Fig. 7.

Application of the recovered connection to a series of new fracture mechanics problems. (A) A prenotched microcantilever, with a modified pentagonal cross-section, is loaded at one end. It is desired to determine the ratio of the stress intensity factor at the crack tip, to the external load, i.e., ${\mathrm{\Gamma }}_{\theta }=K_I/P$. (B) The new problems are formed based on the original one (in Fig. 1) by relaxing the constraint on the bottom angle, $2\theta$, of the pentagonal cross-section. Note that the modified pentagonal cross-section falls in between two rectangular cross-sections. (C) The recovered connection (Eq. 8) is demonstrated to be applicable to these new problems, with ${\mathrm{\Gamma }}_{\pm }$ being modified accordingly. The difference between the prediction by Eq. 8 and the simulation results is less than 10% for different angles, $\theta$, and different configurations, as listed in Table 1.