Upcoming Events & Seminars
Upcoming Events & Seminars
Analytical Mechanics meets Continuum Mechanics: An overview in Biomechanics, Material Defects and Nematic Elastomers
Andrea Pastore (Politecnico di Torino, Italy)
Location: Seminar Room 311B, School of Mathematics & Statistics, University of Glasgow
Date: Thursday, October 2 at 12:00 pm
Abstract: The goal of this presentation is to show how Analytical Mechanics can be an appropriate framework to contextualize some problems in Continuum Mechanics. To this end, we give an overview on some problems of biological and industrial interest in which Analytical Mechanics can provide both mathematical and physical insights. Specifically, we focus on some biomechanics problems, like tumor growth and fiber-reinforced materials, and on problems involving the mechanics of continua with defects, or with a microstructure.
The first part of this contribution is devoted to present a model of growth in a monophasic medium, developed on the basis of the works by Gurtin [1], Cermelli et al. [2] and DiCarlo&Quiligotti [3]. In this case, Analytical Mechanics provides the most natural tools capable of ensuring the adherence of the growth rates predicted by the mechanical model with the experimental evidence supported by biologists [4, 5, 6].
The second part focuses on the discussion of a model of statistical fiber reorientation in biological media, which is obtained by employing the framework of Analytical Mechanics to merge aspects of both configurational and statistical mechanics, while working under classical constitutive assumptions used in the literature of fiber-reinforced materials [7].
Finally, the last part of the presentation focuses on the mechanics of disclinations [8] and on some other problems involving media with microstructure. Also in this case, it will be highlighted the knowledge gained by employing tools and concepts natives of Analytical Mechanics.
References.
[1] Gurtin, M.: Physica D 1996; 92: 178–192.
[2] Cermelli, P., Fried, E., Sellers, S.: Proc R Soc Lond A 2001; 457: 1447–1467.
[3] DiCarlo, A., Quiligotti, S.: Mech Res Commun 2002; 29(6): 449–456.
[4] Grillo, A., Di Stefano, S.: Math Mech Solids 2023; 28(10): 2215–2241.
[5] Grillo, A., Di Stefano, S.: Math Mech Solids 2024; 29(1): 62–70.
[6] Grillo, A., Pastore, A., Di Stefano, S.: J. Elasticity 2025; 157(3): 1–43.
[7] Giammarini, A., Pastore, A., Grillo, A.: Math Mech Solids 2025; Online: 10812865251327765.
[8] Cesana, P., Grillo, A., Morandotti, M., Pastore, A.: SIAM J Appl Math 2025; 85(4): 1361-1386.
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