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Anisotropic finite strain hyperelasticity based on the multiplicative decomposition of the deformation gradient
Author(s) -
AlKinani Raad,
Hartmann Stefan,
Netz Torben
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210137
Subject(s) - hyperelastic material , finite strain theory , isotropy , deformation (meteorology) , decoupling (probability) , anisotropy , multiplicative function , cauchy elastic material , transverse isotropy , tension (geology) , strain energy density function , stress (linguistics) , constitutive equation , mathematics , mathematical analysis , physics , geometry , classical mechanics , materials science , finite element method , composite material , optics , engineering , thermodynamics , linguistics , philosophy , control engineering , moment (physics)
In this contribution a new constitutive model for transversely isotropic materials is presented. The proposed model is based on the multiplicative decomposition of the deformation gradient into one part containing the deformation only in the direction of anisotropy and another part describing the remaining deformation. This clear assignment leads to a decoupling of the stress‐state. The model is investigated analytically in view of simple tension. Moreover, an inhomogenous deformation is solved using a finite elements simulation. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)