Embedded Files
Wang, Z., Wagner, R.J., Chen, T., Shah, S.P., Maiaru, M. and Silberstein, M.N., 2025. Bond exchange reactions as a paradigm for mitigating residual stress in polymer matrix fiber composites. International Journal of Solids and Structures, 313, p.113286. DOI
Ren G, Wang Z, Huang X, Hur D, Pfeifer M.A. Silberstein M.N., Tian Z., 2025. Thermally conductive polyethylene as thermal interface material. Materials Horizons. DOI
Wang, Z., Cai, H., Silberstein, M.N., 2023. A constitutive model for elastomers tailored by ionic bonds and entanglements. Mechanics of Materials, 179,104604. DOI
Du, Z., Yang, Y., Wang, Z., Fan, X. and Lu, T., 2023. A finite strain visco-hyperelastic damage model for rubber-like materials: theory and numerical implementation. Acta Mechanica Sinica, 39(3), 222473. DOI
Cai, H., Wang, Z., Utomo, N.W., Vidavsky, Y., Silberstein, M.N., 2022. Highly stretchable ionically crosslinked acrylate elastomers inspired by polyelectrolyte complexes. Soft Matter 18 (39), 7679–7688. DOI
Tepermeister, M., Bosnjak, N., Dai, J., Zhang, X., Kielar, S.M., Wang, Z., Tian, Z., Suntivich, J., Silberstein, M.N., 2022. Soft ionics: governing physics and state of technologies. Frontiers in Physics, 10, 890845. DOI
Lu, T., Wang, Z., Tang, J., Zhang, W. and Wang, T., 2020. A pseudo-elasticity theory to model the strain-softening behavior of tough hydrogels. Journal of the Mechanics and Physics of Solids, 137, 103832. DOI
Zhang, W., Hu, J., Tang, J., Wang, Z., Wang, J., Lu, T. and Suo, Z., 2018. Fracture toughness and fatigue threshold of tough hydrogels. ACS Macro Letters, 8(1), pp.17-23. DOI
Wang, Z., Tang, J., Bai, R., Zhang, W., Lian, T., Lu, T. and Wang, T., 2018. A phenomenological model for shakedown of tough hydrogels under cyclic loads. Journal of Applied Mechanics, 85(9), p.091005. DOI
An, L., Lu, T., Xu, J., Wang, Z., Xu, M. and Wang, T.J., 2018. Soft sensor for measuring wind pressure. International Journal of Mechanical Sciences, 141, pp.386-392. DOI
Lu Y, Wang Z, Yong H, et al. Modeling effects of gas bubbles on the mechanical behaviors of Ag/Bi-2212 round wires using a double cantilever beam bridge model[J]. Cryogenics, 2016, 77: 65-73. DOI
Research Experience
Research Experience
08/2019- 12/2024 Cornell Universiy
08/2019- 12/2024 Cornell Universiy
Bond exchange reactions as a paradigm for mitigating residual stress in polymer matrix fiber
Polymer matrix fiber composites often suffer from residual stresses due to differences in coefficients of thermal expansion between the fibers and resins, as well as contractile strain of the resins during curing. To address residual stress driven composite failure, we propose the use of vitrimers as composite resins, which can undergo thermally activated, stress alleviating, bond exchange reactions (BERs). We conduct fiber Bragg grating measurements for a single glass fiber within bulk vitrimer. These show that the fiber strain in vitrimers with 5% catalyst is significantly lower than in those with 0% catalyst (minimal BER expected) during both curing and post-curing phases. We developed a finite deformation, micromechanically-inspired model that incorporates curing, thermal processes, and BERs, and then implemented this model it into finite element software to simulate stress evolution within single fiber composite systems. The combination of experimental and computational results reveals that BERs can effectively mitigate, but not eliminate, the residual stress in polymer matrix fiber composites.
