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Overall properties of thin hyperelastic plate at finite strain with edge effects using asymptotic method

type de publication      article dans une revue internationale avec comité de lecture
date de publication 1998
auteur(s) Pruchnicki Erick
journal (abréviation) International Journal of Engineering Science (J ENG SCI)
volume (numéro) 36(9)
  
résumé This paper deals with the homogenization of a periodic composites plate. The constituents of the plate (steel and elastomer) are assumed to obey a hyperelastic law at finite strain. The elastomer is supposed to be nearly incompressible. Both the material moduli and the geometrical data (face shapes) vary periodically with the same period. This period also varies on the same scale as the mean thickness of the plate. Applying the method of two-scale asymptotic developments, the completed macroscopic and microscopic stress–strain relations are derived up to second order. This classical asymptotic theory is correct far enough the boundary of the domain, but it is not valid in the neighbourhood of the boundaries. To obtain a description of stress and strain including the edge effects, we define a new expansion as the sum of the classical terms and the boundary ones. In this way, the effect of respectively only one boundary and two boundaries are treated.
mots clés nonlinear, plate, homogenization, bidimensionnal model
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