Stick-Slip Dynamics in Fiber Bundle Models with Variable Stiffness and Slip Number

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.