Linearization of nonlinear rubber elasticity into nonlocal linear elasticity

Develop a widely accepted procedure for linearizing nonlinear rubber-elasticity theories so that they yield nonlocal linear-elasticity theories, thereby providing a consistent connection between the fundamentally nonlinear elasticity of polymer networks and the nonlocal linear models used to describe elastic microphase separation.

Background

The paper emphasizes that the elasticity of polymer networks and other rubbery materials is fundamentally nonlinear, whereas previous theories of elastic microphase separation have often employed nonlocal linear elasticity. A linear theory should therefore arise as the small-strain limit of a more general nonlinear theory.

The authors state that no widely accepted procedure is known for carrying out this linearization in a way that produces the relevant nonlocal linear-elasticity description. They note that some attempts exist, but identify the general derivation as unresolved and motivate their use of conventional elasticity in the companion framework developed in Part I.