On the origin of size effects in small-strain elasticity of solid polymers

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 eK [N]. The corresponding characteristic length for size effects is obtained as l ¼ ffiffiffiffiffiffiffiffiffiffiffiffi eK =3l q where l 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.