Homogenization of frame lattices leading to second gradient models coupling classical strain and strain-gradient terms

Abstract : We determine in the framework of static linear elasticity the homogenized behavior of three-dimensional periodic structures made of welded elastic bars. It has been shown that such structures can be modeled as discrete systems of nodes linked by extensional, flexural/torsional interactions corresponding to frame lattices and that the corresponding homogenized models can be strain-gradient models, i.e., models whose effective elastic energy involves components of the first and the second gradients of the displacement field. In these papers, there is no coupling between the classical strain and the strain-gradient terms in the expression of the effective energy. In the present paper, under some assumptions on the positions of the nodes of the unit cell, we show that classical strain and strain-gradient strain terms can be coupled. In order to illustrate this coupling we compute the homogenized energy of a particular structure which we call asymmetrical pantographic structure.
Complete list of metadatas

Cited literature [38 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02065135
Contributor : Pierre Seppecher <>
Submitted on : Wednesday, July 17, 2019 - 3:43:13 PM
Last modification on : Wednesday, July 24, 2019 - 10:15:36 AM

File

coupling-vs5.pdf
Files produced by the author(s)

Identifiers

Citation

Houssam Abdoul-Anziz, Cédric Bellis, Pierre Seppecher. Homogenization of frame lattices leading to second gradient models coupling classical strain and strain-gradient terms. Mathematics and Mechanics of Solids, SAGE Publications, 2019, ⟨10.1177/ToBeAssigned⟩. ⟨hal-02065135v2⟩

Share

Metrics

Record views

69

Files downloads

22