TITLE:
The Continuum Stored Energy for Constitutive Modeling Finite Deformations of Polymeric Materials
AUTHORS:
Fuzhang Zhao
KEYWORDS:
Break-Even Stretch, Continuum Stored Energy, Damage Mode, Deformation Mechanism, Finite Elasticity-Plasticity Theory, Polymeric Material
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.7 No.10,
October
31,
2017
ABSTRACT: With symmetries measured by the Lie group and curvatures revealed by differential geometry, the continuum stored energy function possesses a translational deformation component, a rotational deformation component, and an ellipsoidal volumetric deformation component. The function, originally developed for elastomeric polymers, has been extended to model brittle and ductile polymers. The function fits uniaxial tension testing data for brittle, ductile, and elastomeric polymers, and elucidates deformation mechanisms. A clear distinction in damage modes between brittle and ductile deformations has been captured. The von Mises equivalent stress has been evaluated by the function and the newly discovered break-even stretch. Common practices of constitutive modeling, relevant features of existing models and testing methods, and a new perspective on the finite elasticity-plasticity theory have also been offered.