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. To overcome this
overstiffening we use reduced integration (for 4-node quads and 8-node hexas 1
integration point in the middle). Reduced integration solves the volumetric
locking both in theory
and tests.
However now there is a new problem: consider a 4-node quad. Move the nodes on
one edge towards each other, and the other edge in the opposite direction, on
both sides with the same amount. The element is now deformed to the shape of a
trapezium, but the integration point (where your starins are measured) which is
in the middle of the element does not feel any of this deformation. Neither the
vertical nor the horizontal direction changed the length and angle of the mid
lines. That means there is now a deformation which produces no strains, hence no
forces to resist. This pattern can grow unbounded, and easily destroy the whole
simulation. This deformation pattern is called hourglass mode, or zero energy
mode, or kinematic mode etc. We have to stabilize the element against
hourglassing and the energy used to counter this is called hourglass
energy.
Below is a youtube video that I found which shows hourglassing in an Ls-Dyna deck.
Hope that helped!
Below is a youtube video that I found which shows hourglassing in an Ls-Dyna deck.
Hope that helped!
Hi.. HOw this Hour glass effect is countered by Hourglass Cards, What actually the card is doing to counter this effect. Is it like adding some pseudo force? if yes, i cannot visualize the actual behavior. A video with hour glass card and without hour glass card would be helpful..
ReplyDeleteThanks a lot for this explanation