Determination of Poisson’s ratio of polymers for everyone


Poisson’s ratio is defined as the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force. Tensile deformation is considered positive and compressive deformation is considered negative. Poisson’s ratio is a very critical material property needed to predict and understand elastic deformation. At present, novel materials are developed every day and determination of their Poisson’s ration is vital for their engineering applications.

For example Polydimethylsiloxane (PDMS) is widely used as a MEMS material, however, its Poisson’s ratio is not known exactly (0.45 to 0.5). This wide range causes uncertainties when it comes to critical applications requiring accurate values. For instance, if the value of 0.5 is used as the Poisson’s ratio, it would lead to, e.g., an infinite bulk modulus. Often, the linear relationship of the Young’s Modulus to the Shear Modulus is used to determine Poisson’s ratio.

Other techniques involve the use of indentation methods. However, the majority of the available approaches are limited in their accuracy and may be nontrivial to apply, particularly for a soft elastomer like PDMS. Therefore, it is imperative that a versatile yet effective technique for Poisson’s ratio determination be developed.

In a recent research paper published in the research journal, Soft Matter University of Freiburg researchers Angelina Muller (PhD candidate), Matthias Wapler (PhD) and Professor Ulrike Wallrabe developed a novel and accurate method for determining the Poisson’s ratio of PDMS . The researchers from the Laboratory for Microactuators, located at the Department of Microsystems Engineering – IMTEK, used the thermal expansion and an optical surface profilometer in their new approach.

The research team used a technique based on surface deformation due to thermal expansion of PDMS in a cavity. As such, for them to determine an accurate value for the Poisson’s ratio of PDMS using thermal expansion in a set of defined moulds, they had to measure the surface deformation. Consequently, an optical profilometer, which is highly accurate and readily available in most MEMS laboratories, was used for this purpose.

The authors reported that the Poisson’s ratio (υ) of Sylgard 184 was found to be υ = 0.4950 ± 0.0010 and for Sylgard 182, υ = 0.4974 ± 0.0006. Furthermore, they found that for both PDMS types, the coefficient of thermal expansion depended approximately linearly on the curing temperature.

Indeed the study presented a novel approach to accurately determine the Poisson’s ratio using the thermal expansion properties of PDMS and an optical surface scanning device. The main advantage of this novel technique was that it only requires a profilometer, FEM simulations and numerical mathematics to determine the Poisson’s ratio, without any additional tensile testing setup or advanced tracking methods, in particular since tracking the transverse deformation of elastomers to such an accuracy is non-trivial. Altogether, the new method is important because it can be used for almost any kind of soft polymer that can be cured from a liquid at elevated temperatures.

Determination of Poisson’s ratio of polymers for everyone - Advances in Engineering

About the author

Angelina Müller received her bachelor’s and master’s degree in Microsystems Engineering from the University of Freiburg. In her master, she specialized in biomedical engineering, sensors and actuators. She received her PhD in Microsystems Engineering from the University in Freiburg in 2019. Her research focuses on the development of different micro-optical components and systems including the fabrication of aspherical micro-lenses and liquid crystal based devices.


About the author

Ulrike Wallrabe studied physics at Karlsruhe University (today KIT), Germany. In 1992 she received her PhD degree for mechanical engineering on microturbines and micromotors.

From 1989 to 2003 she was with the Institute for Microstructure Technology at Forschungszentrum Karlsruhe (today KIT) working on micro¬actuators and Optical MEMS.

Since 2003, she holds a Professorship for Microactuators at the Department of Microsystems Engineering, IMTEK, at the University of Freiburg, Germany. Her work focus lies in magnetic microsystems including processes for magnetic materials and micro coils and in adaptive optics, using piezo actuators to tune elastic lenses and mirrors.

Since 2012 she is a member of the Cluster of Excellence BrainLinks-BrainTools, and since 2016 she also is Head of Department of IMTEK.

About the author

Matthias Wapler is a research group leader at the Laboratory for Microactuators at the University of Freiburg. He graduated from Imperial College London in Physics in 2005 and completed his Ph.D. on String Theory at the Perimeter Institute for Theoretical Physics and the University of Waterloo, Canada in 2010. After a postdoc position at Seogang University, he changed directions from fundamental physics to engineering and moved to the University of Freiburg, Germany.

He has a wide range of research interests including piezo and micro actuators, adaptive optics, miniature optical systems and magnetic resonance imaging.


Angelina Muller, Matthias C. Wapler and Ulrike Wallrabe. A quick and accurate method to determine the Poisson’s ratio and the coefficient of thermal expansion of PDMS. Soft Matter, 2019, volume 15, page 779.

Go To Soft Matter

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