Polydomain nematic sheets can be designed for desired shape transition, and a typical example is a disc composed of congruent wedges with rank-1 connected director field. Recent theoretical study indicated that such a disc, if infinitesimally thin, tends to become a perfect pyramid upon illumination. Nonetheless, what is the influence of the finite thickness remains unexplored. In the present work, we re-examine this problem by treating the disc as an elastic plate with finite thickness. Analytical solution to the photo-actuated shape is obtained in small deformations, and the influences of the number of domains and the attenuation of photo intensity are discussed in details. The results are expected helpful to the design of related photo-responsive devices.

With specimen size decrease for advanced structural materials, the measured mechanics behaviors display the strong size effects. In order to characterize the size effects, several higher-order theories have been presented in the past several decades, such as the strain gradient theories and the micro-polar theories, etc. However, in each higher-order theory, there are several length scale parameters included, which are usually taken as the material parameters and are determined by using the corresponding theoretical predictions to fit experimental results. Since such kind of experimental approaches needs high techniques, it is very difficult to be performed; therefore, the obtained experimental results are very few until now; in addition, the physical meanings of the parameters still need to be investigated. In the present research, an equivalent linkage method is used to simply determine the elastic length parameters appeared in the elastic strain gradient theory for a series of typical metal materials. We use both the elastic strain gradient theory and the higher-order Cauchy-Born rule to model the materials mechanics behaviors by means of a spherical expanding model and then make a linkage for both kinds of results according to the equivalence of strain energy densities. The values of the materials length parameters are obtained for a series of typical metal systems, such as the face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) metals.

Bistable compliant elements offer excellent advantages in many applications ranging from high precision sensing to energy harvesting. The essential nonlinear mechanics of such elements are strongly coupled with their buckling mode, geometric parameters and loading conditions. The force-displacement plot of bistable curved beams could contain a singular point, which cannot be well modeled by the commonly used smooth cubic function and would cause operational problems due to incorrect predictions of the bistability. In this technical brief, the nonlinear bistable mechanics of a compliant curved beam with both ends fixed is analyzed based on the large deflection finite element theory. By using the multistep displacement loading method, the deformation behaviors and their transition from symmetric to asymmetric modes are numerically studied, which provides insights on the force-displacement curve and the multiple snapping pathways. Furthermore, the influences of the structure parameters on bistable mechanics are analyzed, and a quality factor for identifying the occurrence of singular points is introduced for different loading conditions. Finally, a method for achieving a single smooth snapping pathway is proposed, providing a theoretical basis to the design and control of the bistable compliant structures.

Carbon micro/nanolattice materials, defined as three dimensional (3D) architected metamaterials made of micro/nanoscale carbon constituents, have demonstrated exceptional mechanical properties, including ultrahigh specific strength, stiffness and extensive deformability through experiments and simulations. The ductility of these carbon micro/nanolattices is also important for robust performance. In this work, we present a novel design of using reversible snap-through instability to engineer energy dissipation in 3D graphene nanolattices. Inspired by the shell structure in flexible straws, we construct its graphene counterpart via topological design and demonstrate its snap-through instability through molecular dynamics (MD). One-dimensional (1D) straw-like carbon nanotube (SCNT) and 3D graphene nanolattices are constructed using the unit cell. These graphene nanolattices possess multiple stable states and are elastically reconfigurable. A theoretical model of 1D bi-stable element chain is adopted to understand the collective deformation behavior of the nanolattice. Reversible pseudo plastic behavior with a finite hysteresis loop is predicted and further validated via MD. Enhanced by these novel energy dissipation mechanisms, the 3D graphene nanolattice shows good tolerance to crack-like flaw and is predicted to approach a specific energy dissipation of 233 kJ/kg in a loading cycle with no permanent damage (one order higher than the energy absorbed by carbon steel at failure, 16 kJ/kg). This study provides a novel mechanism for 3D carbon nanolattice to dissipate energy with no accumulative damage and improve resistance to fracture, broadening the promising application of 3D carbon in energy absorption and programmable materials.

