Truss modular Beams with Deformation Energy depending on Higher Displacement Gradients

Jean-Jacques Alibert (1) , Pierre Seppecher (2) , Francesco Dell'Isola (3, 4)

1 Laboratoire d'Analyse Non Linéaire Appliquée
2 IMATH - Institut de Mathématiques de Toulon - EA 2134
3 Dipartimento di Ingegneria Strutturale e Geotecnica
4 Laboratorio Strutture e Materiali Intelligenti - Fondazione Tullio Levi-Civita

Until now, no third gradient theory has been proposed to describe the homogenized energy associated with a microscopic structure. In this paper, we prove that this is possible using pantographic-type structures. Their deformation energies involve combinations of nodal displacements havin the form of second-order or third-order finite differences. We establish the Gamma convergence of these energies to second and third gradient functionals. Some mechanical examples are provided so as to illustrate the special features of these homogenized models.

Domaines: Mécanique [physics.med-ph]

Jean-Jacques Alibert, Pierre Seppecher, Francesco Dell'Isola. Truss modular Beams with Deformation Energy depending on Higher Displacement Gradients. Mathematics and Mechanics of Solids, 2003, pp.23. ⟨hal-00497327⟩