| Author | R.C. Picu |
|---|---|
| Title | A non-local formulation of rubber elasticity |
| Year | 2003 |
| Journal | J. Multiscale Comput. Eng. |
| Volume | 1 |
| Pages | 23-32 |
| Abstract | A non-local formulation of rubber elasticity with applications to nanostructured materials is developed. In general, stress has an entropic and an energetic component. The energetic component is due to short range interactions of the representative atom with its neighbors, while the entropic component is due to chain conformation changes upon deformation. In rubbers, the entropic component is dominant. Both components are intrinsically non-local; stress at a point depends on the deformation in a whole neighborhood of that point. This property becomes important when the deformation field varies significantly over a distance comparable with the internal length scale of the material (large gradients). Here, non-local formulations are derived for both the energetic and the entropic components of stress for a system of polymeric chains. For small deformations, linear non-local elasticity may be used for the energetic component of stress and a kernel may be derived within the integral formalism of non-local elasticity. The entropic component is highly non-linear and no kernel may be separated. The implications of considering a non-local description for nanostructured materials in place of the conventional local one are discussed. |