Arbitrary Lagrangian-Eulerian Method

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Advantages of Arbitrary Lagrangian-Eulerian Finite Element Techniques

     The arbitrary Lagrangian-Eulerian (ALE) is a finite element formulation in which the computational system is not a prior fixed in space (e.g. Eulerian-based finite element formulations) or attached to material (e.g. Lagrangian-based finite element formulations). ALE-based finite element simulations can alleviate many of the drawbacks that the traditional Lagrangian-based and Eulerian-based finite element simulations have.

     When using the ALE technique in engineering simulations, the computational mesh inside the domains can move arbitrarily to optimize the shapes of elements, while the mesh on the boundaries and interfaces of the domains can move along with materials to precisely track the boundaries and interfaces of a multi-material system. 

     ALE-based finite element formulations can reduce to either Lagrangian-based finite element formulations by equating mesh motion to material motion or Eulerian-based finite element formulations by fixing mesh in space.  Therefore, one finite element code can be used to perform comprehensive engineering simulations, including heat transfer, fluid flow, fluid-structure interactions and metal-manufacturing.


Applications of Arbitrary Lagrangian-Eulerian Finite Element Techniques

     ALE techniques can be applied to many engineering problems, for example,

     In addition, by employing other existing technology, such as identification and modification of topology, adaptive mesh, local remeshing and parallel computation, the robustness, efficiency and application areas of ALE finite element code can be enhanced.  For more information about such related technology, please refer to Development of CRACK3D.


Demonstration of ALE-based Finite Element Simulation

     A general two-dimensional finite element code was developed based on the ALE formulation. This code can be used to perform numerical simulations of two-dimensional and axisymmetric engineering problems associated with large deformation. 

    An example is given below for demonstration of the capabilities and robustness of the ALE-based finite element code.  The general-purpose commercial code ANSYS was used as a post-processing tool to visualize the simulation results.


Simulation of Punch Forging Process of Metal

Animation of mesh motion Animation of Von Mises stress Animation of equivalent plastic strain


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