# Abaqus – Tips and Tricks Vol 1

## Abaqus – Tips and Tricks: When to use what Elements?

For a 3D stress analysis, ABAQUS offers different typess of linear and quadratic hexahedral elements, a brief description is as below;

1. Linear Hexahedral: C3D8 further subdivided as C3D8R, C3D8I, and C3D8H
2. Quadratic Hexahedral: C3D20 further subdivided as C3D20R, C3D20I, and C3D20H, C3D20RH
3. Linear Tetrahedral: C3D4 further subdivided as C3D4R, and C3D4H
4. Quadratic Tetrahedral: C3D10 further subdivided as C3D10M, C3D10I and C3D10MH
5. Prisms: C3D6 further subdivided as C3D6R, and C3D6H

In three-dimensional (3D) finite element analysis, two types of element shapes are commonly utilized for mesh generation: tetrahedral and hexahedral. While tetrahedral meshing is highly automated, and relatively does a good job at predicting stresses with sufficient mesh refinement, hexahedral meshing commonly requires user intervention and is effort intensive in terms of partitioning. Hexahedral elements are generally preferred over tetrahedral elements because of their superior performance in terms of convergence rate and accuracy of the solution.

The preference for hexahedral elements(linear and uadratic) can be attributed to the fact that linear tetrahedrals originating from triangular elements have stiff formulations and exhibit the phenomena of volumetric and shear locking. Hexahedral elements on the other hand have consistently predicted reasonable foce vs loading (stiffness) conditions, material incompressibility in friction and frictionless contacts. This has led to modeling situations where tetrahedrals and prisms are recommended when there are frictionless contact conditions and when the material incompressibility conditiona can be relaxed to a reasonable degree of assumption.

A general rule of thumb is if the model is relatively simple and you want the most accurate solution in the minimum amount of time then the linear hexahedrals will never disappoint.

Modified second-order tetrahedral elements (C3D10, C3D10M, C3D10MH) all mitigate the problems associated with linear tetrahedral elements. These element offer good convergence rate with a minimum of shear or volumetric locking. Generally, observing the deformed shape will show of shear or volumetric locking and mesh can be modified or refined to remove these effects.

C3D10MH can also be used to model incompressible rubber materials in the hybrid formulation. These variety of elements offer better distribution of surface stresses and the deformed shape and pattern is much better. These elements are robust during finite deformation and uniform contact pressure formulation allows these elements to model contact accurately.

The following are the recommendations from the house of Abaqus(1);

• Minimize mesh distortion as much as possible.
• A minimum of four quadratic elements per 90o should be used around a circular hole.
• A minimum of four elements should be used through the thickness of a structure if first-order, reduced-integration solid elements are used to model bending.

1. Abaqus Theory and Reference Manuals, Dassault Systemes, RI, USA