By Lucian Pasieka

In nature, there are materials that consist of a variety of individual structures (molecular chains), which only demonstrate their desired characteristics as coupled systems. An example of this kind in the field of mechanics is the interplay between elastic and damping components. In the human body, elasticity and damping are coupled in a very impressive manner: in tissue, in the muscles but also in blood vessel walls. All these materials are so-called polymers as shown in figure [1].

These “systems” have a very high degree of complexity from a mechanical point of view and possess the property of a pronounced adaptability to external influences and stresses.
In engineering and in many examples from daily life, we utilize these properties by employing materials such as bio-materials, polyurethans or elastomers. The mechanical properties of polymers depend on the type of dynamic load (frequency and amplitude) and on temperature.

In the case of high-performance polymers (e.g. thermoplastics), the properties and modeling demands are quite complex [1].  However, some other polymers, like elastomers, can be described i a simpler way by focusing only on their elastic (“spring”) and viscous (“damper”) properties. Usually, models, designs and calculations do not look at these two properties individually, but consider their combination wich is called viscoelasticity.  

Viscoelastic material behavior can be explained with the help of thermodynamics, where free energy depends on entropy. The thermodynamic free energy is a concept useful in the thermodynamics of chemical or thermal processes in engineering and science. The change in free energy is the maximum amount of work that a thermodynamic system can perform in a process at constant temperature, and its sign indicates whether a process is thermodynamically favorable or forbidden. The free energy is a thermodynamic state function that depends on temperature, internal energy and entropy where the latter two are state functions themselves:

F: = U – TS (F: free energy, U: internal energy; T: Temperature; S: Entropy) [2]

Entropy is an important concept in the branch of physics known as thermodynamics. The molecular interpretation of entropy makes it possible to calculate the entropy of a polymer molecule and elastomer elements (or components, bodies). The maximum value of entropy exists in the natural state. Under tensile stress entropy decreases. Entropy is responsible for the elasticity of elastomers. [3]

Another characteristic of elastomers is that properties, i.e. stress relaxation, depend on temperature and time. Stress relaxation describes how polymers relieve stress under constant strain caused by molecular movement and rearrangement processes. Furthermore, by implementing mathematical models of these systems, it is possible to utilize computer simulations to better characterize materials in-situ.  

The principles of elasticity and damping are so closely linked that we can hardly imagine them existing alone.

References:

1. Bergström, J.: Mechanics of Solid Polymers, 1^stEdition – Elsevier 2015
2. https://en.wikipedia.org/wiki/Thermodynamic_free_energy
3. Müller, I.: Thermodynamics, Pitman 1985, ISBN 0-273-08577-8, p 287 ff