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Today, tunable soft elastomeric actuators due to their remotely-controllability, fast-response and stiffening have gained great attention. This article aims to develop analytical and numerical tool...

Shape memory polymers are a class of smart materials, which are capable of fixing their deformed shapes, and can return to their original shape in reaction to external stimulus such as heat. Also due to their exceptional properties, they are mostly used in four-dimensional printing applications. To model and investigate thermomechanical response of shape memory polymers mathematically, several constitutive equations have been developed over the past two decades. The purpose of this research is to provide an up-to-date review on structures, classifications, applications of shape memory polymers, and constitutive equations of thermally responsive shape memory polymers and their composites. First, a comprehensive review on the properties, structure, and classifications of shape memory polymers is conducted. Then, the proposed models in the literature are presented and discussed, which, particularly, are focused on the phase transition and thermo-viscoelastic approaches for conventional, two-way as well as multi-shape memory polymers. Then, a statistical analysis on constitutive relations of thermally activated shape memory polymers is carried out. Finally, we present a summary and give some concluding remarks, which could be helpful in selection of a suitable shape memory polymer constitutive model under a typical application.

Dielectric actuators (DEAs), because of their exceptional properties, are well-suited for soft actuators (or robotics) applications. This article studies a multi-stimuli thermo-dielectric-based soft actuator under large bending conditions. In order to determine the stress components and induced moment (or stretches), a nominal Helmholtz free energy density function with two types of hyperelastic models are employed. Non-linear electro-elasticity theory is adopted to derive the governing equations of the actuator. Total deformation gradient tensor is multiplicatively decomposed into electro-mechanical and thermal parts. The problem is solved using the second-order Runge-Kutta method. Then, the numerical results under thermo-mechanical loadings are validated against the finite element method (FEM) outcomes by developing a user-defined subroutine, UHYPER in a commercial FEM software. The effect of electric field and thermal stimulus are investigated on the mean radius of curvature and stresses distribution of the actuator. Results reveal that in the presence of electric field, the required moment to actuate the actuator is smaller. Finally, due to simplicity and accuracy of the present boundary problem, the proposed thermally-electrically actuator is expected to be used in future studies and 4D printing of artificial thermo-dielectric-based beam muscles.

Magnetorheological elastomers (MREs) are polymers reinforced by ferromagnetic particles that show magnetic dependent behavior. Mixing MREs with reinforcing fibers can create a new class of material so-called “MRE composites, MRECs” with additional functionalities and properties. Here, using a Generalized Maxwell model, we proposed a new magnetic-dependent rheological model by considering the hysteresis phenomenon for MREs to predict the dynamic damping responses of MREC plates reinforced by fibers in the frequency domain. We also investigated the influence of magnetic flux intensity, the volume fraction of the fiber, the orientation angle of the fibers, the number of layers, as well as the fiber-to-matrix stiffness ratio on the natural frequency, loss factor, and mode shapes of MRECs plates. Our results suggest that homogenously increasing the elastic properties of the MRECs through the spatial distribution of fibers and changing the fiber-to-matrix stiffness ratio can effectively tailor the dynamic properties of MRECs. Tailoring these properties can provide additional freedom for the fabrication of 4D-printed MRE-based composites.

Non-affine deformations enable mechanical metamaterials to achieve their unusual properties while imposing implications for their structural integrity. The presence of multiple phases with different mechanical properties results in additional non-affinity of the deformations, a phenomenon that has never been studied before in the area of extremal mechanical metamaterials. Here, we studied the degree of non-affinity, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document}Γ, resulting from the random substitution of a fraction of the struts,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{h}$$\end{document}ρh, that make up a lattice structure and are printed using a soft material (elastic modulus = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{s}$$\end{document}Es) by those printed using a hard material (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{h}$$\end{document}Eh). Depending on the unit cell angle (i.e., \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta $$\end{document}θ = 60°, 90°, or 120°), the lattice structures exhibited negative, near-zero, or positive values of the Poisson’s ratio, respectively. We found that the auxetic structures exhibit the highest levels of non-affinity, followed by the structures with positive and near-zero values of the Poisson’s ratio. We also observed an increase in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document}Γ with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{E}_{h}}{{E}_{s}}$$\end{document}EhEs and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{h}$$\end{document}ρh until \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{{E}_{h}}{{E}_{s}}$$\end{document}EhEs =104 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{h}$$\end{document}ρh= 75%-90% after which \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document}Γ saturated. The dependency of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document}Γ upon \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{h}$$\end{document}ρh was therefore found to be highly asymmetric. The positive and negative values of the Poisson’s ratio were strongly correlated with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document}Γ. Interestingly, achieving extremely high or extremely low values of the Poisson’s ratio required highly affine deformations. In conclusion, our results clearly show the importance of considering non-affinity when trying to achieve a specific set of mechanical properties and underscore the structural integrity implications in multi-material mechanical metamaterials.

