Yarn simulations with sharp edges

This paper is concerned with a traction-based Completed Adjoint Double Layer Boundary Element Method to solve for the surface traction of a system of rigid particles embedded in an elastic matrix. The main feature of the method is a single layer representation of the displacement field, which leads to a system of second-kind integral equations for the traction field, the extreme eigenvalue of which could be deflated, allowing iterative solution strategies to be effectively applied. The method is therefore most suitable for large-scale simulations of particulate solids. The method is benchmarked against some known analytic solutions, including the difficult stress singularity problems at sharp edges. The effectiveness of the method in dealing with a large number of inclusions is also demonstrated with an elongational deformation problem involving up to 25 inclusions.

This work presents the development of an explicit/implicit particle finite element method (PFEM) for the 2D modeling of metal cutting processes. The purpose is to study the efficiency of implicit and explicit time integration schemes in terms of precision, accuracy and computing time. The formulation for implicit and explicit time marching schemes is developed, and a detailed study on the explicit solution steps is presented. The PFEM remeshing procedures for insertion and removal of particles have been improved to model the multiple scales of time and/or space of the solution. The detection and treatment of the rigid tool contact are presented for both, implicit and explicit schemes. The performance of explicit/implicit integration is studied with a set of different two-dimensional orthogonal cutting tests of AISI 4340 steel at cutting speeds ranging from 1 m/s up to 30 m/s. It was shown that if the correct selection of the time integration scheme is made, the computing time can decrease up to 40 times. It allows us to affirm that the computing time of the PFEM simulations can be excessive due to the used time marching scheme independently of the meshing process. As a practical result, a set of recommendations to select the time integration schemes for a given cutting speed are given. This is intended to minimize one of the negative constraints pointed out by the industry when using metal cutting simulators.

Insulator-based dielectrophoresis (iDEP) has been increasingly used for particle manipulation in various microfluidic applications. It exploits insulating structures to constrict and/or curve electric field lines to generate field gradients for particle dielectrophoresis. However, the presence of these insulators, especially those with sharp edges, causes two nonlinear electrokinetic flows, which, if sufficiently strong, may disturb the otherwise linear electrokinetic motion of particles and affect the iDEP performance. One is induced charge electroosmotic (ICEO) flow because of the polarization of the insulators, and the other is electrothermal flow because of the amplified Joule heating in the fluid around the insulators. Both flows vary nonlinearly with the applied electric field (either DC or AC) and exhibit in the form of fluid vortices, which have been utilized to promote some applications while being suppressed in others. The effectiveness of iDEP benefits from a comprehensive understanding of the nonlinear electrokinetic flows, which is complicated by the involvement of the entire iDEP device into electric polarization and thermal diffusion. This article is aimed to review the works on both the fundamentals and applications of ICEO and electrothermal flows in iDEP microdevices. A personal perspective of some future research directions in the field is also given.

SummaryAn adaptive substepping explicit integration scheme is developed for a porosity‐dependent hydro‐mechanical model for unsaturated soils. The model is referred to as the modified σ–Θ model in this paper, which features the employment of the subloading surface plasticity and the stress–saturation approach. On numerical aspects, convex/nonconvex subloading surfaces in the σ–Θ space may result in incorrect loading–unloading decisions during the integration. A new loading–unloading decision method is developed here to solve the problem and then embedded into the explicit integration scheme for the modified σ–Θ model. In addition, to enhance the accuracy of the explicit integration, local errors from both hydraulic and mechanical components are included in the error control for each substep. A drift correction method is also developed to ensure the state point lies on the subloading surface in the σ–Θ space within a set error level. The performance of the loading–unloading decision method for the modified σ–Θ model is discussed through comparing it with the conventional loading–unloading decision method. The importance of involving the hydraulic component in the error control is also demonstrated. The accuracy and efficiency of the proposed adaptive substepping explicit integration scheme for the modified p–Θ model are also studied via several numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper high order time integration schemes are investigated for the integration of uid-structure interaction (FSI) model problem with deforming domains. The integration algorithm consists of a partitioned scheme in which a combination of implicit and explicit (IMEX) high order Runge-Kutta time integration schemes is used: the uid and structure systems are decoupled at their interface and both systems are integrated using the implicit system under a given boundary condition at the interface. The inuence of this boundary condition (the coupling term) is integrated using the explicit Runge-Kutta scheme. The uid dynamics are written in the arbitrary Lagrange Eulerian formulation to cope with the deforming uid mesh. An expression is proposed for the mesh face velocities of the deforming mesh such that the discrete geometric conservation law is satised. For the model problem numerical investigations are made into the eciency of these high order time integration schemes compared to lower order methods. The IMEX scheme retains the order of the implicit and explicit schemes and obtains the same accuracy as a second order staggered scheme for less computational work.

A longstanding problem in the study of sediment transport in gravel-bed rivers is related to the physical mechanisms governing bed resistance and particle motion. To study this problem, we investigated the motion of coarse spherical glass beads entrained by a steady shallow turbulent water flow down a steep two-dimensional channel with a mobile bed. This experimental facility is the simplest representation of sediment transport on the laboratory scale, with the tremendous advantages that boundary conditions are perfectly controlled and a wealth of information can be obtained using imaging techniques. Flows were filmed from the side by a high-speed camera. Using image processing software made it possible to determine the flow characteristics such as particle trajectories, their state of motion (rest, rolling, or saltating motion), and flow depth. In accordance with earlier investigations, we observed that over short time periods, sediment transport appeared as a very intermittent process. To interpret these results, we revisited Einstein's theory on sediment and derived the statistical properties (probability distribution and autocorrelation function) of the key variables such as the solid discharge and the number of moving particles. Analyzing the autocorrelation functions and the probability distributions of our measurements revealed the existence of long-range correlations. For instance, whereas theory predicts a Binomial distribution for the number of moving particles, experiments demonstrated that a negative binomial distribution best fit our data, which emphasized the crucial role played by wide fluctuations. These frequent wide fluctuations stemmed particle entrainment and motion being collective phenomena rather than individual processes, contrary to what is assumed in most theoretical models.

