Modeles Multiparticulaires Des Materiaux Multicouches M4_5n et   M4_(2n+1)M Pour L'Analyse Des Effets De Bord Multiparticle Models of   Multilayered Materials M4_5n and M4_(2n+1)M for Edge Effect Analysis
  The Multiparticle Models of Multilayered Materials (models M4) are developed to analyze easily the 3D stress fields which produce delamination or transverse crackings in laminates. The M4 models are built from 3D approximate stress fields in z per layer and the Hellinger-Reissner's formulation. Here-in we express two of these models: the M4_5n model of which the kinematics, with 5n fields (n: number of layers), is the one of n Reissner's plates and, the M4_(2n+1)M model of membrane with 2n+1 fields. The latter gives simple analytic solutions and a concentrated edge force per unit length that could be a natural support for the criteria of delamination. We illustrate this concept by the analytic resolution of (0 deg, 90 deg)s in traction and give some results for more complex stackings. 
Armelle Chabot (LCPC/SMIT), Alain Ehrlacher (LAMI)