Plane bias extension test for a continuum with two inextensible families of fibers: A variational treatment with Lagrange multipliers and a perturbation solution

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:81

Article

dell'Isola, Francesco¹  Della Corte, Alessandro²  Greco, Leopoldo³  Luongo, Angelo³ 

[1] Univ Roma La Sapienza, Dept Struct & Geotech Engn, Via Eudossiana 18, I-00184 Rome, Italy

[2] Univ Roma La Sapienza, Doctoral Sch Theoret & Appl Mech, Via Eudossiana 18, I-00184 Rome, Italy

[3] Univ Aquila, Int Res Ctr Math & Mech Complex Syst M&MoCS, Via Gronchi 18, I-67100 Laquila, Italy

关键词: Inextensible fibers;    Generalized continua;    Variational treatment;    Perturbation analysis;   

DOI  :  10.1016/j.ijsolstr.2015.08.029

来源: Elsevier

【 摘 要 】

In the present paper, a system constituted by two families of nearly inextensible fibers is studied. The interest towards this kind of structures, which can be suitably modeled by 2D continua with inextensible curves, comes form both theoretical and applicative motivations. Indeed, the advantageous weight/strength ratio and the particularly safe behavior in fractures make them attractive in many engineering fields, while the mechanical properties displayed by them are theoretically interesting and still not well understood in full generality. We focused on dead-loading traction boundary-value problems assuming particular forms for the deformation energy associated to every node of the structure. The main result of the paper consists in the determination of the nonlinear integral equations describing fibers directions for a specific class of deformation energies. A perturbative analysis of a particular solution is also performed, and some physical justification for one of the considered forms for the energy density are provided in the Appendix. (C) 2015 Elsevier Ltd. All rights reserved.

【 授权许可】

Free