2014
DOI: 10.1098/rspa.2013.0817
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A reduced-order model from high-dimensional frictional hysteresis

Abstract: Hysteresis in material behaviour includes both signum nonlinearities as well as high dimensionality. Available models for component-level hysteretic behaviour are empirical. Here, we derive a loworder model for rate-independent hysteresis from a high-dimensional massless frictional system. The original system, being given in terms of signs of velocities, is first solved incrementally using a linear complementarity problem formulation. From this numerical solution, to develop a reduced-order model, basis vector… Show more

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Cited by 10 publications
(21 citation statements)
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“…Differing somewhat from Biswas & Chatterjee [ 1 ], here we consider the intuitively simpler high-dimensional frictional system sketched in figure 1 . In this n -dimensional model (with n large), each spring has stiffness 1/ n , and friction coefficients at the slip sites are As indicated in the figure, u ( t ) is a displacement input to the system, for which a force f ( t ) is needed.…”
Section: New Frictional Systemmentioning
confidence: 99%
See 2 more Smart Citations
“…Differing somewhat from Biswas & Chatterjee [ 1 ], here we consider the intuitively simpler high-dimensional frictional system sketched in figure 1 . In this n -dimensional model (with n large), each spring has stiffness 1/ n , and friction coefficients at the slip sites are As indicated in the figure, u ( t ) is a displacement input to the system, for which a force f ( t ) is needed.…”
Section: New Frictional Systemmentioning
confidence: 99%
“…We solve equation ( 2.1 ) incrementally by casting it first into an LCP (as described in Biswas & Chatterjee [ 1 ]) and then by using Lemke's algorithm (as implemented by Miranda & Fackler [ 13 ]). There is in fact a large literature on solving friction problems using the LCP; readers interested in the theory may consult, e.g.…”
Section: New Frictional Systemmentioning
confidence: 99%
See 1 more Smart Citation
“…However, the experimental observations are not always aligned with the consideration above, particularly in the unsteady environmental conditions such as the oscillations in relative velocity. Therefore, some engineering investigations have revealed that the frictional dynamics can be multi-valued, which means the friction force travels along different paths during the DS and the AS, and forms a non-reversible curve as reported in (Becker and Mahin, 2013;Biswas and Chatterjee, 2014;Neis et al, 2011;Outirba and Hendrick, 2014;Stefański et al, 2006;Wojewoda et al, 2008). The main reason for this phenomenon is the temporal lag between the variations of the friction force and the relative velocity.…”
Section: Introductionmentioning
confidence: 99%
“…Many formulations have been proposed to account for the dissipation in solid media (see e.g. [12,10,2,47,8]), however, herein, with aiming at analyzing the internal mechanisms of dissipation in concrete when no relevant damage phenomena occur at the macroscopic level, the internal dissipation is assumed to be related to the relative motion of micro-crack faces following the same spirit of several papers [46,43,59,36,81,84,78]. The basic idea was to introduce a new (scalar) variable characterizing, in an average way, these micro-sliding along the micro-crack faces with a proper constitutive relation describing the evolution of this variable and its coupling with the Coulomb friction force.…”
Section: Introductionmentioning
confidence: 99%