In this paper, it is argued that science of discontinua represents a major paradigm shift in how scientific research is done. First, a historical perspective is given, followed by key aspects of discontinuum simulations and its potential in aiding research and development. This is followed by a philosophical perspective on equivalence of matter and information as inspired by Aristotle’s quest for souls

When a dynamic earthquake rupture propagates on a fault in the Earth’s crust, the medium around the fault is dynamically damaged due to stress concentrations around the rupture tip. Recent field observations, laboratory experiments and canonical numerical models show the coseismic off-fault damage is essential to describe the coseismic off-fault deformation, rupture dynamics, radiation and overall

Uniqueness of solutions to the SPH integral formulation of the hydrostatic problem, and the convergence of such solution to the exact linear pressure field, are theoretically demonstrated in this paper using Fourier analytical techniques. This problem involves the truncation of the kernel when the Dirichlet boundary condition (BC) on the pressure is imposed at the free surface. Certain hypotheses are

By using nonlocal discrete force functions, peridynamics (PD) can effectively deal with the problems involving discontinuities and singularities. As a continuum-based particle method, the material point method (MPM) and its advanced version, generalized interpolation material point method (GIMP), use local and nonlocal spatial discretization, respectively, to effectively simulate large deformations

The symbol was introduced incorrectly inside the “Time-stepping the solution” box, directly under the “Compute first Piola–Kirchhoff stress tensor Pi” as in “Appendix A” listing.

Due to its simplicity and robustness, smooth particle hydrodynamics (SPH) has been widely used in the modelling of solid and fluid mechanics problems. Through the years, various formulations and stabilisation techniques have been adopted to enhance it. Recently, the authors developed JST–SPH, a mixed formulation based on the SPH method. Originally devised for modelling (nearly) incompressible hyperelasticity

This work explores different particle-based approaches for the simulation of space–fractional diffusion equations in unbounded domains. We rely on smooth particle approximations and consider five different methods for estimating the fractional diffusion term. The first method is based on a direct differentiation of the particle representation, following the Riesz definition of the fractional derivative

A new corrective scheme for the derivative-free (DF) smoothed particle hydrodynamics (SPH) method is proposed to compute the first- and second-order derivatives. To demonstrate the ability of the new corrective scheme, the first- and second-order derivatives of the given function were computed when the particles were uniformly and irregularly distributed. The nonlinear convection–diffusion problems

We present a numerical procedure for elastic and nonlinear analysis (including fracture situations) of solid materials and structures using the discrete element method. It can be applied to strongly cohesive frictional materials such as concrete and rocks. The method consists on defining nonlocal constitutive equations at the contact interfaces between discrete particles using the information provided

A mesoscale modeling of magneto-rheological damper is performed by using dissipative particle dynamics method. Bounce-back and periodic boundary conditions are used, and the model is validated by Couette flow, Poiseuille flow and flow through a micro-tube. Shear stress and damping behavior are probed with considering hysteresis condition. Three electrical coils are placed inside MR damper, control

Particles slide and roll on each other when a granular medium is sheared. Consequently, the tribological properties, such as inter-particle friction and adhesion, play a major role in influencing their bulk failure and rheology. Although the influence of roughness on adhesion and friction of contacting surfaces is known, the incorporation of the surface roughness in the numerical modelling of granular

This paper presents a hybrid discrete bubble-lattice Boltzmann–discrete element modelling framework for simulating gas-charged sediments, especially in the seabed. A discrete bubble model proposed in chemical engineering is adapted in the coupled discrete element/lattice Boltzmann method to model the migration of gas bubbles in saturated sediments involving interactions between gas bubbles and fluid/solid

In this study, a reduced-order model for a deformable particle is introduced and implemented in the framework of discrete element method (DEM) with the application in biological cells such as red blood cell (RBC). In this model, a single deformable particle comprises a clump of rigid constituent spheres whose centroids are interconnected utilizing mathematical elastic bonds. To preserve the deformability

In this work, a detailed investigation on the effects of particle diameter on the fluidization characteristics of gas–particle flows inside a bubbling gas–solid fluidized bed has been carried out. The studies are performed using an in-house flow solver developed employing the Eulerian–Eulerian two-fluid model. Simulations carried out using the solver indicate that particle diameter has significant

The truck escape ramp is a clump of pebbles that is located alongside downgrades. As the pebbles are randomly placed in arrester beds, few studies have been conducted on simulation methods of the irregularly shaped pebbles. This paper proposed a pebble DEM model to analyze the micro-contact mechanism of the pebbles. Based on a polynomial algorithm, the 7th fit was selected and the coefficients of the

Underwater structures can be seriously damaged by a metal jet associated with underwater explosion. Three main modes—Shaped Charge Jet, Jetting Projectile Charge and Explosive Formed Projectile—are included for traditional metal jets. Compared with the traditional ones, an annular jet may cause more serious damage into a target. Hence, a comparison for the entire process of annular and general jets

In ice-covered regions, the upward–downward ice-breaking cones are applied widely to reduce the ice load on the vertical jacket offshore platforms. The ice load is affected by the diameter of cone at the water level. In particular, the sea ice can impact on the vertical portion of the platform which is beyond the covered area of the upward–downward cone under the extreme low or high water level. In

The stable discharge of particles through the hopper plays a key role in many industrial applications. In order to investigate the discharge characteristics of binary particles in a rectangular hopper with an inclined bottom, the discrete element method (DEM) was used to simulate the discharge process. The accuracy of DEM was validated by comparing calculated and experimental values. The influences

