Effect Of Memory And Reinforcement On The Propagation And Morphology Of Fracture In A Two-Dimensional Mass-Spring System

We investigate the interplay of damage accumulation and structural reinforcement in the fatigue failure of a two-dimensional mass-spring system. Damage accumulation is captured in the model such that the damage of a spring at a certain time depends on its entire deformation history. Structural reinforcement, on the other hand, is implemented by increasing the breaking thresholds of the springs [Esleta and Monterola,Comp. Phys. Comm.20081]. We demonstrate that consistent with known empirical laws, in the presence of memory, the lifetimetfof the system subjected to a stress amplitude σ0is a power law$(t_f\sim \sigma_0^{-\gamma})$. As damage accumulation memoryf0is incorporated into the system, the transition from non-power law (f0= 0, no memory) to power law distribution is observed. Preservation of the power law behavior (equal value of γ) is guaranteed even when the system's lifetime is prolonged through static reinforcement. Finally, our model demonstrates that strengthening the stress memory of spring elements leads to more scattered crack patterns, a result that agrees phenomenologically with existing experiments.