Analysis of Stiffness Variations in Context of Strain-, Stress-, and Energy-Controlled Processes

In compounded material systems, such as rubber, a wide range of properties can be achieved by design. This flexibility poses a challenge–how to balance stiffness against other considerations, such as energy dissipation under dynamic loading, fatigue, etc. Negotiating this balance requires that adequate account be taken of how a given mechanical input (i.e., strain, stress, energy) is controlled, and how other mechanical outputs vary as the stiffness changes. We outline here a simple analysis by which these considerations can be managed. The analysis is based on a novel split of the elasticity law into work-conjugate parts: one representing generally that which is to be held constant, and the other representing that which occurs in reaction to imposed control. The split gives rise to a scalar parameter suitable for quantifying the degree to which a given 1D mechanical process is strain-, energy-, or stress-controlled. The physical sense of the parameter is illustrated through the example of a two-spring system, where one spring represents the subject material, and the other represents the mechanical environment in which the material operates. The example shows that the parameter concisely summarizes the effects of the environment on the operating conditions of the material. We also provide a simple example illustrating how the parameter can be used to rank the fatigue performance of a set of compounds, taking into account the stiffness and the test control mode.