A complete finite element treatment for the fully coupled implicit ALE formulation

Multiphysics numerical modelling of backward flow forming process of AISI 5140 steel

Computational fluid dynamics (CFD) is increasingly becoming the tool of choice for researchers and engineers facing complex fluid flow problems. One area of CFD that has attracted significant attention in recent years is the development of meshless or mesh-free methods[1]. These methods have so far been used in many applications like fracture mechanics, astrophysics and fluid flow. The key advantage of meshless methods over mesh-based methods like finite volume (FV) and finite element (FE) methods is its non-requirement of pre-specified connectivity between nodes in order to derive approximation and interpolation. This leads to the ability of finite difference (FD) methods to treat irregular domains and boundaries. A direct result of this is another advantage of mesh-free methods having the adaptability for problems involving large movement or wholesale motion of boundaries or embedded bodies. In this area, it has the edge over composite or overset grid methods in being able to use only one coordinate frame.A convecting meshless scheme for boundary driven fluid flow is described. This scheme can be applied to self-propulsion problems, or, in general, flows involving motion of rigid or deformable bodies embedded within the flow.The generalized finite difference method[2] (GFD) was chosen this scheme. A meshless cloud of nodes is embedded around the body surface along with the structured Cartesian background nodes for the entire flow field. By incorporating a subdomain for each node and its neighbours, the use of Taylor series expansion enables the derivatives to be found. Two forms of incompressible momentum equations are used: the standard Eulerian form in primitive variables for the structured nodes and the Arbitrary Lagrangian-Eulerian (ALE) form for the meshless cloud of nodes. GFD with moving least squares approximation is used for spatial discretization of the convecting meshless nodes. The projection method with Crank-Nicolson discretization is used to achieve second order accurate time discretization. Following prescribed body motion or fluid structure interaction, the meshless cloud acquire new locations in the next time step and the momentum equations in ALE form can then be solved.Test cases were performed to verify code usability and method accuracy and convergence. The simulation of the decaying vortex has been a popular benchmark for the gauging of accuracy. Basically the exact solutions of the time-dependent function values are known and both residues and absolute errors were calculated. Solving using different grid sizes proved the present method to be of second order spatial accuracy. The meshless method was then tried on the driven cavity flow at Reynolds number 1000. The results were well-compared with popular benchmark results[4]. In considering the effects of implementing the convecting meshless nodes across a normal flow field, the decaying vortex was again simulated, with a moving patch of nodes within the Cartesian field. The residues were well controlled and the errors were not significantly increased. Finally, a couple of external flows cases were simulated, basically on a flow past a stationary bluff body and a flapping ellipse inside an enclosed body of fluid.Future works in the pipeline include writing a parallel code for larger scale simulation and simulating oscillating cylinders and flapping of elliptic aerofoil(s).

Abstract. Material Extrusion (MEX) and by extension Fused Deposition Modeling (FDM) is a popular Additive Manufacturing (AM) process used to fabricate complex parts. FDM as of recent is no longer solely utilized for prototyping parts but also used for producing functional components in industrial and research applications. The investigation of material properties of these FDM parts by experimental means is a time-consuming task. Therefore, the use of numerical simulation methods is highly required. Since 1993, various Finite Element Analysis (FEA) models are found in literature attempting to effectively simulate FDM parts utilizing many formulations, each with their pros and cons. The present study aims to compare Lagrangian and Arbitrary Lagrangian-Eulerian (ALE) finite element formulations in simulating tensile loading for FDM parts. The efficiency and precision of the aforementioned methods is evaluated in the numerical simulation of the tensile loading of an ASTM D638 standard geometry ABS specimen utilizing both ABAQUS/Explicit and ABAQUS/Standard. Utilizing a paper from the literature for experimental validation, this study additionally provides insight into explicit and implicit models’ computational efficiency, focusing on the advantages of explicit models for this application. The effects of mesh element type and size on results are also studied for each method. Based on these results, some useful guidelines for selecting the most suitable model of tensile loaded FDM parts are presented.

