A theory of magneto-elastic nanorods obtained through rigorous dimension reduction

0554516 - ÚTIA 2023 RIV US eng J - Článek v odborném periodiku
Ciambella, J. - Kružík, Martin - Tomassetti, G.
A theory of magneto-elastic nanorods obtained through rigorous dimension reduction.
Applied Mathematical Modelling. Roč. 106, č. 1 (2022), s. 426-447. ISSN 0307-904X. E-ISSN 1872-8480
Grant CEP: GA ČR(CZ) GF19-29646L
Institucionální podpora: RVO:67985556
Klíčová slova: Magnetic actuation * Non-simple materials * Distributed torques * Variational convergence * Size effects
Obor OECD: Pure mathematics
Impakt faktor: 5, rok: 2022
Způsob publikování: Omezený přístup
http://library.utia.cas.cz/separaty/2022/MTR/kruzik-0554516.pdf https://www.sciencedirect.com/science/article/pii/S0307904X22000592?via%3Dihub

Starting from a two-dimensional theory of magneto-elasticity for fiber-reinforced magnetic elastomers we carry out a rigorous dimension reduction to derive a rod model that describes a thin magneto-elastic strip undergoing planar deformations. The main features of the theory are the following: a magneto-elastic interaction energy that manifests itself through a distributed torque, a penalization term that prevents local interpenetration of matter, a regularization term that depends on the second gradient of the deformation and models microstructure-induced size effects. As an application, we consider a problem involving magnetically-induced buckling and we study how the intensity of the field at the onset of the instability increases if the length of the rod is decreased. Finally, we assess the accuracy of the deduced model by performing numerical simulations where we compare the two-dimensional and the one-dimensional theories in some special cases, and we observe excellent agreement.
Trvalý link: http://hdl.handle.net/11104/0330287