PH-sensitive hydrogel-based valves: A transient fully-coupled fluid-solid interaction study

pH-sensitive hydrogels are promising materials to be employed in microfluidic devices, especially microvalves. In this paper, a theory of transient swelling of pH-sensitive micro-valve is presented. A transient constitutive model that captures electrical, chemical, and mechanical fields is considered to model the swelling phenomenon. The diffusion of ions into the hydrogel, the electromigration, and convection are described by implementing the Nernst-Planck equation. Assuming Gent model, hydrogel is considered as a compressible hyperelastic material and osmotic pressure is assumed as an external loading. Due to benefits of in-plane valves, a design of the micro-valve is studied. Design simplicity and great sealing are vital factors which can be considered as an advantage of this valve for fabrication. This design and modeling approach has not been used for pH-sensitive hydrogels in earlier works. Thus, we have studied the transient swelling of pH-sensitive hydrogel microvalve, when effects of fluid-structure-interaction are examined on valve performance. It is noted that in most previous studies, equilibrium conditions have been assumed. While considering transient fully-coupled fluid-structure-interaction is necessary to capture a more realistic modeling. The results illustrate that the microvalve blocks the channel much earlier than reaching the equilibrium-state, which implies importance of the transient behavior of hydrogels.

Toughening Mechanism of Unidirectional Stretchable Composite

Composite materials have been long developed to improve the mechanical properties such as strength and toughness. Most composites are non-stretchable which hinders the applications in soft robotics. Recent papers have reported a new design of unidirectional soft composite with superior stretchability and toughness. This paper presents an analytical model to study the toughening mechanism of such composite. We use the Gent model to characterize the large deformation of the hard phase and soft phase of the composite. We analyze how the stress transfer between phases deconcentrates the stress at the crack tip and enhances the toughness. We identify two types of failure modes: rupture of hard phase and interfacial debonding. We calculate the average toughness of the composite with different physical and geometric parameters. The experimental results in literature agree with our theoretical predictions very well.

Modelling the Inflation and Elastic Instabilities of Rubber-Like Spherical and Cylindrical Shells Using a New Generalised Neo-Hookean Strain Energy Function

The application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure ($P$ P ) – inflation ($\lambda $ λ or $v$ v ) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials.

Mechanical behavior of a circular dielectric elastomer membrane under out-of-plane deformation

The mechanical behavior of a circular dielectric elastomer membrane (DEM) under the contact of a rigid ball is studied in this paper. The out-of-plane deformation of the DEM is unfolded to an equivalent in-plane deformation, and the mechanical behavior is further studied through the Helmholtz free energy theory and the Gent model. The theoretical results obtained from the proposed analysis approach are validated through the out-of-plane deformation experiments, and the influence of the DEM's thickness on the mechanical behavior is revealed and explained. Furthermore, the influences of some key dimensional, dynamical and electrical parameters on the DEM's mechanical behavior are investigated and discussed. The research results are helpful for the system analysis of dielectric elastomer actuators and dielectric elastomer generators with out-of-plane deformations.

Nonlinear Resonance Analysis of Dielectric Elastomer Actuators Under Thermal and Isothermal Conditions

In this paper, nonlinear resonance characteristics of a dielectric elastomer actuator are investigated with special consideration on the thermal effects. A finite thermo-elasticity model based on the Gent model is constructed to analyze the vibrational response of the system. The equation of motion is derived via the Euler–Lagrange method. The multiple scales method and the Taylor series expansion are used to solve the governing equation. Nonlinear resonant responses of the system such softening/hardening and jump are explored. Furthermore, the influences of different system parameters including temperature, limiting stretch, damping, mechanical load, relative permittivity and voltage on the frequency response curves are explored. The results are compared with those obtained in the isothermal state, and those solved by numerical methods. It is found that both softening and hardening-type nonlinearities occur in the system in both non-thermal and thermal conditions.

Quantifying the equilibrium swelling responses and swelling-induced snap-through of heterogeneous spherical hydrogels

We employ the finite deformation theory to analyze the inhomogeneous large deformation of a heterogeneous spherical hydrogel subjected to chemo-mechanical loadings. The heterogeneous spherical hydrogel is composed of two concentric spherical hydrogel layers with different material properties. The Gent model is employed for the free energy function of the polymer stretching part in order to tackle the effect of the limiting chain extensibility. The heterogeneous spherical hydrogel is assumed to be perfectly bonded at the interface and is traction free at the external surface. At the internal surface, two boundary conditions are considered: one is internally fixed and the other is internally pressurized. Numerical examples are performed to describe the nonlinear behaviors of a heterogeneous spherical hydrogel when subjected to the swelling and mechanical loadings. For internally fixed case, numerical results show that the limiting chain extensibility and the initial swelling ratio have significant effect on the actuation deformation of a heterogeneous spherical hydrogel. For internally pressurized case, we find that the swelling-induced snap-through instability can be triggered under specified conditions. It is shown that the chemo-mechanical behaviors of the heterogeneous spherical hydrogels can be adjusted by tuning the material properties and the initial swelling ratios.

Fully-Coupled Transient Fluid–Solid Interaction Simulation of the pH-Sensitive Hydrogel-Based Microvalve

The pH-sensitive hydrogels are attractive candidates to act like a microvalve in microfluidic devices. In this study, we build a theory for the transient simulation of a pH-sensitive hydrogel-based microvalve. Three fields are involved in the theory, namely the electrochemical, mechanical and fluid fields. We utilize the Nernst–Planck equation to describe the ionic flux into the hydrogel through diffusion, electrical migration and convection. We model the hydrogel as a compressible isotropic hyperelastic material with the Gent model. Then we implement the theory in a nonlinear finite element framework to simulate the time-dependent fluid–solid interaction (FSI) behavior of the pH-sensitive microvalve. Our focus is on exploring the physics and phenomena involving in the simulation rather than simulating a complex geometry or presenting a new design. We manifest the significance of the FSI by comparing the transient FSI and non-FSI simulation of the microvalve. The most highlighted novelty of our study is accounting for time-dependent effects. The results demonstrate that the microvalve perfectly closes the channel much before it reaches its stationary state and the closing state, which is of high interest in the microvalve study is different from the stationary state.

Towards a physics-based multiscale modelling of the electro-mechanical coupling in electro-active polymers

Owing to the increasing number of industrial applications of electro-active polymers (EAPs), there is a growing need for electromechanical models which accurately capture their behaviour. To this end, we compare the predicted behaviour of EAPs undergoing homogeneous deformations according to three electromechanical models. The first model is a phenomenological continuum-based model composed of the mechanical Gent model and a linear relationship between the electric field and the polarization. The electrical and the mechanical responses according to the second model are based on the physical structure of the polymer chain network. The third model incorporates a neo-Hookean mechanical response and a physically motivated microstructurally based long-chains model for the electrical behaviour. In the microstructural-motivated models, the integration from the microscopic to the macroscopic levels is accomplished by the micro-sphere technique. Four types of homogeneous boundary conditions are considered and the behaviours determined according to the three models are compared. For the microstructurally motivated models, these analyses are performed and compared with the widely used phenomenological model for the first time. Some of the aspects revealed in this investigation, such as the dependence of the intensity of the polarization field on the deformation, highlight the need for an in-depth investigation of the relationships between the structure and the behaviours of the EAPs at the microscopic level and their overall macroscopic response.