The numerical analysis of rolling contact for rubber materials is a challenging task, especially due to the many nonlinearities inherent to the material, large deformations, friction, and energy dissipation, among others. Industrial applications can be found in ball bearings, rollers, and most commonly in tires of vehicles, applications where reliable numerical simulations lead to the improvement of durability, performance and safety. While a transient analysis stands as a practical and powerful tool for the simulation of rotating bodies, the large amount of computational resources required represents its biggest disadvantage. An alternative frequently used lays in a steady state simulation by means of an Arbitrary Lagrangian Eulerian (ALE) formulation, where the rotational velocity and axial loads are assumed to remain constant. Within this framework, the reference configuration is neither attached to the material particles nor fixed in space and special attention should be paid to the history variables of inelastic materials. In this work, a viscoelastic material model is implemented in an in‐house finite element code, based on a generalized Maxwell model. The implementation takes into consideration the contribution of all elements connected in circumferential direction and a consistent linearization is made for each of them, leading to an assembled stiffness matrix with more non‐zero values than a standard one. This approach is combined with smeared reinforcement embedded in base elements. The reinforcing layers are described by a hyperelastic material model, providing additional advantages for the modeling and simulation of reinforced rollers and tires. Numerical results for different examples show the capabilities of this implementation and the efficiency of the numerical algorithms is discussed. Important remarks and an outlook for further research concludes this presentation. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Abstract. This work proposes a new FE model to predict dynamic crack propagation mechanisms in quasi-brittle materials. The numerical strategy uses a Moving Mesh (MM) technique consistent with the Arbitrary Lagrangian-Eulerian (ALE) formulation to reproduce the variation of the geometry of the computational domain caused by dynamically growing cracks. Specifically, the motion of the mesh nodes takes place consistently with conditions dictated by classic Fracture Mechanics, which provide conditions concerning the direction of propagation and the velocity of advancing cracks. As a remarkable key novelty, the proposed method introduces the ALE formulation of the M-integral for extracting Dynamic Stress Intensity Factors (DSIFs) at a moving crack front. This formulation allows extracting fracture variables on deforming elements without losing accuracy. Comparisons with analytical and numerical data are proposed to assess the validity and efficiency of the proposed strategy.

An arbitrary Lagrangian-Eulerian (ALE) approach is used to model the orthogonal metal cutting in a steady state situation. The thermomechanical model includes the effects of elasticity, plasticity, strain rate, large strains and friction with heat generated between the tool and the chip. The ALE formulation can combine the advantages of both the Eulerian and Lagrangian approaches in a single description. Particularly, problems linked to the free surface in a Eulerian description and those linked to severe mesh distortions in a Lagrangian one can be solved by this formulation. The ALE governing equations are briefly reviewed in this paper; finite element and finite volume methods are used for the discretization of the conservation equations and an explicit time integration is adopted. Only the steady state solution is required; the ALE formulation is exploited to update the free and the contact surfaces. The model predicts the thermomechanical quantities, the chip geometry and the cutting forces from the cutting data and the material and friction parameters. Cutting experiments were performed with 42CD4 steel and comparisons of experimental tool forces and chip geometry with the numerical results are presented.

Fluid–structure interaction with ALE formulation and skeleton-based structural models

Thanks to their properties of superelasticity and shape memory effects, SMA wires are often considered for the design of damping devices or actuators coupled to pulleys. In order to dimension such devices for commercialization, it is necessary to develop reliable, robust and fast numerical tools. To this end, simplifying the management of the wire/pulley contact using an Arbitrary Lagrangian–Eulerian (ALE) formulation is an original and effective solution. In this work, the wires are modeled by three-dimensional truss thermo-mechanical finite elements associated with a superelastic law. For each node, the curvilinear abscissa is used as an additional degree of freedom in order to deal with material flow from one element to another. After presenting the ALE formalism and the necessary precautions (advection of variables), as well as the material behavior and thermo-mechanical contact laws at the pulleys, elementary validation tests are studied. Finally, two devices taken from the literature are modeled using the ALE formalism. The results obtained demonstrate the relevance and effectiveness of the approach adopted, as well as the importance of not neglecting friction at the pulleys and thermal effects on the material mechanical response.

