Improvement of some features of finite elements with embedded discontinuities

• Symmetric FE with embedded discontinuities satisfies kinematics and equilibrium.
• A new definition of the traction dependent on the discontinuity length and angle.
• The release energy is related with the length of the path of the discontinuity.
• Numerical examples illustrate the performance of the proposed symmetric formulation.

This paper shows an analysis of the principal features of finite elements with embedded discontinuities. Particularly, two families of this kind of elements are analyzed, kinematically optimal symmetric and statically and kinematically optimal non-symmetric. The analyzed features are the variational formulation, damage model and how the discontinuity is introduced. A new definition of traction vector for symmetric family, dependent on the discontinuity length and the angle, is given. It is shown that kinematics and equilibrium are satisfied, without the problem of fictitious tractions as stated in the literature. To show the validity of this symmetric formulation, representative numerical examples illustrating the performance of the proposed formulation are presented.