Bulk Thermally Conductive Polyethylene as Thermal Interface Materials
As the demand for high-power-density microelectronics rises, overheating becomes the bottleneck that limits device performance. In particular, the heterogeneous integration architecture can magnify the importance of heat dissipation and necessitate electrical insulation between critical junctions to prevent dielectric breakdown. Consequently, there is an urgent need for thermal interface materials (TIMs) with high thermal conductivity and electrical insulation to address this challenge. In this work, we synthesized thermally conductive polyethylene (PE) bars with vertically aligned polymer chains via a solid-state drawing technique to achieve a thermal conductivity of 13.5 W m-1 K-1 with a coverage area of 2.16 mm2. We utilized wide-angle x-ray scattering to elucidate the molecular structural changes that led to this thermal conductivity enhancement. Furthermore, we conducted a device-cooling experiment and showed a 39% hot spot temperature reduction compared to a commercial ceramic-filled silicone thermal pad under a heating power of 3.6 W. Thus, this bulk-scale thermally conductive PE bar with nanoscale structural refinement demonstrated superior cooling performance, offering potential as an advanced thermal interface material for thermal management in microelectronics.
A constitutive model for elastomers tailored by ionic bonds and entanglements
Over the past decade or two, the concept has emerged of using multiple types of weak interactions simultaneously to enhance the mechanical properties of elastomers. These weak interactions include physical entanglements, hydrogen bonds, metal coordination bonds, dynamic covalent bonds, and ionic bonds. The combination of entanglements and ionic bonding has been minimally explored and is particularly exciting because of the broad application space for polyelectrolytes. In this work, a constitutive model framework is developed to describe the response of elastomers with both ionic bonds and entanglements. We formulate a micromechanical model that couples together chain stretching, ionic bond slipping, and entanglement evolution. The ionic bonds provide toughness by enabling plastic deformation in comparison to covalently crosslinked material and add strength compared to a linear polymer. Evolution of the entanglement density is taken as a key mechanism that can govern stiffness, toughness, and self-recovery in elastomers. The model is used to match bulk polyelectrolytes with different fractions of ionic components under a variety of loading histories. The variations in material parameters are then used to help understand the relative importance of different governing mechanisms in the bulk polymers. We show that the theoretical framework can explain our experimental uniaxial tensile experimental results for polyelectrolytes. This model can help to design better material with high stiffness and toughness. We expect that our model can be extended to explain the mechanical behavior of other polyelectrolytes and other soft materials with a wide range of dynamic bonds.
Simulation for a polymer with divalent ionic
Assuming the crosslink will only form through a cation and two anions. When applying a voltage on the surface, some of the cations will dissociate from the polymer chain leading to a decreasing in crosslink density. Therefore, the local concentration can be used to set the upper limit of density. I use COMSOL to simulate the dynamic behavior of ionic in the polymer matrix such as the anion fixed on polymer chain and the cation will move through the electrical field. Setting up the different parameters for the system and based on Nernst-Planck-Poisson (PNP) equation and Comsol, I find the relationship between the critical length, initial condition, and permittivity. Besides, using the simulation result establishes a constitutive model for the Polyelectrolyte with the electrical field.
09/2015-06/2019 Supervisor: Prof. Tiejun Wang & Tongqing Lu, Xi'an Jiaotong University
09/2015-06/2019 Supervisor: Prof. Tiejun Wang & Tongqing Lu, Xi'an Jiaotong University
A finite strain visco-hyperelastic damage model for rubber-like materials: theory and numerical implementation
Many rubber-like materials exhibit hyperelastic, time-dependent, rate-dependent and progressive damage behaviors. In our previous work (Lu et al., 2020), we proposed a hyperelastic damage model to characterize the strain-softening behavior of soft materials. The model modifies the strain energy function of a single chain by introducing an internal damage variable D and then maps the deformation of chains to the macroscopic deformation. In this work, we extend this model to incorporate the time-dependent viscous effect using the Prony series-based nonlinear theory. We further implement the finite strain viscohyperelastic damage model into finite element software ABAQUS by a user material subroutine UMAT. We use the experimental data of a kind of acrylic polymer under uniaxial tension in literature to calibrate the model parameters, including 4 time-independent parameters and 6 time-dependent parameters. We then use the calibrated parameters to simulate the uniaxial tension and stress relaxation of the acrylic polymer specimen with a complex geometry. The simulated results agree with the experimental data with a remarkable accuracy.
