Smoothed reduction of fracture mechanics solutions to 1D cracked models

Simulating the behaviour of structural members with defects and cracks is an important task in various engineering fields. In fracture mechanics the primary objective is to determine the extreme stress field near the crack that may produce unstable crack growth. In the field of structural health monitoring, the variation of measurable structure’s responses due to the existence of cracks is of interest. These responses may refer to static or dynamic strains and displacements, eigenfrequencies and/or eigenmodes etc. A new representation model for cracked bars based on the introduction of a stiffness function derived from the analytical solution of a cracked plate is presented herein. The new model, as shown in the test examples considered in the manuscript, captures with satisfactory accuracy effects that are revealed in the 2 or 3 dimensional numerical simulation like the strain field variation near a crack, while preserving simplicity and computational efficiency.