Viscoelastic-Damage Theory Based on a QR Decomposition of Deformation Gradient

Report No. ARL-TR-8840
Authors: John D Clayton, D Freed
Date/Pages: October 2019; 82 pages
Abstract: A novel thermodynamic framework for the continuum mechanical response of nonlinear solids is described. Large deformations, nonlinear hyperelasticity, viscoelasticity, and property changes due to evolution of damage in the material are encompassed. The deformation gradient is decomposed in Gram-Schmidt fashion into the product of an orthogonal matrix Q and an upper triangular matrix R, where the latter can be populated by six independent strain attributes. Strain attributes, in turn, are used as fundamental independent variables in the thermodynamic potentials. A complementary set of internal variables enters the thermodynamic potentials to enable history and rate dependence through viscoelasticity and irreversible stiffness degradation via damage. Governing equations and thermodynamic restrictions imposed by the entropy production inequality are derived. Mechanical, thermodynamic, and kinetic relations are presented for materials of certain cubic or isotropic symmetries. Representative models and example problems demonstrate utility and flexibility of this theory for depicting nonlinear hyperelasticity, large-strain viscoelasticity, and/or damage from cracks or voids, with physically measurable parameters.
Distribution: Approved for public release
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Last Update / Reviewed: October 1, 2019