Journal
MATHEMATICS AND MECHANICS OF SOLIDS
Volume 8, Issue 1, Pages 51-73Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1081286503008001658
Keywords
second gradient theory; third gradient theory; homogenization; Gamma-convergence; finite differences; modular truss beam; pantograph
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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 having the form of second-order or third-order finite differences. We establish the T-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.
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