The performance of Magnetorheological dampers should be analyzed to study the stability of Magnetorheological fluid and its configuration. To this end, in this study a prototype Magnetorheological fluid is presented. The fluid consists of stabilized Silicone dioxide (SiO2) nanoparticles, Stearic acid, Phosphoric acid and micron-sized soft ferromagnetic carbonyl iron particles. To assure the authentic performance, sedimentation and magneto-rheometry tests are conducted. Also, a prototype of double-tube Magnetorheological damper with double magnetic components is fabricated by using the mentioned magnetorheological fluid characteristics. Damping force measurement test is carried out to measure the damping force in various electrical currents. The Kwok model is employed to examine the analytical model predictions against the experiments. Furthermore, a general evolution is presented using the neural network algorithm. It is demonstrated that the damping force in saturated current is almost five times higher than in the zero current. In addition, the derived evolution for the damping force has a high performance to predict the response of the Magnetorheological damper in other electrical currents.

Today, the rational combination of materials and design has enabled the development of bio-inspired lattice structures with unprecedented properties to mimic biological features. The present study aims to investigate the mechanical performance and energy absorption capacity of such sophisticated hybrid soft–hard structures with gradient lattices. The structures are designed based on the diversity of materials and graded size of the unit cells. By changing the unit cell size and arrangement, five different graded lattice structures with various relative densities made of soft and hard materials are numerically investigated. The simulations are implemented using ANSYS finite element modeling (FEM) (2020 R1, 2020, ANSYS Inc., Canonsburg, PA, USA) considering elastic-plastic and the hardening behavior of the materials and geometrical non-linearity. The numerical results are validated against experimental data on three-dimensional (3D)-printed lattices revealing the high accuracy of the FEM. Then, by combination of the dissimilar soft and hard polymeric materials in a homogenous hexagonal lattice structure, two dual-material mechanical lattice statures are designed, and their mechanical performance and energy absorption are studied. The results reveal that not only gradual changes in the unit cell size provide more energy absorption and improve mechanical performance, but also the rational combination of soft and hard materials make the lattice structure with the maximum energy absorption and stiffness, in comparison to those structures with a single material, interesting for multi-functional applications.

Nowadays, shape memory polymers (SMPs)-based devices are required to be much smarter to produce large shape memory recovery and recovery force with lower working temperatures in order to enable multi-functionality in them. They could play a vital role in the advancement of multi-functional soft robot manipulators, biomedical tools and wearable devices where the working temperatures is a key challenge and must be around the body temperature, or in sustainable smart systems with low energy consumption. The aim of this paper is to introduce thermo-electro-magneto-responsive fibrous SMPs (TEMFSMPs) as a new class of SMPs with highly enhanced shape recovery and recovery force and reduced working temperature. A three-dimensional constitutive model is developed to simulate thermo-electro-magneto-visco-hyperelastic behaviors of SMPs under large deformation for the first time. Constitutive relations are derived by adopting an electro-magneto-visco-hyperelasticity theory and implementing it in a thermo-mechanical cycle of SMPs. To improve the strength of thermo-electro-magneto-responsive SMPs, a bunch of fibers is also embedded into the SMP matrix. Then, the proposed model for thermo-electro-magneto-responsive fibrous shape memory polymers (TEMFSMPs) under uniaxial tension and complex loading regimes such as simultaneous torsion and extension are solved semi-analytically. In addition, the thermo-mechanical response through the proposed model is validated via available SMP experimental tests. Numerical results reveal that electro-magnetic features can significantly enhance shape memory recovery and recovery force of TEMFSMPs and lower their working temperatures. It is found that the electro-magnetic field, the orientation, and stiffness of fibers can effectively be set to tune the shape memory effect and bio-applicability of TEMFSMPs with highly enhanced stress/strain recovery and reduced working temperature.

