Arbitrary Lagrangian-Eulerian Finite Element Formulation Research Articles

An arbitrary Lagrangian–Eulerian finite element formulation for a poroelasticity problem stemming from mixture theory

A finite element formulation is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid. The governing equations stem from mixture theory and the application is motivated by the study of interstitial fluid flow in brain tissue. The formulation is based on the adoption of an arbitrary Lagrangian–Eulerian (ALE) perspective. We focus on a flow regime in which inertia forces are negligible. The stability and convergence of the formulation is discussed, and numerical results demonstrate agreement with the theory.

Biomechanical parameters of the brain under blast loads with and without helmets

Computational results on biomechanics of brain for a human head model with and without a helmet under the blast loading are presented. The blast propagation is simulated using the hybrid method combining the multi-material arbitrary Lagrangian-Eulerian finite element formulation and empirical blast load equations. A three dimensional model of a combat helmet is integrated with a validated 50th percentile human head-neck model. The blast-head model interactions are modelled using a penalty-based fluid-structure interaction algorithm. Biomechanical data parameters of the head/brain such as intracranial pressures and maximum shear stress are recorded and compared both with and without a helmet. The results are studied the severity of the blast under different values for the high explosive explosions and the efficiency of the wearing ballistic impact under the blast situation.

An ALE finite element method for baffled fuel container in Yawing motion

A computational analysis of engineering problems with moving domain or/and boundary according to either Lagrangian or Eulerian approach may encounter inherent numerical difficulties, the extreme mesh distortion in the former and the material boundary indistinctness in the latter. In order to overcome such defects in classical numerical approaches, the ALE (arbitrary Lagrangian Eulerian) method is widely being adopted in which the finite element mesh moves with arbitrary velocity. This paper is concerned with the ALE finite element formulation, aiming at the dynamic response analysis of baffled fuel-storage container in yawing motion, for which the coupled time integration scheme, the remeshing and smoothing algorithm and the mesh velocity determination are addressed. Numerical simulation illustrating theoretical works is also presented.

Analysis of fluid-structure interaction by an arbitrary Lagrangian-Eulerian finite element formulation

In this paper, the interaction fluid–rigid body is analysed by a finite element procedure that incorporates the arbitrary Lagrangian–Eulerian (ALE) method into a well-known two-step projection scheme. The flow is assumed to be two-dimensional, incompressible and viscous, with no turbulence models being included. The flow past a circular cylinder at ℛℯ=200 is first analysed, for fixed and oscillating conditions. The dependence of lock-in upon the shift between the mechanical and the Strouhal frequencies, for a given amplitude of forced vibration, is illustrated. The aerodynamic forces and the wake geometry are compared for locked-in conditions with different driving frequencies. The behaviour of a rectangular cylinder (B/D=4) at ℛℯ=500 (based on height D) is also analysed. The flutter derivatives associated with aerodynamic damping (H1* and A2* in Scanlan's notation) are evaluated by the free oscillation method for several values of reduced flow speed above the Strouhal one (namely for 3≤U*≤8). Torsional flutter was attained at U*≥5, with all the other situations showing stable characteristics. Copyright © 1999 John Wiley & Sons, Ltd.

Analysis of fluid–structure interaction by an arbitrary Lagrangian–Eulerian finite element formulation

Analysis of fluid–structure interaction by an arbitrary Lagrangian–Eulerian finite element formulation

An arbitrary Lagrangian-Eulerian finite element method for incompressible hyperelasticity

In this paper, we present an arbitrary Lagrangian-Eulerian (ALE) formulation for large deformation analysis of incompressible hyperelastic materials, which are often employed for modeling rubber-like materials. Conventional ALE formulations, which have been successfully applied to not only fluids but also solid materials with rate constitutive equations, are usually described in velocity-based variables. Thus, in the application of such formulations to hyperelasticity, the velocity needs to be integrated in the time variable to obtain the deformation gradient necessarily appearing in hyperelastic material modeling. However, such integration is expensive and difficult to evaluate precisely. From such aspects, we propose a new ALE finite element formulation which directly incorporates the total deformation to avoid integration of velocity-based variables and can deal with arbitrary mesh motion by considering the variation of geometric mappings. Some basic numerical results are also given to illustrate the validity of our formulation.