Mesh motion techniques for the ALE formulation in 3D large deformation problems

Efficient mesh motion techniques are a key issue to achieve satisfactory results in the arbitrary Lagrangian–Eulerian (ALE) finite element formulation when simulating large deformation problems such as metal‐forming. In the updated Lagrangian (UL) formulation, mesh and material movement are attached and an excessive mesh distortion usually appears. By uncoupling mesh movement from material movement, the ALE formulation can relocate the mesh to avoid distortion. To facilitate the calculation process, the ALE operator is split into two steps at each analysis time step: UL step (where deformation due to loading is calculated without convective terms) and Eulerian step (where mesh motion is applied). In this work, mesh motion is performed by new nodal relocation methods, developed for eight‐node hexahedral elements, which can move internal and boundary nodes, improving and concentrating the mesh in critical zones. After mesh motion, data is transferred from the UL mesh to the relocated mesh using an expansion of stresses in a Taylor's series. Two numerical applications are presented, comparing results of UL and ALE formulation with results found in the literature. Copyright © 2004 John Wiley & Sons, Ltd.     

A novel approach based on ALE and delamination fracture mechanics for multilayered composite beams

A novel approach able to predict debonding or fracture phenomena in multilayered composite beams is proposed. The structural model is based on the first-order shear deformable laminated beam theory and moving mesh strategy developed in the framework of Arbitrary Lagrangian–Eulerian (ALE) formulation. The former is utilized to evaluate fracture parameters by using a multilayer approach, in which a low number of interface elements are introduced along the thickness, whereas the latter is utilized to reproduce crack tip motion due to the crack extension produced by moving boundaries. The model is able to avoid computational complexities introduced by an explicit crack representation in bi-dimensional structures, in which typically high computational efforts are expected for handling moving boundaries. To this aim, a moving mesh strategy is proposed for the first time in the context of beam modeling based on a multilayered configuration. Such an approach, essentially based on ALE formulation, is able to reproduce interfacial crack paths by using a low number of computational elements. The numerical method is proposed in the framework of the finite element formulation for a quasi-static or dynamic evolution of the crack tip front. In order to investigate the accuracy and to validate the proposed methodology, comparisons with experimental data and existing formulations available from the literature are developed. Moreover, a parametric study in the framework of dynamic fracture is developed to investigate the capability of the proposed model to reproduce more complex loading cases.     

The fixed‐mesh ALE approach applied to solid mechanics and fluid–structure interaction problems

In this paper we propose a method to solve Solid Mechanics and fluid–structure interaction problems using always a fixed background mesh for the spatial discretization. The main feature of the method is that it properly accounts for the advection of information as the domain boundary evolves. To achieve this, we use an Arbitrary Lagrangian–Eulerian (ALE) framework, the distinctive characteristic being that at each time step results are projected onto a fixed, background mesh. For solid mechanics problems subject to large strains, the fixed‐mesh (FM)‐ALE method avoids the element stretching found in fully Lagrangian approaches. For FSI problems, FM‐ALE allows for the use of a single background mesh to solve both the fluid and the structure. Copyright © 2009 John Wiley & Sons, Ltd.     

An arbitrary Lagrangian–Eulerian finite element method for finite strain plasticity

This paper presents a new arbitrary Lagrangian–Eulerian (ALE) finite element formulation for finite strain plasticity in non‐linear solid mechanics. We consider the models of finite strain plasticity defined by the multiplicative decomposition of the deformation gradient in an elastic and a plastic part ( F = F ^e F ^p), with the stresses given by a hyperelastic relation. In contrast with more classical ALE approaches based on plastic models of the hypoelastic type, the ALE formulation presented herein considers the direct interpolation of the motion of the material with respect to the reference mesh together with the motion of the spatial mesh with respect to this same reference mesh. This aspect is shown to be crucial for a simple treatment of the advection of the plastic internal variables and dynamic variables. In fact, this advection is carried out exactly through a particle tracking in the reference mesh, a calculation that can be accomplished very efficiently with the use of the connectivity graph of the fixed reference mesh. A staggered scheme defined by three steps (the smoothing, the advection and the Lagrangian steps) leads to an efficient method for the solution of the resulting equations. We present several representative numerical simulations that illustrate the performance of the newly proposed methods. Both quasi‐static and dynamic conditions are considered in these model examples. Copyright © 2003 John Wiley & Sons, Ltd.     

