Abstract
In this paper, we study the dynamic fracture of a dissimilar chain composed of two different mass-spring chains and connected with other springs. The propagation of the fault (crack) is realized under externally applied moving forces. In comparison with a homogeneous double chain, the considered structure displays some new essential features of steady-state crack propagation. Specifically, the externally applied forces are of a different strength, unlike a static case, and should be appropriately chosen to satisfy the equilibrium of the structure. Moreover, there exists a gap in the range of crack speeds where the steady-state fracture cannot occur. We analyse the admissibility of solutions for different model parameters and crack speeds. We complement analytical findings with numerical simulations to validate our results.This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.
Highlights
One of the most addressed questions in dynamic problems of fracture is the establishment of the limits of the crack propagation
The limiting crack speed in homogeneous solids is predicted to be a fraction of the Rayleigh speed [1], and a series of experiments [2,3,4,5,6] and numerical simulations [7,8] demonstrate the growth of instabilities when the crack begins to move at high speed
In his paramount works [21,22], Slepyan developed a method for linking the microscopic discrete models of dynamic fracture and phase transitions to their macroscopic limits
Summary
One of the most addressed questions in dynamic problems of fracture is the establishment of the limits of the crack propagation. Steady-state fault propagation in a dissimilar structure is analysed in [19,20], where the technique developed by Slepyan for crack propagation in lattice structures has been used In his paramount works [21,22], Slepyan developed a method for linking the microscopic discrete models of dynamic fracture and phase transitions to their macroscopic limits. His results showed the instability of the energy release rate behaviour at low crack speeds, which was later studied in [23], to provide a connection with experimental observations [24,25]. We derive expressions for the loading parameters which allow further comparisons with the numerical simulations
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