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.
Highlights
Constitutive modeling for finite deformations of polymeric materials requires accurate theoretical predictions combined with experimental characterizations
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 two ductile polymeric materials selected for uniaxial tension tests are low-density polyethylene (LDPE) and isotactic polypropylene
Summary
Constitutive modeling for finite deformations of polymeric materials requires accurate theoretical predictions combined with experimental characterizations. The current theories of plasticity can only maintain the numerical stability in terms of normality of the incremental plastic strain vector and convexity of initial and subsequent yield surfaces but cannot accurately predict plastic deformations in general modes, as noticed by Michno and Findley (1976) [10]. For resolving the existing issues of accurate predictions, physical relevancies, and finite elastic-plastic deformations, a physically relevant and mathematically covariant stored energy function is needed. The main objectives, are to fit the CSE function to experimental data for three types of isotropic polymer materials, to study their deformation mechanisms and damage modes, to examine the validity of von Mises equivalent stress and equivalent strain equations, and to recommend a new approach for the finite elasticity-plasticity theory
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