The Material Point Method (MPM) is a numerical technique that combines a fixed Eulerian background grid and Lagrangian point masses to simulate materials which undergo large deformations. Within the original MPM, discontinuous gradients of the piecewise-linear basis functions lead to the so-called grid-crossing errors when particles cross element boundaries. Previous research has shown that B-spline

The discrete element method (DEM) is a powerful tool for simulating complex mechanical behaviors which discretizes the targeted medium with particles. The properties of particle assemblies used in DEM simulations directly impact the behavior of the simulated medium. It is thus of critical importance to generate particle assemblies so as to (1) avoid any bias induced by their fabric and (2) conform

Fine and cohesive powders typically exhibit low packing density, with solid volume fraction around 0.3. Discrete element modelling (DEM) of particulate materials and processes typically employs spherical particles which have much larger solid fractions (e.g. 0.64 for dense random packing of frictionless spheres). In this work a range of quasi-spherical particles are designed, represented by a number

In this work, we present a newly developed workflow to study the combined effect of shear and normal stresses upon a preexisting fracture plane. This workflow is used to study the behavior of both single grain and polycrystalline materials, with varying material properties. The surface roughness and aperture of preexisting fractures are highly dependent upon the dynamic stress behavior within rock

From its inception, the combined finite discrete element method has used a distributed potential contact force algorithm to resolve interaction between finite elements. The contact interaction algorithm relies on evaluation of the contact force potential field. The problem with existing algorithms is that the potential field introduces artificial numerical non-smoothness in the contact force. This

Three-dimensional imaging techniques, such as X-ray computed tomography, have been used to scan realistic particle geometries. However, these techniques are labor intensive, time-consuming, and costly to obtain a large number of particles. Therefore, it is desirable if computers can be taught to generate realistic particles based on given morphological properties. This paper develops a particle generation

Simulations of multi-body dynamics for computer graphics, 3D game engines, or engineering simulations often involve contact and articulated connections to produce plausible results. Multi-body dynamics simulations generally require accurate contact detection and induce high computational costs because of tiny time increments. As higher accuracy and robustness are continually being sought for engineering

Theoretical analysis and nowadays advanced numerical simulations for bedload particle transport widely share a popular assumption: All sediments are spherical and can be simplified as spheres, which apparently differs from reality. In order to explore the shape effects of sediment particles on their transport and to find out the possible consequence originated from the spherical assumption, a particle

This paper presents a new three-dimensional thermo-mechanical (TM) coupling approach for thermal fracturing of rocks in the finite–discrete element method (FDEM). The linear thermal expansion formula is implemented in the context of FDEM according to the concept of the multiplicative split of the deformation gradient. The presented TM formulation is derived in the geo-mechanical solver, enabling thermal

We present an open-source software RKPM2D for solving PDEs under the reproducing kernel particle method (RKPM)-based meshfree computational framework. Compared to conventional mesh-based methods, RKPM provides many attractive features, such as arbitrary order of continuity and discontinuity, relaxed tie between the quality of the discretization and the quality of approximation, simple h-adaptive refinement

An improved version of the solid–liquid coupled material point method (MPM) is proposed to simulate ground collapses with fluidization involving transition processes from soil structures to flowing mixture. A water-saturated soil is assumed based on porous media theory, and the physical quantities of the soil and water phases are assigned to two separate sets of particles (material points). The main

Meshfree discretization of surface partial differential equations is appealing, due to their ability to naturally adapt to deforming motion of the underlying manifold. In this work, we consider an existing scheme proposed by Liang et al. reinterpreted in the context of generalized moving least squares (GMLS), showing that existing numerical analysis from the GMLS literature applies to their scheme

Meshfree methods for solid mechanics have been in development since the early 1990’s. Initial motivations included alleviation of the burden of mesh creation and the desire to overcome the limitations of traditional mesh-based discretizations for extreme deformation applications. Here, the accuracy and robustness of both meshfree and mesh-based Lagrangian discretizations are compared using manufactured

Flow drill screw (FDS) joining is a modern mechanical fastening technique for connecting metal parts in lightweight car structures. Finite element simulation of FDS joining probably is one of the biggest challenges for CAE engineers in automotive applications. This is mainly because finite element methods inevitably encounter utmost numerical difficulties associated with meshing issues in modeling

In this work, a coupling method between the bond-based peridynamics model for solids and the updated Lagrangian particle hydrodynamics (ULPH) model of fluids is developed to simulate interaction between ice and seawater. The ULPH (Tu and Li in J Comput Phys 348:495–513, 2017) is the latest development of using non-local differential operators to model Navier–Stokes equations of Newtonian fluids, which

The material point method (MPM) has not been evaluated in a systematic manner for the fully coupled thermodynamic fluid–structure interaction (FSI) cases. Since the constitutive models and heat transfer in solid and fluid materials are quite different, a fully coupled computational scheme is designed in this paper for simulating the FSI with the MPM, in which the governing equations for both solid

The failure of a weak snow layer underlying a cohesive slab is the primary step in the release process of a dry snow slab avalanche. The complex and heterogeneous microstructure of snow limits our understanding of failure initiation inside the weak layer, especially under mixed-mode shear-compression loading. Further complication arises from the dependence of snow strength on the loading rate induced

In the discrete element simulation of granular materials, the modelling of contacts is crucial for the prediction of the macroscopic material behaviour. From the tribological point of view, friction at contacts needs to be modelled carefully, as it depends on several factors, e.g. contact normal load or temperature to name only two. In discrete element method (DEM) simulations the usage of Coulomb's