Connecting mem-models with classical theories

A family of mem-models, including the mem-dashpots, mem-springs, and most recently, mem-inerters, is emerging as a new and powerful way of capturing complex nonlinear behaviors of materials and systems under various types of dynamic loads involving different frequency, amplitude, and loading histori...

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Bibliographic Details
Published in:Nonlinear dynamics 2021, Vol.103 (2), p.1321-1344
Main Authors: Pei, Jin-Song, Gay-Balmaz, François, Luscher, Darby J., Beck, James L., Todd, Michael D., Wright, Joseph P., Qiao, Yu, Quadrelli, Marco B., Farrar, Chuck R., Lieven, Nicholas A. J.
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Continuum damage mechanics
Control
Dynamic loads
Dynamical Systems
Engineering
Hybrid systems
Integrals
Load history
Mechanical Engineering
Original Paper
Ratcheting
Springs (elastic)
State space models
System effectiveness
Vibration
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Summary:A family of mem-models, including the mem-dashpots, mem-springs, and most recently, mem-inerters, is emerging as a new and powerful way of capturing complex nonlinear behaviors of materials and systems under various types of dynamic loads involving different frequency, amplitude, and loading histories (e.g., hysteresis). Under the framework of nonlinear state-space representation and hybrid dynamical systems, mem-springs may be formulated to effectively represent an inherent degradation of material state. It is shown in this study, for the first time, how the absement (time integral of strain/displacement), a signature state variable for a mem-spring, can be connected with the damage variable, a key quantity in continuum damage mechanics. The generalized momentum (time integral of stress), on the other hand, is shown to be efficient in modeling strain ratcheting via the concept of mem-dashpot. It is also shown in this study, for the first time, how two formulations of the memcapacitive system models (for mem-springs) are special cases of the Preisach model.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-020-06084-6