Arbitrary Lagrangian–Eulerian method in plasticity of pressure-sensitive material: application to powder forming processes

In this paper, an application of Arbitrary Lagrangian–Eulerian (ALE) method is presented in plasticity behavior of pressure-sensitive material, with special reference to large deformation analysis of powder compaction process. In ALE technique, the reference configuration is used for describing the motion, instead of material configuration in Lagrangian, and spatial configuration in Eulerian formulation. The convective term is used to reflect the relative motion between the mesh and the material. Each time-step is divided into the Lagrangian phase and Eulerian phase. The convection term is neglected in the material phase, which is identical to a time-step in a standard Lagrangian analysis. The stresses and plastic internal variables are converted to account the relative mesh-material motion in the convection phase. The ALE formulation is then performed within the framework of a three-invariant cap plasticity model in order to predict the non-uniform density distribution during the large deformation of powder die pressing. The plasticity model is based on a hardening rule with the isotropic and kinematic material functions. The constitutive elasto-plastic matrix and its components are derived by using the definition of yield surface, material functions and non-linear elastic behavior, as function of hardening parameters. Finally, the numerical examples are performed to illustrate the applicability of the computational algorithm in modeling of powder forming process and the results are compared with those obtained from Lagrangian simulation in order to demonstrate the accuracy of proposed model.     

Stress integration and mesh refinement for large deformation in geomechanics

This paper first discusses alternative stress integration schemes in numerical solutions to large‐ deformation problems in hardening materials. Three common numerical methods, i.e. the total‐Lagrangian (TL), the updated‐Lagrangian (UL) and the arbitrary Lagrangian–Eulerian (ALE) methods, are discussed. The UL and the ALE methods are further complicated with three different stress integration schemes. The objectivity of these schemes is discussed. The ALE method presented in this paper is based on the operator‐split technique where the analysis is carried out in two steps; an UL step followed by an Eulerian step. This paper also introduces a new method for mesh refinement in the ALE method. Using the known displacements at domain boundaries and material interfaces as prescribed displacements, the problem is re‐analysed by assuming linear elasticity and the deformed mesh resulting from such an analysis is then used as the new mesh in the second step of the ALE method. It is shown that this repeated elastic analysis is actually more efficient than mesh generation and it can be used for general cases regardless of problem dimension and problem topology. The relative performance of the TL, UL and ALE methods is investigated through the analyses of some classic geotechnical problems. Copyright © 2005 John Wiley & Sons, Ltd.     

Updated Lagrangian/Arbitrary Lagrangian–Eulerian framework for interaction between a compressible neo‐Hookean structure and an incompressible fluid

We propose a numerical method for a fluid–structure interaction problem. The material of the structure is homogeneous, isotropic, and it can be described by the compressible neo‐Hookean constitutive equation, while the fluid is governed by the Navier–Stokes equations. Our study does not use turbulence model. Updated Lagrangian method is used for the structure and fluid equations are written in Arbitrary Lagrangian–Eulerian coordinates. One global moving mesh is employed for the fluid–structure domain, where the fluid–structure interface is an ‘interior boundary’ of the global mesh. At each time step, we solve a monolithic system of unknown velocity and pressure defined on the global mesh. The continuity of velocity at the interface is automatically satisfied, while the continuity of stress does not appear explicitly in the monolithic fluid–structure system. This method is very fast because at each time step, we solve only one linear system. This linear system was obtained by the linearization of the structure around the previous position in the updated Lagrangian formulation and by the employment of a linear convection term for the fluid. Numerical results are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

