Abstract
We present an extension of fiber bundle models to describe the mechanical response of systems which undergo a sequence of stick-slip cycles taking into account the changing stiffness and the fluctuating number of slip events of local material elements. After completing all stick-slip cycles allowed, fibers can either ultimately break or can keep their final stiffness leading to softening or hardening of the bundle, respectively. Under the assumption of global load sharing we derive analytic expressions for the constitutive response of the bundle with both quenched and annealed disorder of the failure thresholds where consecutive slips occur. Our calculations revealed that on the macro-scale the bundle exhibits a plastic behavior, which gets more pronounced when fibers undergo a higher number of stick-slip cycles with a gradually degrading stiffness. Releasing the load a permanent deformation remains, which increases monotonically for hardening bundles with the maximum deformation reached before unloading starts, however, in the softening case a non-monotonous behavior is obtained. We found that the macroscopic response of hardening bundles is more sensitive to fluctuations of the number of stick-slip cycles allowed than of the softening ones. The quenched and annealed disorder of failure thresholds gives rise to the same qualitative macro-scale behavior, however, the plastic response is found to be stronger in the annealed case.
Highlights
Fibre bundle models (FBM) are one of the most important theoretical approaches to the damage and fracture of disordered materials [1]
We presented an extension of fiber bundle models of stick-slip dynamics incorporating the effect of stiffness change of the fibers after slip events, and the fluctuations of the number of stick-slip cycles fibers can experience under an increasing external load
Stick-slip dynamics implies that when the load of a fiber exceeds its local strength the fiber does not break, instead it slips which increases its relaxed length
Summary
Fibre bundle models (FBM) are one of the most important theoretical approaches to the damage and fracture of disordered materials [1]. During the past decades subsequent developments of the model have demonstrated that varying the mechanical response [16] (brittle, plastic) and rheological (visco-elastic) behavior [17,18,19,20] of individual fibers, the degree of strength disorder [21,22,23], range of load sharing (local, global) [11, Stick-Slip Dynamics in FBMs. 24, 25] following breaking events, and the way of loading [19, 20, 26] (quasi-static, creep, fatigue) the model is able to capture a broad spectrum of materials’ behavior. We demonstrate that the stick-slip dynamics results in a plastic behavior on the macro-scale and explore consequences of the new degrees of freedom of the model
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