Hello All,

Say, I have a huge mesh ( ~ 4 M linear tetrahedron elements) out of which 2 % are distorted.

( Note : Mesh quality is calculated using beta = CR / (3.0 * IR) where CR = circumsphere radius, IR = inscribed sphere radius ; for good elements, beta lies between 1 and 3)

I would like to clarify on the following :

1) A highly distorted element results in an ill-conditioned element stiffness matrix or Jacobian matrix for that element.Although few element stiffness matrices may have bad conditioning, the global stiffness matrix should be well conditioned, resulting in obtaining displacement values of reasonable accuracy. Is that a fair conclusion ? [ please disregard shear locking effect here, axially loaded]

2) Then, the strain and stress values for each element are back calculated from the displacement values. My understanding is : [B] is calculated at a Gauss point and strain is calculated as [B] {u} , stress as [C]{strain}, both of which are dependent on values for each element. For a non linear (large deformation) finite element formulation, [B] takes a very complex form( depends on F) , Is the strain and stress calculation the same as mentioned in the non linear formulations as well ?

Where, [B] :stran -displacement matrix, [C] stiffness matrix in Voigt notation, [F] deformation gradient

3) From my simulations, I did observe that for a highly distorted element, the stress values ( dependent on [B] matrix) were spurious . What I don't clearly understand is how the distortion of the element exactly affects the [B] calculation ?

Any help would be greatly appreciated

Thanks,

Prithivi