On the Modeling of Memristive Material Behavior in the Context of the Finite Element Method

Since HP‐Labs developed the first memristor as a technical device in 2008 (cf. [1]), electrical engineers are aware of its potential of revolutionizing electronics (cf. [2]). As analogies have a long tradition in various fields of science it is quite obvious to transfer the idea of the memristor in electric circuit theory to mechanics by electro‐mechanical analogies. This transfer already led to a generalized classification of devices for dynamical systems [3]. In particular, a mechanical memristor for a system with one single degree of freedom is a displacement‐dependent dashpot. To investigate the behavior of continuous solids which show memristive properties, the development of suitable three‐dimensional material models is desired. Thus, this paper investigates the implementation of a memristive material model in the context of the Finite Element Method. Therefore, one‐dimensional memristive material models are analyzed and a continuum‐mechanical, memristive material model is developed based on an adaption of the KELVIN‐VOIGT‐Model. Example problems are simulated to verify the characteristics of this material class. In particular, the slipknot‐shaped hysteresis of the stress‐strainrate‐curve and the memory effect can be shown. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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