Wiggly strain localizations in peridynamic bars with non-convex potential. (1st May 2018)

• Record Type: Journal Article
• Authors: Aguiar, Adair R.; Royer-Carfagni, Gianni F.; Seitenfuss, Alan B.
• Is Part Of: International journal of solids and structures. Volume 138(2018)
• Page Start: 1
• Page End: 12
• Publication Date: 2018-05-01
• Subjects: Peridynamics -- Non-convex energy -- Bistable long-range interactions -- Folding-unfolding states -- Hierarchical structure -- Biological systems; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2017.12.023
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: We discuss the static states of a peridynamic nonlinear elastic bar of finite length in a hard device, which represents a continuum description of a complex hierarchical structure with interacting long-range crosslinkers, of the type encountered in biological systems. The nonlocal character of the model requires that edge conditions are defined on a boundary layer with the same length of the horizon, affecting the solution in the bulk interior. Assuming that the constituent microscopic ligaments contain bistable units governed by a non-convex potential, we show that the development of coexisting folded-unfolded phases, either synchronized or unsynchronized, induces in the displacement field the formation of undulations at a micro-scale of the length of the horizon, associated with strain localizations triggered at the bar ends. The equilibrium paths, found numerically with a pseudo-arc-length continuation method, become unstable within a certain range of elongation, suggesting the possible occurrence of a negative-stiffness response.