On nonlinear thermo-electro-mechanics in the context of electro-active polymers
Applied Mechanics, Statics and Dynamics
Final Report Abstract
In this research project the geometrical and constitutive nonlinear material behavior of electrically active materials under a combination of thermal, electric and mechanical loading was investigated. After establishing the underlying principles of electro-mechanics, a mathematical framework for the simulation of an incompressible material undergoing large deformations was derived, which is capable of capturing the thermo-electro-mechanical nature of the problem. Subsequently, the derived system of equations was linearized and discretized for the implementation into a finite element code using the open source finite element library Deal II. Simultaneously, the thermo-electro-mechanical material response of the dielectric elastomers VHB 4905TM and Elastosil P7670TM was investigated experimentally. With the data sets obtained in these experiments and specified versions of the derived modeling framework, the appropriate material parameters could be identified. The main results of the current work can be summarized as: • Derivation of a general framework for the formulation of a thermodynamically consistent energy function, that correctly reproduces the response of a material under thermo-electro-mechanical loading that behaves incompressible at constant temperatures. Furthermore, a temperature dependency of the mechanical material parameters could be incorporated by the assumption of a temperature-dependent specific heat capacity. • The investigation of VHB 4905TM revealed viscoelastic behavior with a strongly pronounced rate dependency of the material response in the range of strain rates from 0.025 s^−1 to 0.2 s^−1 . Furthermore, the results of the thermo-mechanical tests indicated a pronounced sensitivity towards temperature changes in the range between room temperature and 60 ◦ C, that influences both the elastic and viscous response of the material. Furthermore, cyclic loading tests under the influence of an electric field showed the capability of VHB 4905TM to deform under an electric stimulus. Finally, the material was tested under a combined thermo-electro-mechanical loading combining all of the fields under consideration. It could be observed that both an increase in the material temperature and the application of an electric fields resulted in a reduction of the observed force during the experiments. • In the case of pure Elastosil P7670TM , the viscous characteristics of the mechanical behavior were found to be significantly less pronounced when compared to VHB, considering the size of the hysteresis and the rate independent material response during cyclic loading tests. Upon the addition of filler particles, the behavior of the composite showed, however, distinct viscoelastic characteristics that increased with an increase in particle concentration. Furthermore, the material behavior could be considered as temperature independent in the tested range between room temperature and 100 ◦ C. The electro-mechanical response of pure Elastosil was found to be significantly less pronounced compared to the case of VHB, which was attributed to the higher stiffness of the material. The addition of filler particles lead to an increase in the electric permittivity in combination with an increase in the material stiffness. Nevertheless, the electro-mechanical coupling characteristics could be enhanced significantly. • By properly specifying the respective energy contributions it could be shown that the derived modeling approach is capable of closely replicating the thermo-electro-viscoelastic material behavior of both the highly temperature sensitive VHB 4905TM and the response of the unfilled and filled Elastosil P7670TM . In the case of VHB, temperature coupling functions for the elastic and viscous material response were introduced, whereas in the case of Elastosil a modified formulation of the elastic and viscous energy function were used in order to simulate the effect of the BaTiO3 particles.
Publications
- “On nonlinear thermo-electro-elasticity,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 472, no. 2190, p. 20160170, 2016
M. Mehnert, M. Hossain, and P. Steinmann
(See online at https://doi.org/10.1098/rspa.2016.0170) - “Numerical modelling of nonlinear thermo-electro-elasticity,” Mathematics and Mechanics of Solids, vol. 22, no. 11, pp. 2196–2213, 2017
M. Mehnert, J.-P. Pelteret, and P. Steinmann
(See online at https://doi.org/10.1177%2F1081286517729867) - “Towards a thermo-magneto-mechanical coupling framework for magnetorheological elastomers,” International Journal of Solids and Structures, vol. 128, pp. 117–132, 2017
M. Mehnert, M. Hossain, and P. Steinmann
(See online at https://doi.org/10.1016/j.ijsolstr.2017.08.022) - “Numerical modeling of thermo-electro-viscoelasticity with field-dependent material parameters,” International Journal of Non-Linear Mechanics, vol. 106, pp. 13–24, 2018
M. Mehnert, M. Hossain, and P. Steinmann
(See online at https://doi.org/10.1016/j.ijnonlinmec.2018.08.016) - “On the influence of the coupled invariant in thermo-electroelasticity,” in Generalized Models and Non-classical Approaches in Complex Materials 1, pp. 533–554, Springer, 2018
M. Mehnert, T. Mathieu-Pennober, and P. Steinmann
(See online at https://doi.org/10.1007/978-3-319-72440-9_28) - “Experimental and numerical investigations of the electro-viscoelastic behavior of VHB 4905TM,” European Journal of Mechanics-A/Solids, vol. 77, p. 103797, 2019
M. Mehnert, M. Hossain, and P. Steinmann
(See online at https://doi.org/10.1016/j.euromechsol.2019.103797) - “On the influence of the compliant electrodes on the mechanical behavior of VHB 4905,” Computational Materials Science, vol. 160, pp. 287–294, 2019
M. Mehnert and P. Steinmann,
(See online at https://doi.org/10.1016/j.commatsci.2019.01.011) - “Behavior of vibration energy harvesters composed of polymer fibers and piezoelectric ceramic particles,” Sensors and Actuators A: Physical, vol. 303, p. 111699, 2020
R. Hasegawa, M. Mehnert, J. Mergheim, P. Steinmann, and K. Kakimoto
(See online at https://doi.org/10.1016/j.sna.2019.111699) - “On thermo-viscoelastic experimental characterization and numerical modelling of VHB polymer,” International Journal of Non-Linear Mechanics, vol. 118, p. 103263, 2020
Z. Liao, M. Hossain, X. Yao, M. Mehnert, and P. Steinmann
(See online at https://doi.org/10.1016/j.ijnonlinmec.2019.103263) - “A complete thermo-electro-viscoelastic characterization of dielectric elastomers - Part II: Continuum modelling approach,” Journal of the Mechanics and Physics of Solids, p. 104625, 2021
M. Mehnert, M. Hossain, and P. Steinmann
(See online at https://doi.org/10.1016/j.jmps.2021.104625) - “A complete thermo-electro-viscoelastic characterization of dielectric elastomers, Part I: Experimental investigations,” Journal of the Mechanics and Physics of Solids, p. 104603, 2021
M. Mehnert, M. Hossain, and P. Steinmann
(See online at https://doi.org/10.1016/j.jmps.2021.104603) - “A geometrically exact continuum framework for light-matter interaction in photo-active polymers I. Variational setting,” International Journal of Solids and Structures, vol. 226, p. 111073, 2021
M. Mehnert, W. Oates, and P. Steinmann
(See online at https://doi.org/10.1016/j.ijsolstr.2021.111073)
