The Faculty of Industrial Engineering Novo mesto with Section of Mechanics kindly invites you to the scientific research webinar. The webinar will take place on Wednesday 8th of June 2022 at 17.00 CET. The guest speaker will be prof. A Russell Davies from Cardiff University (UK). The title of the webinar is: ON CONTINUOUS AND DISCRETE RELAXATION SPECTRA.
Boltzmann’s Theory of Linear Viscoelasticity was formulated 150 years ago, and still plays a fundamental role in the characterization of viscoelastic materials. The key material function introduced by Boltzmann is the relaxation modulus, or equivalently, the memory kernel. In any laboratory, it is now an everyday occurrence to represent these functions by a Dirichlet series of exponentials, each decaying in time at different rates, with positive coefficients. The coefficients and decay rates are known as the discrete relaxation spectrum of the material, and can be obtained, with care, by fitting the series to experimental stress relaxation data. For suitable materials, discrete spectra may also be determined by fitting dynamic mechanical data, i.e., storage and loss moduli from oscillatory shear.
The discrete spectrum selects a small number of relaxation times which are meant to represent the linear viscoelastic behaviour of the material. This selection is not unique: different methods of curve fitting give rise to different discrete spectra, each of which can fit the data equally well. Yet, at fixed pressure and temperature, Boltzmann’s theory predicts the existence of a unique continuous spectrum of relaxation times over an infinite range of positive values. Very little was known about the mathematical nature of the continuous spectrum until recently. Under two simple and plausible conditions, it is possible to identify the function space in which the continuous spectrum resides. In this talk, I will discuss this function space in simple terms, and show how it may be used to convert any discrete spectrum to its underlying continuous counterpart.
Connection to the Zoom: https://uni-lj-si.zoom.us/j/92559614641?pwd=S3FJZVp0L0VBYXpvWUg2blZjWERrZz09
Meeting ID: 925 5961 4641
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