Nonlinear dynamic behaviors and PID control of viscoelastic dielectric elastomer balloons

As a type of intelligent electroactive polymer, dielectric elastomer (DE) exhibits viscoelastic properties. It’s worth pointing out that the relaxation time has great significance for studying the mechanical behavior of viscoelastic polymer. In this paper, a generalized Maxwell model is used to describe the viscoelastic property of dielectric elastomer balloon. Meanwhile, a theoretical model with multiple relaxation times is used and the natural frequency of small amplitude oscillation is derived. Subsequently, the model is validated by comparing with experimental results. The model with double relaxation times can describe the deformation of the dielectric elastomer balloon effectively. Then the effect of relaxation time and shear modulus on the dynamic response of DE balloon is studied. Furthermore, the dielectric elastomer balloons in practical application exhibit the strong nonlinearity and the viscoelastic dissipation. Therefore, it is important to precisely control the dynamic response. The proportional-integral-differential (PID) controller in the form of nonlinear combination is adopted to control the above nonlinear dynamic systems actively. The results indicate that it is feasible to achieve desired control effect.

EXPERIMENTAL RESEARCH ON VISCOELASTICITY PROPERTY OF DIFFERENT LAYERS PERIODONTAL LIGAMENT UNDER COMPRESSION

The periodontal ligament (PDL) exhibits different material mechanical properties along the long axis of the teeth. To explore the creep and the relaxation effects of dissimilar layers of PDL, this paper took the central incisors of porcine mandibular as experimental subjects and divided them perpendicular to the teeth axis into five layers. Creep experiments and relaxation experiments on five layers were conducted to obtain the creep compliance and relaxation modulus at different layers. Linear elastic model, generalized Kelvin model, and generalized Maxwell model were used to describe the major characteristics of the PDL: Instantaneous elasticity, creep and relaxation. Fitting accuracy of three-parameter, five-parameter, and seven-parameter of the model was compared, and the constitutive equations of different layers were established by the least square method. The results presented that the creep strain and the relaxation stress of PDL were exponentially correlated with time under different loading conditions. Different layers showed a significant effect on the creep strain and relaxation stress of PDL. Along the long axis of the teeth, the changing rule of the creep compliance and relaxation modulus of each layer showed quite the contrary, and the instantaneous elastic modulus first decreased to the minimum, then increased to the maximum. Higher instantaneous elastic modulus led to lower creep compliance and higher relaxation modulus. The generalized Kelvin model and the generalized Maxwell model well characterized the creep and relaxation properties of PDL. Fitting accuracy increased with the number of model parameters. The relaxation time of PDL was about one order of magnitude shorter than the creep retardation time, which indicated that the relaxation effect lasted shorter than the creep effect.

Numerical Analysis of Space Deployable Structure Based on Shape Memory Polymers

Shape memory polymers (SMPs) have been applied in aerospace engineering as deployable space structures. In this work, the coupled finite element method (FEM) was established based on the generalized Maxwell model and the time–temperature equivalence principle (TTEP). The thermodynamic behavior and shape memory effects of a single-arm deployment structure (F-DS) and four-arm deployment structure (F-DS) based on SMPs were analyzed using the coupled FEM. Good consistency was obtained between the experimental data and simulation data for the tensile and S-DS recovery forces, verifying that the coupled FEM can accurately and reliably describe the thermodynamic behavior and shape memory effects of the SMP structure. The step-by-step driving structure is suitable for use as a large-scale deployment structure in space. This coupled FEM provides a new direction for future research on epoxy SMPs.

MODELLING OF TIME-DEPENDENT BEHAVIOUR OF PARTICULATE THERMOSET POLYMERS

A preliminary study of a numerical model describing the behaviour of polymer-based composites is presented. The numerical model consists of three main parts. The first is the microplane M4 model, which is the main part of the model and is used to simulate elastoplastic behaviour and damage. The second part consists of a generalized Maxwell model, which adds the effect of linear creep of the material to the calculation. The last part is a free volume model that extends the linear creep to the nonlinear creep. The creep is calculated on the deviatoric part of the normal stress of each microplane, which allows the model to capture the polymer behaviour adequately without adjusting the free volume of the model.

