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Large deformation problems are frequently encountered in various fields of geotechnical engineering. The particle finite element method (PFEM) has been proven to be a promising method to solve large deformation problems. This study aims to develop a computational framework for modelling the hydro-mechanical coupled porous media at large deformation based on the PFEM.

The PFEM is extended by adopting the linear and quadratic triangular elements for pore water pressure and displacements. A six-node triangular element is used for modelling two-dimensional problems instead of the low-order three-node triangular element. Thus, the numerical instability induced by volumetric locking is avoided. The Modified Cam Clay (MCC) model is used to describe the elasto-plastic soil behaviour.

The proposed approach is used for analysing several consolidation problems. The numerical results have demonstrated that large deformation consolidation problems with the proposed approach can be accomplished without numerical difficulties and loss of accuracy. The coupled PFEM provides a stable and robust numerical tool in solving large deformation consolidation problems. It is demonstrated that the proposed approach is intrinsically stable.

The PFEM is extended to consider large deformation-coupled hydro-mechanical problem. PFEM is enhanced by using a six-node quadratic triangular element for displacement and this is coupled with a four-node quadrilateral element for modelling excess pore pressure.

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 highlight the possibilities of a novel Lagrangian formulation in dealing with the solution of the incompressible Navier‐Stokes equations with very large time steps.

The design of the paper is based on introducing the origin of this novel numerical method, originally inspired on the Particle Finite Element Method (PFEM), summarizing the previously published theory in its moving mesh version. Afterwards its extension to fixed mesh version is introduced, showing some details about the implementation.

The authors have found that even though this method was originally designed to deal with heterogeneous or free‐surface flows, it can be competitive with Eulerian alternatives, even in their range of optimal application in terms of accuracy, with an interesting robustness allowing to use large time steps in a stable way.

With this objective in mind, the authors have chosen a number of benchmark examples and have proved that the proposed algorithm provides results which compare favourably, both in terms of solution time and accuracy achieved, with alternative approaches, implemented in in‐house and commercial codes.

The purpose of this paper is to evaluate the possibilities of the particle finite element method for simulation of free surface flows.

A numerical simulation of a number of examples for which experimental data are available is performed. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Some examples are chosen from the civil engineering field: a study of the flow over a flip bucket is analyzed for both 2D and 3D models, and the flow under a planar sluice gate is studied in 2D. Other examples, such as a 2D and 3D “dam break” with an obstacle are taken from the smooth particle hydrodynamics literature.

Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Different mesh sizes are considered for evaluating their influence on the final solution.

Details of the input data for all the examples studied are given. The aim is to identify benchmark problems for future comparisons between different numerical approaches for free surface flows.

The purpose of this paper is to present the composite finite element method (CFEM), with Cⁿ(n≥0) continuity so it improves the accuracy of the finite element method (FEM) for solving second‐order partial differential equations (PDEs) and also, can be used for solving higher order PDEs.

In this method, the nodal values in the conventional FEM have been replaced by the appropriate nodal functions. Based on this idea, a procedure has been proposed for obtaining the CFEM−Cⁿ shape functions based on the CFEM−Cⁿ⁻¹ shape functions as follows: the nodal values in the CFEM−Cⁿ⁻¹ have been replaced by deliberately selected nodal functions so that the smoothness of the CFEM−Cⁿ⁻¹ shape functions increase.

The proposed method has the following properties: first, its shape functions have simple explicit forms with respect to the natural coordinates of elements and consequently, the required integrals for calculation of stiffness matrix can be evaluated numerically by low‐order Gauss quadratures; second, numerical investigations show that the CFEM with Cⁿ(n>1) continuity leads to more accurate results in comparison with the FEM; third, in multi‐dimensional problems, the curved boundaries are modeled more accurately by the proposed method in comparison with the FEM; fourth, this method can treat with the weak discontinuities such as the interface between different materials, as simple as the FEM does; and fifth, this method can successfully model Kirchhoff plate problems.

This method is an improvement of the moving particle FEM and reproducing kernel element method. Despite these two methods, CFEM shape functions have simple explicit forms with respect to the natural coordinates of elements.

Current modellings of granular collapse are lack of considering the effect of soil density. This paper aims to present a numerical method to analyse the collapse of granular column based on the critical-state soil mechanics.