Fracture behavior of Shape Memory Polymers (SMPs) and their self-healing property is one of the up-to-date subjects through the literature, where only a few researches have been conducted. Nowadays, because of the exceptional properties of SMPs and their implementation in 4D printing, they are most taken into attention. In this study, thermomechanical coupling effect on 3D fracture analysis of SMPs in large deformation regime has been investigated. Firstly, a thermo-visco-hyperelastic model is implemented to model the thermomechanical cycle of the SMP in the stress-free strain-recovery as well as the fixed-strain-stress-recovery processes. Motivated by fracture analysis and self-healing properties of SMPs, both 2D and 3D fracture analysis are conducted through various feasibility applications, such as flow control valve, pressure control valve, filtration and drug delivery capsule. Moreover, the ability of the analysis is shown through examining different parameters could affect the SMP response, such strain rate (or applied strain), temperature rate and memory recovery. Finally, the results show the ability of the numerical modeling in the aforesaid applications to design, analyze, and fabricate these applications.

The rise of a new class of smart materials known as electro-magnetorheological elastomers (EMREs) requires comprehensive understanding of their electro-magneto-visco-hyperelastic behaviors. The aim of this paper is to develop a generalized three-dimensional (3D) continuum-based framework of the electro-magneto-visco-hyperelastic behaviors of EMREs. The finite strain model is established based on the linear viscoelasticity theory and non-linear electro-magneto-elastic framework. As EMRE devices can be used in a cylindrical shape undergoing shear and normal stresses in many engineering applications like artificial muscles, a boundary-value problem simulating torsion–extension deformations of EMRE cylinders is developed in the finite strain regime and solved semi-analytically. The behaviors of EMRE cylinders under different loading conditions such as purely mechanical loading, purely electric loading as well as full coupling between mechanical, electric and magnetic loading are studied in detail. Influence of different parameters such as electric field, magnetic field, applied strain (-rate) and their coupling on the induced moment and axial force of the EMRE cylinder as well as its relaxation and creep under torsion–extension loading is also examined. It is shown that EMREs have adaptive capability and great potential in applications where the stiffness needs to be controllable. Due to simplicity and accuracy, the model is expected to be used in the future studies dealing with the analysis of EMREs in particular cylinders under torsion–extension developments like 4D printing of artificial EMRE-based cylindrical muscles.

Shape memory polymers (SMPs) are a group of smart materials that, by applying an external stimulation such as the temperature, retrieve their permanent shape from a temporary one. SMP nanocomposites have been developed to improve the mechanical, thermal, electrical, and magnetic properties of SMPs for potential applications in e.g. medical equipment, sensors, actuators, and drug delivery systems. In this research, SMP is reinforced with Coiled carbon nanotubes (CCNT) due to its geometric properties which let material tolerate higher strains and improve thermomechanical properties of SMP. In this paper, the effect of addition of CCNT on thermomechanical response of SMP under large deformations is numerically investigated. Employing a thermo-visco-hyperelastic constitutive model for SMP, a cubic representative volume element is realized using Monte Carlo algorithm. The effect of inclusion's geometry (e.g. spring length or aspect ratio, pitch or number of coils of CCNT), volume fraction, as well as their distribution on the thermomechanical properties of SMP/CCNT composite in two stress- and shape recovery processes in different heating rates and pre-strains is studied using Finite Element technique. Results reveal that increasing the volume fraction up to 0.6%, leads to a 15% rise in the effective stress in the nanocomposite. Increasing the spring length of the CCNT, the strain recovery of the nanocomposite increases about 8%. It is shown that when the mechanical loading is parallel to the CCNTs orientation, the stress is about 25% larger than when the loading is perpendicular to the unidirectional CCNTs. But for the strain recovery, the orientation does not play an important role in the strain recovery.