2. Choice of finite elements

We are in the presence of two nodal unknowns: displacements \(u\) and damage \(\alpha\).

We consider functions of forms \({P}^{2}\) for \(u\) and \({P}^{1}\) for \(\alpha\).

The quadratic elements, TRIA6 and QUAD8 for 2D, TETRA10, PENTA15 and HEXA20 for 3D, have been developed. The displacement components are assigned to all the nodes of the element while the damage components are only assigned to the vertex nodes. For greater clarity, element TRIA6 is shown below:

The families of Gauss points of the corresponding linear elements are used, which results in under-integration on the movements. Using the families of Gauss points of quadratic elements would involve over-integration for \(\alpha\) causing untimely oscillations.