title: 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 low-order 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 vectors are chosen using the singular value decomposition. The slip direction in generalized coordinates is identified as the minimizer of a dissipation-related function. That function includes terms for frictional dissipation throughsignumnonlinearities at many friction sites. Luckily, it allows a convenient analytical approximation. Upon solution of the approximated minimization problem, the slip direction is found. A final evolution equation for a few states is then obtained that gives a good match with the full solution. The model obtained here may lead to new insights into hysteresis as well as better empirical modelling thereof.
authors.affiliation: Department of Mechanical Engineering , IIT Kanpur , Kanpur, Uttar Pradesh 208016, India.
authors.forename: Saurabh
authors.initials: S
authors.lastname: Biswas
authors.affiliation: Department of Mechanical Engineering , IIT Kanpur , Kanpur, Uttar Pradesh 208016, India.
authors.forename: Anindya
authors.initials: A
authors.lastname: Chatterjee
keywords: frictional system; hysteresis; reduced-order model