The process of charging and discharging of lithium-ion batteries results in the intercalation and ejection of lithium ions in the anode material. The ensuing electro-chemo-mechanical stresses and accompanying microstructural changes lead to a complex state of inelastic deformation and damage in the silicon electrode that cause a significant capacity loss within just a few cycles. In this study, we attempt to understand, from an atomistic viewpoint, the mechanisms underlying the plasticity behavior of Si-anode as a function of lithiation. Conventional molecular dynamics simulations are of limited use since they are restricted to loading rates in the order of 10 8 s −1 . Practical charging-discharging rates are several orders of magni- tude slower, thus precluding a realistic atomistic assessment of the highly rate-dependent mechanical behavior of lithiated silicon anodes via conventional molecular dynamics. In this work, we use a time-scaling approach that is predicated on a combination of a potential energy surface sampling method, minimum energy pathway, kinetic Monte Carlo, and transition state theory, to achieve applied strain rates as low as 1 s −1 . We assess and compare the atomistic mechanisms of plastic deformation in three different lithium concentration structures: LiSi 2 , LiSi, and Li 15 Si 4 for various strain-rates. We find that the strain rate plays a significant role in the alteration of the deformation and damage mechanisms including the evolution of the plastic deformation, nucleation of shear transformation zone, and void nucleation. Somewhat anomalously, LiSi appears to demonstrate (comparatively) the least strain rate sensitivity.

This work examines effects of loading rate on the plastic flow and ductile failure of porous solids exhibiting rate-dependent behaviour relevant to many structural metals. Two different modelling approaches for ductile failure are employed and numerical analyses are performed over a wide range of strain rates. Finite element unit cell simulations are performed to evaluate the macroscopic mechanical response and ductile failure by void coalescence for various macroscopic strain rates. The unit cell results are then used to assess the accuracy of a rate-dependent porous plasticity model, which is subsequently used in strain localization analyses based on the imperfection band approach. Strain localization analyses are conducted for (i) proportional loading paths and (ii) non-proportional loading paths obtained from finite element simulations of axisymmetric and flat tensile specimens. The effects of strain rate are most apparent on the stress–strain response, whereas the effects of strain rate on ductile failure is found to be small for the adopted rate-dependent constitutive model. However, the rate-dependent constitutive formulation tends to regularize the plastic strain field when the strain rate increases. In the unit cell simulations, this slightly increases the strain at coalescence with increasing strain rate compared to a rate-independent constitutive formulation. When the strain rate is sufficiently high, the strain at coalescence becomes constant. The strain localization analyses show a negligible effect of strain rate under proportional loading, while the effect of strain rate is more pronounced when non-proportional loading paths are assigned.

Full three-dimensional cell models containing a small cavity are used to study the effect of plastic anisotropy on cavitation instabilities. Predictions for the Barlat-91 model (Barlat et al., 1991, “A Six-Component Yield Function for Anisotropic Materials,” Int. J. Plast. 7 , 693–712), with a non-quadratic anisotropic yield function, are compared with previous results for the classical anisotropic Hill-48 quadratic yield function (Hill, 1948, “A Theory of the Yielding and Plastic Flow of a Anisotropic Metals,” Proc. R. Soc. Lond. A193 , 281–297). The critical stress, at which the stored elastic energy will drive the cavity growth, is strongly affected by the anisotropy as compared with isotropic plasticity, but does not show much difference between the two models of anisotropy. While a cavity tends to remain nearly spherical during a cavitation instability in isotropic plasticity, the cavity shapes in an anisotropic material develop toward near-spheroidal elongated shapes, which differ for different values of the coefficients defining the anisotropy. The shapes found for the Barlat-91 model, with a non-quadratic anisotropic yield function, differ noticeably from the shapes found for the quadratic Hill-48 yield function. Computations are included for a high value of the exponent in the Barlat-91 model, where this model represents a Tresca-like yield surface with rounded corners.

Left ventricular (LV) volume is a crucial indicator for the assessment of the heart function. However, the current clinical practice cannot be used to monitor the LV volume continuously or warn patients with high risk in time before heart attack occurs in everyday life, resulting in high mortality and morbidity. Here, we theoretically validate the potentiality of a conformal real-time LV deformation-monitoring sensor using piezoelectric materials. The electromechanical relationship between the deformation of the hearts and output voltage signals of the sensors is demonstrated first. End-to-end displacements and deformations of piezoelectric films under cyclic load are derived from the output voltage signals and then compared with experimental values. Then, the real-time LV volumes of a pig and a cow are derived and compared by employing the experimental output voltage signals of the flexible sensor mounted on the LV surface. Finally, by employing the LV volume data of healthy people and patients with various heart diseases in the literature, the theoretical output voltage signals of flexile sensors when mounted on LV surface are calculated and compared. These predicted output voltage signals show significant differences for people with different kinds of cardiac diseases. The results in this study demonstrate that the conformal piezoelectric sensor is fully potential to continuously monitor the cardiac deformation and correspondingly provide timely warning for cardiologists and patients with heart diseases.

