On the origin of size effects in small-strain elasticity of solid polymers (vol 44, pg 1582, 2007)

By S. Nikolov, C. Han, Dierk Raabe. 2007

136 citations recorded by the source corpus.

Abstract The micromechanical origin of size effects in elasticity of solid polymers is discussed in this article. It is shown that size effects related to rotational gradients can be interpreted in terms of Frank elasticity arising from the finite bending stiffness of the polymer chains and their interactions. We derive a relationship between the gradient of the nematic director field, related to the orientation of the polymer segments, and the curvature tensor associated with rotational gradients. In the resulting couple stress model, the total deformation energy of the material contains a Frank elasticity term. The energy contribution from rotational gradients is related to an effective Frank elastic constant K ∼ [N]. The corresponding characteristic length for size effects is obtained as l = K ∼ / 3 μ where μ is the shear modulus. Our estimations suggest that the characteristic length for size effects in polymers is larger than that obtained for small-molecules materials. Experimental data from the literature are also discussed.

Subfields: Biomedical Engineering, Civil and Structural Engineering, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/f6104662dc756afc4125210e0b79705d05115aac

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Citations in the corpus

Micro hot embossing of thermoplastic polymers: a review (2013, unknown): “Afterwards, the influences of cross-link density and molecular of polymer on size effects were deeply investigated by Nikolov et al [37] and Lam et al [38].”
Geometrically nonlinear higher-gradient elasticity with energetic boundaries (2013, background): “…theories: Forest et al. (2000, 2001); Tenek and Aifantis (2001); Sunyk and Steinmann (2003); Forest and Sievert (2003); Maranganti and Sharma (2007); Nikolov et al. (2007); Pozrikidis (2008); Sun et al. (2008); Cihan Tekoglu and Patrick R. Onck (2008); Weissmüller et al. (2010); Shodja and…”
A non-classical Mindlin plate model based on a modified couple stress theory (2011, background): “For polymeric materials containing polymer chains with finite stiffness, l is directly related to the effective Frank constant, which is a microstructural parameter depending on the chain stiffness, the strength of chain interactions, and the cross-link density [28].”