Premium
Modeling of induced anisotropy at large deformations for polymers
Author(s) -
Caylak Ismail,
Mahnken Rolf
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210149
Subject(s) - anisotropy , isotropy , tensor (intrinsic definition) , cauchy distribution , tangent , eigenvalues and eigenvectors , finite element method , constitutive equation , materials science , mathematical analysis , physics , mathematics , geometry , thermodynamics , optics , quantum mechanics
In this work we develop a model to describe the induced plasticity of polymers at large deformations. Polymers such as stretch films exhibit a pronounced strength in the loading direction. The undeformed state of the films is isotropic, whereas after the uni‐axial loading the material becomes anisotropic. In order to consider this induced anisotropy during the stretch process, a spectral decomposition of the inelastic right CAUCHY‐GREEN tensor is done. Therefore, the yield function can be formulated as a function of the anisotropic tensor, where again the anisotropic tensor is a function of the maximum eigenvalue. A backward EULER scheme is used for updating the evolution equations, and the algorithmic tangent operator is derived. The numerical implementation of the resulting set of constitutive equations is used in a finite element program and for parameter identification. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)