Constitutive Modeling of Polymers with Reversible Actuation


Shape memory polymers (SMPs) are a subclass of smart materials, which are able to restore their permanent shapes from their temporary shapes under certain stimuli. SMPs can be divided into one-way SMPs (1W-SMPs) and two-way SMPs (2W-SMPs), and both 1W-SMPs and 2W-SMPs can exhibit multiple shape memory effects. Recently, two-way shape memory effect (2W-SME) has been demonstrated in several types of SMPs. Unlike classical 1W-SME, polymers can switch back and forth repeatedly between two different shapes without subsequent programming procedure. The reversible actuation can be realized either under a constant external tensile load, which is referred to as quasi 2W-SME, or under zero load, which is referred to as true 2W-SME. Most recently, actuation under an external compressive load, which is referred to as advanced 2W-SME, has also been discovered. Test results have shown that semi-crystalline 2W-SMPs exhibit 2W-SME in two distinct regions due to two different mechanisms: one is due to entropic elasticity above the crystallization temperature, and the other is due to melt/crystallization transition below the crystallization temperature. While several constitutive models have been developed over the years for semi-crystalline 2W-SMPs, there is currently a lack of effort towards modeling the true and advanced 2W-SME within the two-mechanism framework.

Therefore, in order to comprehend the intrinsic mechanisms for true and advanced 2W-SME, a constitutive model is highly desired, which can facilitate and enhance future design, synthesis, and application of 2W-SMPs in engineering structures and devices. On this account, Louisiana State University researchers: Dr. Cheng Yan, Dr. Qianxi Yang and led by Professor Guoqiang Li developed a new thermomechanical constitutive model which can capture both the entropic elasticity and melt/crystallization events. Their work is currently published in the International Journal of Mechanical Sciences.

In their approach, the research team first described the balance equations for mass, linear momentum, and angular momentum. Next, a general three-dimensional constitutive model was presented in detail. The researchers then validated the presented model by comparing with the experimental results for a chemically crosslinked cis poly(1,4-butadiene) (cPBD) 2W-SMP with quasi 2W-SME, true 2W-SME and advanced 2WSME, respectively. Lastly, a model sensitivity analysis was conducted to rank the relative importance of the parameters involved in the model.

The authors reported that the modeling results and test results showed reasonable agreement. In fact, it was found that the model captured the three types of 2W-SMEs: quasi 2W-SME, true 2W-SME, and advanced 2W-SME. Further, the researchers found out that proper tensile programming before the first thermomechanical cycle could make a semi-crystalline SMP exhibit all the three types of 2W-SMEs.

In summary, the study developed a new three-dimensional constitutive model within the two-mechanism framework for the quasi 2W-SME, true 2W-SME, and advanced 2W-SME of semi-crystalline polymers. The team reported that by comparing the single parameter effect and combined parameters effect, it was found that focusing on a single parameter can obtain only a limited understanding of the physics. In a statement to Advances in Engineering, Professor Guoqiang Li said their study may serve as a design tool to advance applications of semi-crystalline 2W-SMPs in engineering structures and devices.

Constitutive Modeling of Polymers with Reversible Actuation - Advances in Engineering
A molecular level schematic of how chemically crosslinked 2W-SMP exhibits quasi 2W-SME, true 2W-SME, and advanced 2W-SME. (a) Physically crosslinked network. (b) SMP with prominent chemical crosslinks. (c) Chemically crosslinked 2W-SMP subjected to tension at elevated programming temperature θ_prog. (d) Freezing the specimen to the low temperature θ_low under tension, elongation upon cooling (EUC) appears. (e) Unloading and heating up the specimen to high working temperature θ_work, contraction upon heating (CUH) can be observed and the oriented crystalline lamellae are partially melted. Internal tensile stress is stored in the unmelt portion of the crystallites. (f) Cooling the specimen to θ_low, EUC appears. In the figure, (c) and (d) show quasi 2W-SME (with external tension); (e) and (f) show true 2W-SME (without external tension); (g) and (h) show advanced 2W-SME (with external compression).

About the author

Cheng Yan is currently a PhD student in Louisiana state University. He received his B.S. in Transportation Engineering and Doctoral degree in Engineering Mechanics from Beijing Institute of Technology in 2006 and 2014, respectively. From 2014-2015, he worked as a research scientist in Nanyang Technology University in Singapore. In 2016, he worked as a lecturer in Nanjing University of Science and Technology in China. From 2017, he started to pursue his second Doctoral degree in Engineering Science at Louisiana State University.

His research fields include shape memory polymer modelling by adopting the classical solid mechanics principles and the latest machine learning method, as well as strain-rate effect study for both brittle materials and metals. To data, he has published more than 10 papers in some decent journals, such as ASME Journal of Applied Mechanics, International Journal of Impact Engineering, International Journal of Mechanical Engineering, etc.

Email: [email protected]

His ResearchGate link can be found at

About the author

Qianxi Yang received her Bachelor of Science degree from University of Science and Technology of China in 2010 and completed her Ph.D. degree in Mechanical Engineering at Louisiana State University in 2017, working with Prof. Guoqiang Li. Her PhD thesis work focused on thermomechanical constitutive modeling of shape memory polymers (SMPs) and polymeric artificial muscles. Specifically, her research has used thermodynamics, statistical mechanics, and solid mechanics principles, and has modeled the constitutive behavior of the various stimuli-responsive polymers and polymer composites, including amorphous SMPs, semi-crystalline SMPs, SMP fibers, SMP based artificial muscles, etc. Qianxi has published several first-authored papers in high-profile journals in the area of solid mechanics, such as International Journal of Plasticity, Journal of the Mechanics and Physics of Solids, Applied Physics Letter, etc.

One of her major contribution was to take the lead role in developing a multi-scale thermomechanical modeling framework for polymeric artificial muscles. Subsequently, guided by the prediction result of this model, a higher-performance polymeric artificial muscle made of two-way shape memory polymers was successfully developed, and this work was chosen as the issue cover for Applied Physics Letter.

Her google scholar link can be found at

About the author

Dr. Guoqiang Li received his B.S., M.S., and Ph.D. degrees from Hebei University of Technology, Beijing University of Technology, and Southeast University, respectively, all in Civil Engineering. He received his postdoc training in Mechanical Engineering at Louisiana State University (LSU). He is currently the Major Morris S. & DeEtte A. Anderson Memorial Alumni Professor in Mechanical Engineering and Holder of the John W. Rhea Jr. Professorship in Engineering, in the Department of Mechanical & Industrial Engineering at LSU. His research interest is in the broad area of engineering materials and engineering mechanics, including shape memory polymers, self-healing and recycling of multifunctional polymer composites, construction materials, structural mechanics modeling of composite structures, constitutive modeling of composite materials, additive manufacturing, and data-driven discovery of smart polymers and optimization of biomimetic structures. As of November 2020, he is the holder of 8 US patents, and has 176 papers indexed in ISI Web of Science with more than 6,800 citations and an h-index of 46.

He currently serves as an Associate Editor for ASCE Journal of Materials in Civil Engineering, editorial board member for Elsevier journal of Composites Part B: Engineering, Nature’s journal of Scientific Reports, and specialty section editor of “Solid and Structural Mechanics” in “Frontiers in Mechanical Engineering”. He has received over 30 awards and recognitions for his research, mentoring, and services.

His Google Scholar Page can be found at:


Cheng Yan, Qianxi Yang, Guoqiang Li. A phenomenological constitutive model for semicrystalline two-way shape memory polymers. International Journal of Mechanical Sciences: Volume 177, 1 July 2020, 105552.

Go To International Journal of Mechanical Sciences

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