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International Journal for Multiscale Computational Engineering
A Nonlocal Formulation of Rubber Elasticity
Department of Mechanical Engineering Rensselaer Polytechnic Institute Troy, NY, 12180, USA
A nonlocal 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 nonlocal; stress at a point depends on the deformation in an entire 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, nonlocal formulations are derived for both the energetic and the entropic components of stress for a system of polymeric chains. For small deformations, linear nonlocal elasticity may be used for the energetic component of stress, and a kernel may be derived within the integral formalism of nonlocal elasticity. The entropic component is highly nonlinear and no kernel may be separated. The implications of considering a nonlocal description for nanostructured materials in place of the conventional local one are discussed.
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