Maxwell model geotextile encased stone column in soft soil improvement

In the field of geotechnical – soft soil improvement, the mathematical model or mechanical model is one of the important input parameters for the design calculations or studies. The determination of the appropriateness of the models has a great influence on the accuracy results of design and calculation as well as the sustainable stability of soft ground after improvement. On the contrary, the selection of inadequate calculation models will lead to increased costs of soft soil improvement, possibly even leading to the destabilization of the work and causing immense loss of people and property. Recently, many projects major highway after construction design in use has not meet the requirements of the standard, leading to wasted money and time of individuals, organizations, and the state of post-treatment. Therefore, the research and application of using mathematical or mechanical models in accordance with the new soft soil improvement method will greatly help as well as add additional options for soft soil improvement in Vietnam. The soft soil deformation is not only related to load but also to load time. The change in stress and deformation of weak soil over time is called rheology, and in this study is the viscoelastic behavior. From the above reasons, we try to apply a generalized Maxwell model to explain the viscoelastic behavior of a soft soil. In particular, the time-dependent behavior of a viscoelastic soft soil was represented by using the Maxwell rheological model. The Matlab programming code helps to solve numerically all the equation of the mathematical exhibition of the generalized Maxwell model results. We acknowledge that the generalized Maxwell model is superior in demonstrating the time-dependent behavior of soft soil. The results probably show that this is one of the effective models to predict the behavior of soft soils in ground improvement with GEC.

Visco-thermo-elastic Simulation Approach For Prediction of Cure-induced Residual Stresses in Fiber Reinforced Composites

Liquid composite molding (LCM) has established as a high quality manufacturing process for fiber reinforced composite structures. In order to reduce cycle times significantly, novel fast curing matrix resins are being introduced into series production. These put high requirements on process control and part reproducibility. Problems that may be encountered in this context involve process-induced distortion and surface waviness resulting from anisotropic and cure-dependent material properties. Numerical simulations represent a powerful approach to avoid the use of costly trial-and-error methods. For this reason, a simulation approach is being developed which aims at the prediction of residual stresses and accompanying effects on different length scales. Based on a resin characterization comprising reaction kinetics, cure-dependent relaxation modulus as well as thermal expansion and pressure-dependent chemical shrinkage, a generalized MAXWELL model is selected to describe the process-related mechanical behavior of the thermoset. Taking into account the influence of the process parameters on the resin properties enables a detailed analysis of process-property-relationships. By this, the developed simulation approach offers the possibility of a comprehensive analysis of both local and global process-induced phenomena and hence prevention of flaws.

NEWMARK ALGORITHM FOR DYNAMIC ANALYSIS WITH MAXWELL CHAIN MODEL

This paper investigates a time-stepping procedure of the Newmark type for dynamic analyses of viscoelastic structures characterized by a generalized Maxwell model. We depart from a scheme developed for a three-parameter model by Hatada et al. [1], which we extend to a generic Maxwell chain and demonstrate that the resulting algorithm can be derived from a suitably discretized Hamilton variational principle. This variational structure manifests itself in an excellent stability and a low artificial damping of the integrator, as we confirm with a mass-spring-dashpot example. After a straightforward generalization to distributed systems, the integrator may find use in, e.g., fracture simulations of laminated glass units, once combined with variationally-based fracture models.

3D Printing of Auxetic Shape-Memory Metamaterial Towards Designable Buckling

As one of the most popular 3D printed metamaterials, the auxetic structure with its tunable Poisson’s ratio has attracted huge amount of attention recently. In this study, we designed an auxetic shape-memory metamaterial, which showed designable buckling responses by using the thermomechanically coupled in-plane instability. The influence of viscoelasticity on in-plane moduli and Poisson’s ratios of shape-memory auxetic metamaterial was experimentally investigated. Based on the generalized Maxwell model and finite-element method, the buckling behaviors and their main influence factors were studied. The analytical results and experimental ones showed a good agreement. Thermomechanical properties of the printed metamaterials govern the temperature and strain rate-dependent buckling, and a controllable transition from the negative to positive Poisson’s ratio in the metamaterials can be achieved. Based on the shape memory effect, the buckled state and the Poisson’s ratio of the metamaterials can be tuned by programmed thermomechanical processes. This study provides a simple and efficient way to generate morphing structures using the designable buckling effect.