Computational issues in the Finite Element with Embedded Discontinuity Method based on non-homogenous displacement jump

The performance of continuum elements with Embedded Discontinuities is analysed in the paper with reference to locking-free response. It is well known that in standard 4-node element models subjected to bending spurious shear stresses arise, that cause an increase in the elastic energy. Quadratic elements do not suffer of this problem. A similar behavior is observed when the element is crossed by a discontinuity. In 4-node elements enriched with constant jump a bending deformation results in a significant locking due to the accumulation of shear stress. Such effect has also been observed in elements where a linear approximation of the jump is used, even though they allow to reproduce a rigid body motion. This is due to the fact that in each subelement a linear approximation of the enhanced displacements is present. In order to avoid locking, in the paper additional local shape functions have been introduced in 4-node and 8-node elements enriched with linear displacement jump. The algorithm has been implemented in an original finite element code, named FracSDA8, able to analyze the initiation and growth of interfaces in the continuum. In the paper some numerical analyses developed in FracSDA8 are described, such as a tensile-bending test on a square plate and a three point bending test.