Professor Francesco Mainardi
University of Bologna, Bologna, Italy
Title: On Models Of Linear Viscoelastity Based On Complete Monotonicity Of The Material
Abstract: We present a survey of rheological models recently introduced by the author and his collaborators in the framework of linear viscoelasticity. These models are characterized by a creep function that changes with continuity with a real parameter. Based on the hereditary theory of linear viscoelasticity, we also derive the corresponding relaxation function by solving numerically a Volterra integral equation of the second kind. In its turn, the relaxation function is shown versus time for different values of the parameter to visualize again the evolution of the related phenomenon. We consider two classes of basic creep models (referred to Lomnitz and Becker respectively) that exhibit logarithmic behavior, from which we investigate the evolution with the selected parameter. Both classes of models exhibit the mathematical characteristics of complete monotonicity that imply the existence of positive distributions of retardation and relaxation times.
Brief Biography of the Speaker: Presently Francesco MAINARDI is a retired professor of Mathematical Physics from the University of Bologna (since November 2013) where he has taught this course since 40 years. Even if retired, he continues to carry out teaching and research activity. His fields of research concern several topics of applied mathematics, including diffusion and wave problems, asymptotic methods, integral transforms, special functions, fractional calculus and non-Gaussian stochastic processes.
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