The large bending of beams made with complex materials finds application in many emerging fields. To describe the nonlinear behavior of these complex materials such as rubbers, polymers and biological tissues, stored energy functions of polynomial-type are commonly used. Using polyconvex and compressible stored energy functions of polynomial-type, in the present paper the equilibrium problem of slender beams in the fully nonlinear context of finite elasticity is formulated. In the analysis, the bending is considered nonuniform, the complete three-dimensional kinematics of the beam is taken into account and both deformation and displacement fields are deemed large. The governing equations take the form of a coupled system of three equations in integral form, which is solved numerically through an iterative procedure. Explicit formulae for displacements, stretches and stresses in every point of the beam, following both Lagrangian and Eulerian descriptions, are derived. By way of example, a complete analysis has been performed for the Euler beam.

Large nonuniform bending of beams with compressible stored energy functions of polynomial-type / Lanzoni, Luca; Tarantino, Angelo Marcello. - In: INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES. - ISSN 0020-7403. - 196:106287(2021), pp. 1-11. [10.1016/j.ijmecsci.2021.106287]

### Large nonuniform bending of beams with compressible stored energy functions of polynomial-type

#### Abstract

The large bending of beams made with complex materials finds application in many emerging fields. To describe the nonlinear behavior of these complex materials such as rubbers, polymers and biological tissues, stored energy functions of polynomial-type are commonly used. Using polyconvex and compressible stored energy functions of polynomial-type, in the present paper the equilibrium problem of slender beams in the fully nonlinear context of finite elasticity is formulated. In the analysis, the bending is considered nonuniform, the complete three-dimensional kinematics of the beam is taken into account and both deformation and displacement fields are deemed large. The governing equations take the form of a coupled system of three equations in integral form, which is solved numerically through an iterative procedure. Explicit formulae for displacements, stretches and stresses in every point of the beam, following both Lagrangian and Eulerian descriptions, are derived. By way of example, a complete analysis has been performed for the Euler beam.
##### Scheda breve Scheda completa Scheda completa (DC)
2021
12-gen-2021
196
106287
1
11
Large nonuniform bending of beams with compressible stored energy functions of polynomial-type / Lanzoni, Luca; Tarantino, Angelo Marcello. - In: INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES. - ISSN 0020-7403. - 196:106287(2021), pp. 1-11. [10.1016/j.ijmecsci.2021.106287]
Lanzoni, Luca; Tarantino, Angelo Marcello
File in questo prodotto:
File
Large bending.2.pdf

Open Access dal 16/04/2023

Descrizione: Articolo principale
Tipologia: Versione dell'autore revisionata e accettata per la pubblicazione
Dimensione 2.14 MB
1-s2.0-S0020740321000229-main.pdf

Accesso riservato

Tipologia: Versione pubblicata dall'editore
Dimensione 1.29 MB
##### Pubblicazioni consigliate

I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11380/1227019`
• ND
• 5
• 5