Abstract
We offer a finite-time stability result for Moreau sweeping processes on the plane with periodically moving polyhedron. The result is used to establish the convergence of stress evolution of a simple network of elastoplastic springs to a unique cyclic response in just one cycle of the external displacement-controlled cyclic loading. The paper concludes with an example showing that smoothing the vertices of the polyhedron makes finite-time stability impossible.
Highlights
Aiming to design materials with better properties, there has been a great deal of work lately where a discrete structure comes from a certain microstructure formulated through a lattice of elastic springs [13], [15], [6], [10]
Recent findings show [4] that a pivotal role in the performance of heterogeneous materials under cyclic loading is played by micro-plasticity
This paper initiates the development of a theory where the distribution of plastic deformations in a network of elastoplastic springs with external loading can be evaluated in just two cycles of the loading
Summary
Aiming to design materials with better properties, there has been a great deal of work lately where a discrete structure comes from a certain microstructure formulated through a lattice of elastic springs [13] (metals), [15] (polymers), [6] (titanium alloys), [10] (biological materials). This relation is used in Corollary 3.6 of the same section in order to give conditions for one-period stability of sweeping process (1.3), i.e. to give conditions which ensure that any solution x(t) of (1.3) merges with its asymptotic limit in a time not exceeding the period T of t → c(t).
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