In the proposed method, a simple critical-state based constitutive model is first adopted and implemented into a finite element code using the coupled Eulerian–Lagrangian technique for large deformation analysis. Simulations of column collapse with various aspect ratios are then conducted for a given initial soil density. The effect of aspect ratio on the final size of deposit morphology, dynamical collapse profiles and the stable region is discussed comparing to experimental results. Moreover, complementary simulations with various initial soil densities on each aspect ratio are conducted.

Simulations show that a lower value of initial density leads to a lower final deposit height and a longer run-out distance. The simulated evolutions of kinetic energy and collapsing profile with time by the proposed numerical approach also show clearly a soil density-dependent collapse process.

To the end, this study can improve the understanding of column collapse in different aspect ratios and soil densities, and provide a computational tool for the analysis of real scale granular flow.

The originality of this paper is proposed in a numerical approach to model granular column collapse considering the influences of aspect ratio and initial void ratio. The proposed approach is based on the finite element platform with coupled Eulerian–Lagrangian technique for large deformation analysis and implementing the critical-state based model accounting for the effect of soil density.

This paper aims to develop a finite element analysis strategy, which is suitable for the analysis of progressive failure that occurs in pressure-dependent materials in practical engineering problems.

The numerical difficulties stemming from the strain-softening behaviour of the frictional material, which is represented by a non-associated Drucker–Prager material model, is tackled using the Cosserat continuum theory, while the mixed finite element formulation based on Hu–Washizu variational principle is adopted to allow the utilization of low-order finite elements.

The effectiveness and robustness of the low-order finite element are verified, and the simulation for a real-world landslide which occurred at the upstream side of Carsington embankment in Derbyshire reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.

The permit of using low-order finite elements is of great importance to enhance computational efficiency for analysing large-scale engineering problems. The case study reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.

The purpose of this paper is to apply the Peridynamic differential operator (PDDO) to incompressible inviscid fluid flow with moving boundaries. Based on the potential flow theory, a Lagrangian formulation is used to cope with non-linear free-surface waves of sloshing water in 2D and 3D rectangular and square tanks.

In fact, PDDO recasts the local differentiation operator through a nonlocal integration scheme. This makes the method capable of determining the derivatives of a field variable, more precisely than direct differentiation, when jump discontinuities or gradient singularities come into the picture. The issue of gradient singularity can be found in tanks containing vertical/horizontal baffles.

The application of PDDO helps to obtain the velocity field with a high accuracy at each time step that leads to a suitable geometry updating for the procedure. Domain/boundary nodes are updated by using a second-order finite difference time algorithm. The method is applied to the solution of different examples including tanks with baffles. The accuracy of the method is scrutinized by comparing the numerical results with analytical, numerical and experimental results available in the literature.

Based on the investigations, PDDO can be considered a reliable and suitable approach to cope with sloshing problems in tanks. The paper paves the way to apply the method for a wider range of problems such as compressible fluid flow.

This paper aims to analyze the abrasive damage of iron ore pellets (IOP) during charge inside day-bins in iron making plants. The rock-ladder structure of day-bin is the spotlight of this study. A numerical-analytical method is used to investigate the main geometrical features of the mentioned structure. Practical results of this study are expected to result in optimization of rock-ladder structure to reduce fine generation and lump formation during pellets downfall on the floors of rock-ladder.

One effective stage of pellets downfall on the floor of rock-ladder was simulated using discrete element method. A special post-process code is used to calculate parameters of pellets collisions for an analytical model which estimates fine generation during collisions. The main damaging mechanism during pellets storage inside day-bin is determined based on the comparison of the numerical-analytical results and industrial reports. Different rock-ladder designs are simulated to find optimal geometry of the rock-ladder structure.

According to the results, 85.4% of fines generation takes place during downfall of IOPs on the floors of rock ladder, and the rest of the fine debris is expected to be generated due to flow down under compressive load and vibratory discharge. The present study suggests an increase in the rock ladder floors distance from 1.63 to 2 m, but this suggestion should be confirmed by another study focusing on the breakage damage of IOPs. The idea of chamfering the floors corners not only removes lump-formation zones but also results in an approximately 5.7% reduction in the fines generation rate.

According to the results, introduced modification ideas for rock-ladder structure can result in lower fine generation, lower lump removal cost and lower manufacturing cost of rock-ladder structure.