A hybrid variational‐collocation immersed method for fluid‐structure interaction using unstructured T‐splines

We present a hybrid variational‐collocation, immersed, and fully‐implicit formulation for fluid‐structure interaction (FSI) using unstructured T‐splines. In our immersed methodology, we define an Eulerian mesh on the whole computational domain and a Lagrangian mesh on the solid domain, which moves arbitrarily on top of the Eulerian mesh. Mathematically, the problem reduces to solving three equations, namely, the linear momentum balance, mass conservation, and a condition of kinematic compatibility between the Lagrangian displacement and the Eulerian velocity. We use a weighted residual approach for the linear momentum and mass conservation equations, but we discretize directly the strong form of the kinematic relation, deriving a hybrid variational‐collocation method. We use T‐splines for both the spatial discretization and the information transfer between the Eulerian mesh and the Lagrangian mesh. T‐splines offer us two main advantages against non‐uniform rational B‐splines: they can be locally refined and they are unstructured. The generalized‐α method is used for the time discretization. We validate our formulation with a common FSI benchmark problem achieving excellent agreement with the theoretical solution. An example involving a partially immersed solid is also solved. The numerical examples show how the use of T‐junctions and extraordinary nodes results in an accurate, efficient, and flexible method. Copyright © 2015 John Wiley & Sons, Ltd.     

A hierarchical sequential ALE poromechanics model for tire‐soil‐water interaction on fluid‐infiltrated roads

This paper introduces a hierarchical sequential arbitrary Lagrangian‐Eulerian (ALE) model for predicting the tire‐soil‐water interaction at finite deformations. Using the ALE framework, the interaction between a rolling pneumatic tire and the fluid‐infiltrated soil underneath will be captured numerically. The road is assumed to be a fully saturated two‐phase porous medium. The constitutive response of the tire and the solid skeleton of the porous medium is idealized as hyperelastic. Meanwhile, the interaction between tire, soil, and water will be simulated via a hierarchical operator‐split algorithm. A salient feature of the proposed framework is the steady state rolling framework. While the finite element mesh of the soil is fixed to a reference frame and moves with the tire, the solid and fluid constituents of the soil are flowing through the mesh in the ALE model according to the rolling speed of the tire. This treatment leads to an elegant and computationally efficient formulation to investigate the tire‐soil‐water interaction both close to the contact and in the far field. The presented ALE model for tire‐soil‐water interaction provides the essential basis for future applications, for example, to a path‐dependent frictional‐cohesive response of the consolidating soil and unsaturated soil, respectively. Copyright © 2017 John Wiley & Sons, Ltd.     

Efficient ALE mesh management for 3D quasi‐Eulerian problems

In computational solid mechanics, the ALE formalism can be very useful to reduce the size of finite element models of continuous forming operations such as roll forming. The mesh of these ALE models is said to be quasi‐Eulerian because the nodes remain almost fixed—or almost Eulerian—in the main process direction, although they are required to move in the orthogonal plane in order to follow the lateral displacements of the solid. This paper extensively presents a complete node relocation procedure dedicated to such ALE models. The discussion focusses on quadrangular and hexahedral meshes with local refinements. The main concern of this work is the preservation of the geometrical features and the shape of the free boundaries of the mesh. With this aim in view, each type of nodes (corner, edge, surface and volume) is treated sequentially with dedicated algorithms. A special care is given to highly curved 3D surfaces for which a CPU‐efficient smoothing technique is proposed. This new method relies on a spline surface reconstruction, on a very fast weighted Laplacian smoother with original weights and on a robust reprojection algorithm. The overall consistency of this mesh management procedure is finally demonstrated in two numerical applications. The first one is a 2D ALE simulation of a drawbead, which provides similar results to an equivalent Lagrangian model yet is much faster. The second application is a 3D industrial ALE model of a 16‐stand roll forming line. In this case, all attempts to perform the same simulation by using the Lagrangian formalism have been unsuccessful. Copyright © 2012 John Wiley & Sons, Ltd.     