A micro-damage constitutive model for rate-dependent Mullins effect and induced residual deformation
Mullins effect, easily observed by stretching polymers, is typically rate-dependent during cyclic loading-unloading as well as exhibits residual deformation after unloading. This rate-dependent mechanical behavior is related to the microstructural damage evolution (including chain scission and network rearrangement) with the consequence of decreasing the system entropy. In this paper, we propose a micro-damage constitutive model to characterize the rate-dependent and residual deformation behavior, where the
associated chain density varies with both deformation gradient and time. The nominal stress results from chain scission (the associated chains evolve with time) and network rearrangement (the associated chains evolve with the deformation gradient). For a small stretch, the microstructural damage does not affect its mechanical behavior, it is the same as the behavior of the hyper-elastic material. For an intermediate stretch, chain scission starts to work, the hysteresis loop is so small and the residual deformation can be neglected. As the stretch increases, network rearrangement predominates the mechanical behavior and results in a large hysteresis loop as well as residual deformation after unloading. This model can consistently explain the experimental results of polyurethane and reported nanocomposite hydrogels well under cyclic loading/unloading. The present model has a wide range of tunability with the parameters of chain distribution, stretch rate, and maximum stretch. It is shown clearly that the residual deformation decreases with chain length and stretch rate, while increases with maximum stretch. Under these conditions, the residual deformation will eventually reach a steady-state. We further simulate multi-cyclic loading behaviors and predict the Mullins effect recovery. These findings lay the ground for providing a general approach to study both the rate-dependent Mullins effect and residual deformation of various polymeric materials.
A pseudo-elasticity theory to model the strain-softening behavior of tough hydrogels
We develop a large deformation theory to model the strain-softening behavior of tough hydrogels. We introduce an additional thermodynamic variable to the free energy function for a single chain. Combined with the eight-chain model, we connect the chain deformation behavior to the network deformation. This model is a direct extension of classical constitutive model for rubber with only one additional parameter, which controls the softening and stiffening of the stress-stretch curve.
A phenomenological model for shakedown of hydrogels under cyclic loads
Recent experiments report that when a tough hydrogel is subject to cyclic loads, the maximum stress decreases cycle by cycle and reaches a steady state after thousands of cycles, denoted as the shakedown phenomenon. We develop a phenomenological model to describe the shakedown of tough hydrogels under prolonged cyclic loads for the first time. We specify a new evolution law of damage variable in multiple cycles, motivated by the experimental observations. Our model fits the experimental data remarkably well, including the features of Mullins effect, residual stretch and stress shakedown. The model is also suitable for PAAM/PAMPS and PAAM/alginate double-network hydrogels.
Asymptotic analysis of crack tip fields for hydrogels in plane strain
Based on the large deformation theory, we establish the equilibrium equations and boundary conditions coupled with the diffusion. According to the asymptotic method, equilibrium equations and boundary conditions, we calculate the crack tip fields in the initial state. Dimensional analysis indicates that the diffusion process is self-similar. By the self-similar process, we are capable of getting the evolution of stress field at the crack tip field as solvent diffuses using the asymptotic method.
Soft sensor for measuring wind pressure
A soft double layered capacitive sensor is designed to measure pressure in the wind flowing environment. One layer acts as an active capacitor to measure the magnitude of wind pressure and the other layer acts as a passive capacitor to differentiate the positive and negative pressure. We simultaneously record electrical signals from both active and passive capacitor under different angles with a home-made circuit. A static experiment is conducted in parallel to calibrate the measured electrical signals to pressure by a linear fit. The designed sensor is of high sensitivity, low cost, non-destructive and easy to implement on a large area of an object, such as the bullet train, solar panels or a building.
