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Connecting mem-models with classical theories

Pei, Jin-Song and Gay-Balmaz, François and Luscher, Darby J. and Beck, James L. and Todd, Michael D. and Wright, Joseph P. and Qiao, Yu and Quadrelli, Marco B. and Farrar, Chuck R. and Lieven, Nicholas A. J. (2021) Connecting mem-models with classical theories. Nonlinear Dynamics, 103 (2). pp. 1321-1344. ISSN 0924-090X. doi:10.1007/s11071-020-06084-6.

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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.

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Pei, Jin-Song0000-0002-1042-1859
Additional Information:© 2021 Springer Nature B.V. Received 10 August 2020; Accepted 09 November 2020; Published 16 January 2021. Professor Jin-Song Pei acknowledges the University of Oklahoma for the teaching release offered in the fall of 2019 and the hospitality of Professor Raimondo Betti at Columbia University. Dr. Gay-Balmaz was partially supported by the ANR project GEOMFLUID, ANR-14-CE23-0002-0. Dr. Marco Quadrelli’s research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the NASA Aeronautics and Space Administration. In particular, Jin-Song Pei and Marco B. Quadrelli acknowledge the Oklahoma NASA EPSCoR for the Faculty Research Initiation Fellowship. Government sponsorship acknowledged. The authors declare that they have no conflict of interest.
Funding AgencyGrant Number
Agence Nationale pour la Recherche (ANR)ANR-14-CE23-0002-0
Subject Keywords:Mem-models; Absement; Generalized momentum; Nonlinear state-space representation; Hybrid dynamical system; Continuum damage mechanics; Damage variable; Strain ratcheting; Wiechert model; Classical Preisach model
Issue or Number:2
Record Number:CaltechAUTHORS:20210125-105420859
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Official Citation:Pei, JS., Gay-Balmaz, F., Luscher, D.J. et al. Connecting mem-models with classical theories. Nonlinear Dyn 103, 1321–1344 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107708
Deposited By: Tony Diaz
Deposited On:26 Jan 2021 20:05
Last Modified:16 Nov 2021 19:05

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