An adaptive substepping explicit integration scheme with a novel loading-unloading decision method is developed here for the non-isothermal unified hardening (UH) model. The non-isothermal UH model includes a convex subloading surface in the $$p$$p---$$q$$q plane and a nonconvex subloading surface in the $$p$$p---$$T$$T plane. Because of the convex/nonconvex subloading surfaces, the conventional loading-unloading decision method used in stress integration schemes may lead to incorrect elasticity/elastoplasticity judgements. In addition, the conventional loading-unloading decision method is unable to determine the division point that separates the elastic segment from the elastoplastic segment. A simple but robust method, the double cosine (DC) method, is proposed in this paper to solve loading-unloading decision problems. The proposed DC method is then embedded into an adaptive substepping explicit integration scheme to implement the non-isothermal UH model. The accuracy and efficiency of the DC method are discussed by comparing the method with the conventional loading-unloading decision method (the CV method) and the root-finding loading-unloading decision method (the RF method). The performance of the proposed scheme with the DC method is also discussed.

In this paper we prove several theorems concerning the motion of a particle in a random environment. The trajectory of a particle is the solution of the differential equation $dx(t)/dt=V(x(t))$, where $V(x) = v + \varepsilon^{1-\alpha} F(x), \; 0\leq\alpha\leq 1,$ $v$ is a constant vector, $F$ is a mean-zero fluctuation field and $\varepsilon^{1-\alpha}$ is a parameter measuring the size of the fluctuations. We show that both in case of a motion of a single particle and of a particle system considered in the macroscopic coordinate system moving along with velocity $v$ [i.e., $x \sim (x-vt)/\varepsilon^{\alpha}, \; t\sim t/\varepsilon^2$] the diffusion approximation holds provided that $F$ is divergence free. Moreover we show how to renormalize trajectories to obtain a similar result for non-divergence-free fields. These results generalize theorems due to Khasminskii and to Kesten and Papanicolaou.

A tendon-driven robot inspired from the bird neck is studied in this paper. The objective is to propose numerical integrations for this robot. The classical explicit and implicit Euler integration schemes can be used on this robot. When the elasticity in the tendons is not considered, these schemes are stable and give similar numerical integration results but the explicit implementation is faster. By considering the dynamics of the robot joints on one hand and the dynamics of the motors on the other hand, we propose two Euler integration schemes, explicit and implicit, that take into account the elasticity in the tendons. These schemes rely on the dynamics of the robot joints on the one hand, and on the dynamics of the motors on the other hand and it links them by the tendon elastic model. We observe that with the tendon elasticity model, the explicit integration becomes unstable, depending on the time step, while the implicit one stays stable. The numerical integration that uses this implicit scheme with tendon elasticity allows one to obtain more precise results, while the model of the system is more realistic. Moreover, the evolution of the tendon elongation during a desired motion can be obtained while they are computed in the integration scheme.

In this work, a 2D pore pressure cohesive zone model is presented to simulate the hydraulic fracture propagation in naturally fractured formation, in which the fracturing process is governed by a bilinear cohesive zone model equipped with Coulomb's friction law and the fluid flow within the hydraulic fracture is described by the lubrication equation. In this model, fluid leak‐off into rock matrix is ignored and a fully explicit temporal integration scheme is adopted to overcome the convergence issue of conventional implicit scheme (eg, Newton‐Raphson method). The advantage of the proposed model is that it does not require any special crossing criterion to determine the interaction behavior when the hydraulic fracture hits the natural fracture. Implementation of the model was described in detail, and then, the model was verified with well‐known analytical solution of KGD problem and criteria of hydraulic fracture crossing natural fracture. The capability of the proposed model to capture the interaction behavior between hydraulic fracture and natural fracture was demonstrated by the good agreement of the modeling result and analytical solution. Several numerical cases were performed to investigate the impact of key factors on fracture network evolution during hydraulic fracturing treatment. Results show that fracture network is not only governed by the spatial distribution of natural fracture, but also greatly affected by the initial hydraulic aperture of natural fracture and in situ stress contrast.

An explicit integration scheme for finite-deformation plasticity in finite-element methods

Unconditionally stable meshless integration of time-domain Maxwell’s curl equations

Explicit integration of a thermo-mechanical model for clays

We present a novel hybrid method to allow large time steps in explicit integrations for the simulation of deformable objects. In explicit integration schemes, the time step is typically limited by the size and the shape of the discretization elements as well as by the material parameters. We propose a two-step strategy to enable large time steps for meshes with elements potentially destabilizing the integration. First, the necessary time step for a stable computation is identified per element using modal analysis. This allows determining which elements have to be handled specially given a desired simulation time step. The identified critical elements are treated by a geometric deformation model, while the remaining ones are simulated with a standard deformation model (in our case, a corotational linear Finite Element Method). In order to achieve a valid deformation behavior, we propose a strategy to determine appropriate parameters for the geometric model. Our hybrid method allows taking much larger time steps than using an explicit Finite Element Method alone. The total computational costs per second are significantly lowered. The proposed scheme is especially useful for simulations requiring interactive mesh updates, such as for instance cutting in surgical simulations.

A GPU-based numerical manifold method for modeling the formation of the excavation damaged zone in deep rock tunnels