Fatigue fracture of Nanocomposite hydrogels (Co-author)
Doing experiments to study the fatigue behavior of Nanocomposite hydrogels under the pure shear condition, we find that the stress-strain curve changes cycle by cycle and then reach a steady state after thousands of cycles. We get the threshold of Nanocomposite hydrogels for fatigue fracture.
07/2015-08/2015 Supervisor: Prof. Wei-Chung Wang , National Tsing Hua University
07/2015-08/2015 Supervisor: Prof. Wei-Chung Wang , National Tsing Hua University
Topography measurement of thin films by using Coherent Gradient Sensor system
Coherent Gradient Sensor (CGS) system, a shear interferometry method, is developed to measure the full field curvatures of thin film systems. We obtain the interferogram of the speculum which is made of a BK7 glass substrate and the aluminum films. By using the Fourier transform and the phase wrapping algorithm, we get the distribution of phase from the interference fringe, and calculate the curvature of thin films. We are capable knowing the topography of films.
10/2014-05/2015 Supervisor: Prof. Huadong Yong , Lanzhou University
10/2014-05/2015 Supervisor: Prof. Huadong Yong , Lanzhou University
Modeling effects of gas bubbles on the mechanical behaviors of Ag/Bi-2212 round wires using a double cantilever beam bridge model
Fabricating as an isotropic round wire, Bi2Sr2CaCu2Ox (Bi2212) superconductors material is 30% void space in the wire, such as gas bubbles, which have a larger influence on the property of the wire. Based on the double cantilever beam model and critical state theory, the mechanical behavior of Bi2212 wire is studied for decreasing field. Two different damage mechanisms are discussed using the strain energy release rate and strain of bridge. The results show that the large gas bubble can increase the strain of bridge. The central filaments with gas bubble are easier to be damaged than the edge filaments with gas bubble.
03/2014-04/2015 Supervisor: Prof. Jizeng Wang , Lanzhou University
03/2014-04/2015 Supervisor: Prof. Jizeng Wang , Lanzhou University
[Hui-Chun Chin and Tsung-Dao Lee Chinese Undergraduate Research Endowment (CURE)]
[Hui-Chun Chin and Tsung-Dao Lee Chinese Undergraduate Research Endowment (CURE)]
Design and optimization of micro and nano-scale lithium-ion batteries electrode structure based on a coupling principle between ion diffusion and mechanical deformation
Coupled with the ion diffusion and mechanical deformation, the electrode surface of lithium-ion batteries conducts a “Surface Locking” behavior. We design a novel electrode with composite layers to reduce the surface stress and avoid the surface locking phenomenon. At the same time, the critical current and the charging rate will be improved by giving some pre-strain. We use the simulation to verify the novel electrode of lithium-ion batteries.
Presentations
Presentations
Wang Z, Wagner R.J., Chen T, Silberstein M.N., Bond Exchange Reactions to Mitigate Residual Stress in Polymer Composites, SEM annual conference, Vancouver, WA, June 3-6, 2024.
Wang Z, Cai H, Silberstein, M.N., A constitutive model for elastomers tailored by ionic bonds and entanglements, SES Annual Technical Meeting, Minneapolis, MN, Oct 9 – 11, 2023.
Wang Z, Cai H, Silberstein, M.N., A constitutive model for elastomers tailored by ionic bonds and entanglements, International Mechanical Engineering Congress & Exposition (IMECE), Columbus, US, Oct 30 – Nov 3, 2022.
Wang Z, Tang J, Bai R, Zhang W, Lian T, Lu T, Wang T. A phenomenological model for shakedown of tough hydrogels under cyclic loads, National Conference on Solid Mechanics in China, Harbin, China, Nov 23 – 25, 2018.
Wang Z, Lu T, Wang T. A rate dependent constitutive model for nanocomposite hydrogel, Hokkaido Summer Institute & International Soft Matter, Hokkaido, Japan, Jul 29 – Aug 12, 2017.
Wang Z, An L, Lu T, Xu J, et al. Soft sensor for measuring wind pressure. The 2nd Symposium on Software Robotics Theory and Technology, Hangzhou, China, Dec 23 – 25, 2016.
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