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What are Hourglassing and ALE?

dear friends

can you explain "hourglassing" and "ale" exactly?

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dear friends

can you explain "hourglassing" and "ale" exactly?

Hello Amiratrian!

ALE: it is a mixture of Lagrangian and Eulerian discretization. Lagrangian is when the mesh deforms with the matertial, and Eulerian is when you have a fixed mesh in the space, adn the material flows from one cell to another. Lagrangian is easier to handle (particularly the definition of boundary conditions) but in cases with large deformation the mesh could be highly distorted, and the calculation becomes inaccurate, or even fail. In Eulerian the material flows within the cells, hence the accuracy is better for large deformation, because there is no mesh disortion at all. However, the treatment of BC is not an easy task, and the flow of material requires convection algorithms. Traditionally Lagrangian is more suited for solid mechanics, and Eulerian for fluid mechanics, but recently Eulerian is more involved in large deformation solid mechanics. ALE (Arbitrary Lagrangian-Eulerian) is a mixture of both, where after a lagrangian deformation the boundaries of the elements (within an ALE-region) are moved  - so there is material transport across the boundaries (eulerian) - and the distortion of the elements does not become extensive. This procedure is made in every 1-10 timestep, depending on the simulation. ALE combines the advantage of both methods: you can use the easy BC-definition on the outer edge of the ALE-region (which is lagrangian), and the moving element edges within the ALE-region helps to provide reasonable accuracy. Ideally suited for metal forming, where the large deformation could cause severe distortion.

Hourglassing: the standard numerical integration (e.g. 2x2 Gaussian quadrature for a bilinear quad, 2x2x2 for a trilinear hexa) has some flaws when combined with incompressible material. The  displacements in the mesh are orders of magnitude smaller than in the reality. This is called volumetric locking. Incompressibility is not as rare as one would think, since e.g. most plastic matrial models or many hyperelastic material models assume isochoric deformation. To cure this overstiffening we use reduced integration (for 4-node quads and 8-node hexas 1 integration point in the middle). Theory and tests show that reduced integration solves the volumetric lockin. But with this procedure we introduce another problem: consider a 4-node quad. Move the nodes on the lower edge towards each other, and on the upper edge in the other direction, on both side with the same amount. What you now have is a trapezoid, so your element is deformed. But your integration point (where your starins are measured) is in the middle of the element, and it did not feel anything of this deformation. Neither in the vertical nor in the horizontal direction changed the length and angle of your middle lines! So you have a deformation which produces no strains, hence no forces to resist. This pattern can grow unbounded, and easily destroy your whole simulation. This deformation pattern called hourglass mode, or zero energy mode, or kinematic mode etc. Bottom line is you have to stabilize your element against hourglassing, so you have to build in some artificial stiffness to prevent this kind of deformation - up to a certain level, because beam bending uses this deformation. There are several methods for this, you should check some textbooks.

Both topics are thoroughly discussed in Belytschko's book (Nonlinear Finite Elements for Continua and Structures), far better than I have described them. However I hope, I gave you some insight.

Best regards,

Andras

 

Matt Lewis's picture

I would just like to add that drinking ale from an hourglass is a thoroughly bad idea.

 Matt Lewis
Los Alamos, New Mexico

Hi,

I wonder if anyone know how to apply ALE in abaqus/explicit for microstructure (two different material region) with or without cohesive element between them.

Best Regards 

Sir/Madam,

I am Dipak kumar doing work in thermal fatigue in thermal barrier coatings sysetm.I am using Abaqus for simulating.In material properties data, what is power law multiplier,Eq. stress order and Time order under plasticity conditions.We have already creep exponent and creep prefactor terms as a function of temperatures.

Sir/Madam,

what is selection criteria of 4 noded plane 13 element in Abaqus?4 noded plane 13 element is mantioned in Ansys.

Thank you

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