A realizable constitutive model for fiber-reinforced Neo-Hookean solids

M. I. IDIART; O. LOPEZ-PAMIES

Tandil

Congreso; XVIII Congreso sobre Métodos Numéricos y sus Aplicaciones; 2009

Asociación Argentina de Mecánica Computacional

We provide a closed-form analytical expression for theeffective stored-energy function of Neo-Hookean solids reinforced bya random distribution of anisotropic cylindrical fibers, subject togeneral finite-strain loading conditions. The expression is obtainedby means of a homogenization constitutive theory recently proposedby the authors (Lopez-Pamies O., Idiart M.I. Fiber-reinforcedhyperelastic solids: A realizable homogenization constitutivetheory. J. Eng. Math., submitted) to determine themechanical response of fiber-reinforced hyperelastic solids. Thecentral idea in this theory is to devise a special class of randommicrogeometries ---by means of an iterated homogenization proceduretogether with an exact dilute result for sequential laminates---that allows to compute exactly the macroscopic response of theresulting fiber-reinforced solid. The derived constitutive relationsincorporate direct microstructural information up to the two-pointstatistics. Since the resulting effective stored-energy function isrealizable, in the sense that it is exact for a given class ofmicrogeometries, it is guaranteed to be theoretically sound and togive physically sensible predictions. The predictions of the modelare illustrated through stress-strain relations and loss ofellipticity criteria. The mechanical stability of fiber-reinforcedNeo-Hookean solids is analyzed in the light of the new predictions.