A multiscale stabilized ALE formulation for incompressible flows with moving boundaries

This paper presents a variational multiscale stabilized finite element method for the incompressible Navier–Stokes equations. The formulation is written in an Arbitrary Lagrangian–Eulerian (ALE) frame to model problems with moving boundaries. The structure of the stabilization parameter is derived via the solution of the fine-scale problem that is furnished by the variational multiscale framework. The projection of the fine-scale solution onto the coarse-scale space leads to the new stabilized method. The formulation is integrated with a mesh moving scheme that adapts the computational grid to the evolving fluid boundaries and fluid-solid interfaces. Several test problems are presented to show the accuracy and stability of the new formulation.     

ALE stress update for transient and quasistatic processes

A key issue in Arbitrary Lagrangian–Eulerian (ALE) non-linear solid mechanics is the correct treatment of the convection terms in the constitutive equation. These convection terms, which reflect the relative motion between the finite element mesh and the material, are found for both transient and quasistatic ALE analyses. It is shown in this paper that the same explicit algorithms can be employed to handle the convection terms of the constitutive equation for both types of analyses. The most attractive consequence of this fact is that a quasistatic simulation can be upgraded from Updated Lagrangian (UL) to ALE without significant extra computational cost. These ideas are illustrated by means of two numerical examples. © 1998 John Wiley & Sons, Ltd.     

Arbitrary Lagrangian–Eulerian finite element analysis of strain localization in transient problems

Non-local models guaranty that finite element computations on strain softening materials remain sound up to failure from a theoretical and computational viewpoint. The non-locality prevents strain localization with zero global dissipation of energy, and consequently finite element calculations converge upon mesh refinements to non-zero width localization zones. One of the major drawbacks of these models is that the element size needed in order to capture the localization zone must be smaller than the internal length. Hence, the total number of degrees of freedom becomes rapidly prohibitive for most engineering applications and there is an obvious need for mesh adaptivity. This paper deals with the application of the arbitrary Lagrangian–Eulerian (ALE) formulation, well known in hydrodynamics and fluid–structure interaction problems, to transient strain localization in a non-local damageable material. It is shown that the ALE formulation which is employed in large boundary motion problems can also be well suited for non-linear transient analysis of softening materials where localization bands appear. The remeshing strategy is based on the equidistribution of an indicator that quantifies the interelement jump of a selected state variable. Two well known one-dimensional examples illustrate the capabilities of this technique: the first one deals with localization due to a propagating wave in a bar, and the second one studies the wave propagation in a hollow sphere.     

Modelling the structural response of GLARE panels to blast load

This paper deals with the structural response of fully-clamped quadrangular GLARE panels subjected to an intense air-blast load using the commercial finite element software, LS-DYNA. A cohesive tie-break algorithm is implemented to model interfacial debonding between adjacent plies. The blast loads was simulated using a ConWep blast algorithm and a multi-material ALE formulation with fluid–structure interaction to determine the performance of each method. Numerical model validation have been performed considering case studies of GLARE panels subjected to spherical explosive charges of C-4, for which experimental data on the back face-displacement and post-damage observations were available. Excellent agreement of mid-point deflections and evidence of severe yield line deformation were presented and discussed against the performed blast tests.     

考虑强液-固耦合效应的发动机液阻悬置动态特性仿真研究

以某轿车发动机液阻悬置为研究对象,运用INTESIM强液-固有限元方法建立了其动态特性分析的强液-固耦合有限元模型,仿真分析了其静、动刚度特性,并和实验结果进行了对比,验证了仿真研究结果的有效性,说明利用INTESIM强液-固耦合有限元方法可以有效的仿真液阻悬置的动态特性。