ON A FINITE ELEMENT WITH EMBEDDED DISCONTINUITIES FOR NUMERICAL MODELING OF FRACTURE

A finite element to capture strong discontinuities in fracture simulations is analyzed. The element belongs to the family of symmetric (variationally consistent) elementally enriched finite elements with embedded discontinuities and provides a kinematically optimal description of the strain field. The original element, by Lofti and Shing, is modified to remove the typical failure to pass the patch test. The variational format is set in a rate form so that the resulting formulation is made incremental along the time-like parameter, instead of in total form. As a result, elemental constant stress solutions can be fulfilled in elastic regimes and partially (time-step size dependent) satisfied in the fracture regimes. The resulting element is then expected to increase robustness in comparison with unsymmetrical elements of the same family and not to exhibit stress-locking. The element is implemented in the context of the Continuum Strong Discontinuity Approach (CSDA) using an isotropic continuum damage model and its performance is checked through the three-dimensional numerical simulation of the classical splitting test in fracture mechanics of concrete.