<p>We present a versatile open-source FEM-based multi-physics numerical code GALES for volcanic and general-purpose problems. The code is developed/applied to a suite of problems in magma and volcano dynamics. The software is written in modern C++ and is parallelized using OpenMPI and  Trilinos libraries. GALES comprises several advanced solvers for 2D and 3D problems dealing with heat transfer, compressible to incompressible mono and multi-fluid flows in Eulerian and Arbitrary Lagrangian-Eulerian (ALE) formulations, Elastic (static and dynamic) deformation of solids and fluid-solid interaction. Fluid solvers account for both Newtonian and non-Newtonian rheologies. Solvers account for transient as well as steady problems. Non-linear problems are linearized using Newton's method. All solvers have been thoroughly verified and validated on standard benchmarks. The software is regularly used for high-performance computing (HPC) on our local cluster machines at INGV, Pisa, Italy. Recently, we analyzed the performance of the code by a series of strong-scaling tests conducted on the Marenostrum supercomputer at the Barcelona Supercomputing Centre (BSC) up to 12288 cores. The results revealed a computational speedup close to ideal and above satisfactory levels as long as the element/core ratio is sufficiently large, making GALES an excellent choice for utilizing HPC resources efficiently for complex magma flow and rock dynamics problems.</p>

Due to the significant health and economic impact of blood vessel diseases on modern society, its analysis is becoming of increasing importance for the medical sciences. The complexity of the vascular system, its dynamics and material characteristics all make it an ideal candidate for analysis through fluid structure interaction (FSI) simulations. FSI is a relatively new approach in numerical analysis and enables the multi-physical analysis of problems, yielding a higher accuracy of results than could be possible when using a single physics code to analyse the same category of problems. This paper introduces the concepts behind the Arbitrary Lagrangian Eulerian (ALE) formulation using the penalty coupling method. It moves on to present a validation case and compares it to available simulation results from the literature using a different FSI method. Results were found to correspond well to the comparison case as well as basic theory.

In order to reveal the adjustment principle of prestressed cutting on the residual stress of hardened bearing steel GCr15, a three-dimensional thermal elastic-viscoplastic finite element model was developed using an Arbitrary Lagrangian Eulerian (ALE) formulation. Several key simulation techniques including the material constitutive model, constitutive damage law and contact with friction were discussed, simulation of chip formation during prestressed cutting was successfully conducted. At the prestresses of 0 MPa, 341 MPa and 568 MPa, distributions of residual stress on machined surface were simulated and experimentally verified. The results indicated that residual compressive stress on machined surface were achieved and actively adjusted by utilizing the prestressed cutting method; meanwhile, within the elastic limit of bearing steel material, the higher applied prestress leads to the more prominent compressive residual stress in the surface layer and subsequently the higher fatigue resistance of the part.

Unmanned surface vehicles (USVs) have great application prospects in defense, environmental surveillance and offshore energy due to their cost-effectiveness and long-duration mission ability. The structural safety issues induced by the prolonged cyclic wave loading on such small-sized marine structures, such as fatigue failure mechanism, represent an important research topic. In order to characterize the loading process, a piston-type numerical wave flume with wave absorption setting is constructed using the Arbitrary Lagrangian Eulerian (ALE) formulation, and the fluid–structure interaction (FSI) simulations are performed. Simulated wave profiles are measured and compared with corresponding analytical wave solutions to verify the accuracy of target waves. The wave absorption effect is verified by comparing the velocities of water particles in different water regions. Then, different impact scenarios are performed by applying a range of the applicable target waves. Simulated wave forms, impact scenes along with the computed wave load data are presented, and the impact process is analyzed. As a result, the FSI simulations demonstrate cyclic loading characteristics of small-sized floating structures subjected to wave impacts, and the constructed ALE numerical wave flume possesses the extensibility for the simulation of nonlinear water wave impact scenarios.

A 2D Finite Element Model set up using the Arbitrary Lagrangian Eulerian (A.L.E) formulation proposed in Abaqus/Explicit (v6.4) is employed to predict serrated chip formation during cutting process. No artificial criterion is employed to create the chip or to initiate serrated chip formation. The sensitivity of serrated chip prediction to numerical and process parameters is analyzed in this paper. Experimental tests in orthogonal cutting conditions on machining of AISI-4140 with coated and uncoated cemented-carbide inserts were carried out to validate numerical results. They showed significant influence of cutting speed and rake angle on the serrated chip phenomena. The comparison between numerical and experimental results showed a good qualitative agreement and underlined the outstanding influence of the element dimensions employed in Finite Element Modeling (F.E.M.) tests.

An adaptive mesh rezoning scheme for moving boundary flows and fluid–structure interaction

A comparative study of the opening and closing process of two types of mechanical heart valves using ALE finite element method