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Microscopic and macroscopic instabilities in finitely strained porous and fibre reinforced elastomers

The present work is a detailed study of the connections between microstructural instabilities and their macroscopic manifestations — as captured through the effective properties — in finitely strained porous and fiber–reinforced elastomers, subjected to finite, plane–strain deformations. The work uses the powerful second–order homogenization (S.O.H.) technique, initially developed for random media, to study the onset of failure in periodic microstructure elastomers and to compare the results to more accurate finite element method (F.E.M.) calculations. The influence of different void/fiber distributions (random and periodic), initial volume fraction, matrix constitutive law and pore/inclusion cross–section on the microscopic buckling (for periodic microgeometries) and macroscopic loss of ellipticity (for all microgeometries) is investigated in detail. In addition, constraints to the principal solution due to various types of local failure modes are also addressed, thus giving a complete picture of the different possible failure mechanisms present in this class of elastomeric composites.

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