Active origami-inspired designs, which incorporate active materials such as electroactive polymers and magnetoactive elastomers into self-folding structures, have shown good promise in engineering applications. In this article, finite element analysis models are developed for several bending and folding configurations that incorporate a combination of active and passive material layers, such as electroactive polymer-actuated unimorph benders based on single and multilayer electroactive polymers, electroactive polymer-actuated notched unimorph folding configurations, and a multi-field actuated bimorph configuration. Constitutive relations are developed for both electrostrictive and magnetoactive materials to model the coupled behaviors explicitly. Shell elements are adopted for their capacity of modeling thin films, relatively low computational cost, and ability to model the intrinsic coupled behaviors in the active materials under consideration. The electrostrictive coefficients are measured and then used as input in the constitutive modeling of the coupled behavior. The magnetization of the magnetoactive elastomer is measured and then used to calculate the magnetic torque as a function of the special orientation, which leads to spatial deformation of the magnetoactive elastomers. The objective of the study is to validate the constitutive models implemented through the finite element analysis method to simulate multi-field coupled behaviors of the active origami configurations. Through quantitative comparisons, simulation results show good agreement with experimental data. By investigating the impact of material selection, location, and geometric parameters, this finite element analysis approach can be used in design of self-folding structures, reducing trial-and-error iterations in experiments.
The incorporation of smart materials such as electroactive polymers and magnetoactive elastomers in origami structures can result in active folding using external electric and magnetic stimuli, showing promise in many origami-inspired engineering applications. In this study, 3D finite element analysis (FEA) models are developed using COMSOL Multiphysics software for three configurations that incorporate a combination of active and passive material layers, namely: (1) a single-notch unimorph folding configuration actuated using only external electric field, (2) a double-notch unimorph folding configuration actuated using only external electric field, and (3) a bifold configuration which is actuated using multi-field (electric and magnetic) stimuli. The objectives of the study are to verify the effectiveness of the FEA models to simulate folding behavior and to investigate the influence of geometric parameters on folding quality. Equivalent mechanical pressure and surface stress are used as external loads in the FEA to simulate electric and magnetic fields, respectively. Compared quantitatively with experimental data, FEA captured the folding performance of electric actuation well for notched configurations and magnetic actuation for a bifold structure, but underestimated electric actuation for the bifold structure. By investigating the impact of geometric parameters and locations to place smart materials, FEA can be used in design, avoiding trial-and-error iterations of experiments.
Origami — the Japanese art of folding — has inspired various engineering applications for several decades due to its ability to manipulate complex shapes. In our study, multi-field actuated self-folding Origami structures are developed with the implementation of two classes of smart materials: relaxor ferroelectric polymers and magneto-active elastomers (MAEs). The chosen relaxor ferroelectric is P(VDF-TrFE-CTFE), a P(VDF)-based terpolymer and the MAE is a PDMS substrate with embedded barium hexaferrite particles. At the macroscale, this study involves the modeling of the large deformation of a bimorph comprising the aforementioned magnetically and electrically actuated materials using a 1D analytical model derived from the equilibrium of a differential element. The large deformation is extracted from curvatures solved at each point for the resulting differential equation of the equilibrium state. On the microscale, this study also considers the nonlinear behavior of the smart materials. The nonlinear dielectric response of the relaxor ferroelectric polymer is captured by an electric field-dependent electrostrictive coefficient derived from a microstructure-based energy balance for the electrostriction of the terpolymer. The energy density function is postulated to be composed of an elastic contribution described by the Arruda-Boyce hyperelastic model and an electric contribution based on dipole-dipole interactions. On the other hand, a magnetic field-dependent torque drives the actuation of the MAEs, which is also dependent on the orientation of the material to the field. The integration of the micro and macro components results in an analytical model of a 1D, multi-layered flat structure that can be numerically solved for displacements under combined fields. The model is compared with well-matching experimental results of a unimorph and a bimorph structure as validation. The experiments measured the tip displacement of the beam under combined fields for a quantitative analysis. The study takes the analysis further by optimizing parameters such as geometry, field strengths, and the combination of active layers for relevant target shapes.
With the development of smart materials such as electroactive polymers and magnetoactive elastomers, active origami structures, where desired folded shapes can be achieved using external electric and magnetic stimuli, are showing promising potential in many engineering applications. In this study, finite element analysis (FEA) models are developed in 3-D using COMSOL Multiphysics software for unimorph bending and folding actuated using a single external field, and a bi-fold configuration which is actuated using multi-field stimuli. The objectives of the study are: 1) to investigate folding behavior and effects of geometric parameters, and 2) to maximize actuation for a given stimulus. Experimentally determined mechanical pressures and moments are applied as external loads to simulate electric and magnetic fields, respectively. Good agreement is obtained in the tip displacement and folding angles between the simulation and experiments, which demonstrates the effectiveness of the FEA model.
Active origami designs, which incorporate smart materials such as electroactive polymers (EAPs) and magnetoactive elastomers (MAEs) into mechanical structures, have shown good promise in engineering applications. In this study, finite element analysis (FEA) models are developed using COMSOL Multiphysics software for two configurations that incorporate a combination of active and passive material layers, namely: 1) a single-notch unimorph folding configuration actuated using only external electric field and 2) a bimorph configuration which is actuated using both electric and magnetic (i.e. multifield) stimuli. Constitutive relations are developed for both electrostrictive and magnetoactive materials to model the coupled behaviors directly. Shell elements are adopted for their capacity of modeling thin films, reduction of computational cost and ability to model the intrinsic coupled behaviors in the active materials under consideration. A microstructure-based constitutive model for electromechanical coupling is introduced to capture the nonlinearity of the EAP’s relaxor ferroelectric response; the electrostrictive coefficients are then used as input in the constitutive modeling of the coupled behavior. The magnetization of the MAE is measured by experiment and then used to calculate magnetic torque under specified external magnetic field. The objective of the study is to verify the effectiveness of the constitutive models to simulate multi-field coupled behaviors of the active origami configurations. Through quantitative comparisons, simulation results show good agreement with experimental data, which is a good validation of the shell models. By investigating the impact of material selection, location, and geometric parameters, FEA can be used in design, reducing trial-and-error iterations in experiments.
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