects and the mitigation performance depends on the shape, structure and location of the baffles. Considering the balance of sloshing mitigation performance and the complexity in structure and design, the I shaped and T shaped baffles can be good choices to mitigate sloshing effects.

The presented methodology and findings can be helpful in practical engineering applications, especially in ocean engineering and problems with large sloshing effects.

The SPH method is a meshfree, Lagrangian particle method, and therefore it is an attractive approach for modeling liquid sloshing with material interfaces, free surfaces and moving boundaries. In most previous literature, only simple baffles are investigated. In this paper, more complicated baffles are investigated, which can be helpful in practical applications and engineering designs.

In oil/gas exploitations of ice-covered cold regions, conical offshore structures are designed to reduce ice force and to avoid the ice-induced intense vibrations of vertical structures. The purpose of this paper is to investigate the interaction between ice cover and conical offshore structures, the discrete element method (DEM) is introduced to determine the dynamic ice loads under different structure parameters and ice conditions.

The ice cover is dispersed into a series of bonded spherical elements with the parallel bonding model. The interaction between ice cover and conical offshore structure is obtained based on the DEM simulation. The influence of ice velocity on ice load is compared well with the experimental data of Hamburg Ship Model Basin. Moreover, the ice load on a conical platform in the Bohai Sea is also simulated. The ice loads on its upward and downward ice-breaking cones are compared.

The DEM can be used well to simulate the ice loads on conical structures. The influences of ice velocity, ice thickness, conical angle on ice loads can be analyzed with DEM simulations.

This DEM can also be applied to simulate ice loads of different offshore structures and aid in determining ice load in offshore structure designs.

Continuum-based discrete element method is an explicit numerical method, which is a combination of block discrete element method (DEM) and FEM. When simulating large deformation problems, such as cutting, blasting, water-like material flowing, the distortion of elements will lead to no convergence of the numerical system. To solve the convergence problem, a particle contact-based meshfree method (PCMM) is introduced in. The paper aims to discuss this issue.

PCMM is based on traditional particle DEM, and use particle contacts to generate triangular elements. If three particles are contact with each other, the element will be created. Once elements are created, the macroscopic constitutive law could be introduced in. When large deformation of element occurs, the contact relationship between particles will be changed. Those elements that do not meet the contact condition will be deleted, and new elements that coincide with the relationship will be generated. By the deletion and creation of elements, the convergence problem induced by element distortion will be eliminated. To solve FEM and PCMM coupled problems, a point-edge contact model is introduced in, and normal and tangential springs are adopted to transfer the contact force between particles and blocks.

According to the deletion and recreation of elements based on particle contacts, PCMM could simulate large deformation problems. Some numerical cases (i.e. elastic field testing, uniaxial compression analysis and wave propagation simulation) show the accuracy of PCMM, and others (i.e. soil cutting, contact burst and water-like material flowing) show the rationality of PCMM.

In traditional particle DEM, contact relationships are used to calculate contact forces. But in PCMM, contact relationships are adopted to generate elements. Compared to other meshfree methods, in PCMM, the element automatic deletion and recreation technique is used to solve large deformation problems.

The purpose of this paper is to establish a new two-phase Discrete Element Method (DEM) model to investigate the movement of fresh concrete which consists of mortar and aggregate. The established DEM model was adopted to simulate the mixing process of fresh concrete based on the commercial software package PFC3D. The trajectories of particles and particle clusters were recorded to analyze the mixing behavior from different scales. On one hand, the macro-scale movement was obtained to make the mixing process visualization. On the other hand, the relative micro movement of the single particle and particle clusters was also monitored to further study the mixing mechanism of the fresh concrete.

A new two-phase DEM model was designed to simulate the movement of fresh concrete which consists of mortar and aggregate. The linear-spring dashpot model was used to model all the contacts between particle and particle/wall to characterize the viscidity of fresh concrete. Moreover, two sets of parallel bond models were employed to characterize the contact between the mortar particles and mortar/coarse aggregate particles, namely the pbond1 and pbond2. The hybrid treatment enables the current DEM model to handle the yield behavior.

The mixing process of fresh concrete is mainly composed by the transportation in the x-direction and the overturn and fall off in the y- and z-directions. With these movements in different directions, the concrete particles can be fully mixed in the mixing drum.

A new two-phase DEM model was proposed and used to simulate the mixing process of fresh concrete. The outcomes of the simulation would be helpful for making the transporting truck visualization and the movement behavior of fresh concrete observable. The model can provide dynamic information of particles to reveal the interaction mechanism of fresh concrete in the truck mixer which is extremely difficult to obtain on-line in physical experiments or building site.

The permeate flux in microfiltration (MF) declines sharply with time due to membrane fouling, which seriously restricts its use in industrial applications. The purpose of this paper is to investigate particles deposition in MF processes, and propose a three-dimensional numerical model that focuses on particle-fluid flow and considers both permeable boundary conditions and cake deposition.

The two-ways coupling model was solved using Euler-Lagrange methods in which the suspended particle was traced by a hard sphere model and the fluid was simulated using large eddy model.

The numerical results predicted based on this model demonstrated the permeate flux increased as trans-membrane pressure and inlet velocity increased but decreased with an increase in feed concentration.

Good agreement was observed between the values obtained with the model and experimental values from the literature. The error is less than 20 per cent both permeate flux and cake thickness. In addition, a precise visualisation of cake morphology with filtration time was provided.

These analyses allowed for an estimation of the three-dimensional motion of suspended particles in turbulent flow. It saves manpower and financial resources for experiment, which possess important theoretical and industrial significance.

The purpose of this paper is to propose a new yield function for granular materials based on microstructures.

A biaxial compression test on granular materials under different stress paths is numerically simulated by distinct element method. A microstructure parameter S that considers both the arrangement of granular particles and the inter-particle contact forces is proposed. The evolution of the microstructure parameter S under the simulated stress paths is analyzed, from which a yield function for granular materials is derived. The way of determining the two parameters involved in the yield function is proposed.

The new yield function is calibrated using the test data of one sand and two rockfill materials. The shape of the new yield surface is similar to that of the Cam-clay model.

The paper proposes a microstructure parameter S, which considers both the arrangement of granular particles and the inter-particle contact forces. From the evolution of S, a yield function for granular materials is derived. The proposed yield function has a simple structure and the parameters are easy to be determined, leading to a feasible realization of engineering application.