Dielectric elastomers (DEs) is one of the promising artificial muscle for soft robots and flexible devices. As one of the key issues for practical applications, the control of DE actuators remains challenging due to the large actuation, electromechanical coupling, and viscoelastic dissipation. Feedforward control and proportional integral derivative (PID) feedback control are recently studied for the control of DE actuators. The control performance is still limited due to the complex dynamic behavior of DE actuators with both nonlinearities and modeling uncertainties. This paper proposes a model-based feedback control for DE actuator, considering nonlinearity of large deformation, electromechanical coupling, and the modeling uncertainties. A nonlinear motion model is proposed and verified by parameter identification experiments. Based on the nonlinear model, we demonstrate a robust control strategy including nonlinear model compensation and robust feedback to decrease the tracking error. The experimental results verify that the control strategy possesses excellent validity to the DE actuator with improved performance compared to the previous strategy of feedforward and PID feedback control. The system design and control strategy of this paper may guide the future design and application of DE actuators, soft robots, and flexible devices.

This paper presents thermally actuated hierarchical metamaterials with large linear and rotational motion made of passive solids. Their working principle relies on the definition of a triangular bi-material unit that uses temperature changes to locally generate in its internal members distinct rates of expansion that translate into anisotropic motions at the unit level and large deployment at the global scale. Obtained from solid mechanics theory, thermal experiments on fabricated proof-of-concepts and numerical analysis, the results show that introducing recursive patterns of just two orders of the hierarchy is highly effective in amplifying linear actuation at levels of nearly nine times the initial height, and rotational actuation of almost 18.5 times the initial skew angle.

As a type of architectured material, knitted textiles exhibit global mechanical behavior which is affected by their microstructure defined at the scale at which yarns are arranged topologically given the type of textile manufactured. To relate local geometrical, interfacial, material, kinematic and kinetic properties to global mechanical behavior, a first-order, two-scale homogenization scheme was developed and applied in this investigation. In this approach, the equivalent stress at the far field and the consistent material stiffness are explicitly derived from the microstructure. In addition, the macrofield is linked to the microstructural properties by a user subroutine which can compute stresses and stiffness in a looped finite element (FE) code. This multiscale homogenization scheme is computationally efficient and capable of predicting the mechanical behavior at the macroscopic level while accounting directly for the deformation-induced evolution of the underlying microstructure.

We investigate the behavior of soft magnetoactive periodic laminates under remotely applied magnetic field. We derive explicit formulae for the induced deformation due to magnetic excitation of the laminates with hyperelastic magnetoactive phases. Next, we obtain the closed-form formulae for the velocities of long transverse waves. We show the dependence of the wave velocity on the applied magnetic intensity and induced strains, as well as on the wave propagation direction. Based on the long wave analysis, we derive closed-form formulae for the critical magnetic field corresponding to the loss of macroscopic stability. Finally, we analyze the transverse wave band gaps appearing in magnetoactive laminates in the direction normal to the layers. We illustrate the band gap tunability—width and position—by magnetically induced deformation.

In the past decades, various novel functions (i.e., negative Poisson's ratio, zero thermal expansion) have been obtained by tailoring the microstructures of the cellular structures. Among all the microstructures, the horseshoe topology shows a J-shaped stress–strain curve, which is quite different from the conventional materials. It can be inferred that the 2D lattice structure with horseshoe microstructure will also exhibit excellent out-of-plane impact resistance since the spider silk also exhibits the J-shaped stress–strain curve. In this paper, the out-of-plane sphere impact of 2D truss lattice structure is conducted using finite element method (FEM) simulation. The point has been made that, by replacing the direct-line beam to horseshoe curved beam, the out-of-plane impact resistance has been greatly improved. The most curved beam structure is found to have the best out-of-plane performs with the maximum energy absorption and the minimum passing through velocity.

In this work, we study the effect of network architecture on the nonlinear elastic behavior and strength of athermal random fiber networks of cellular type. We introduce a topology modification of Poisson–Voronoi (PV) networks with convex cells, leading to networks with stochastic nonconvex cells. Geometric measures are developed to characterize this new class of nonconvex Voronoi (NCV) networks. These are softer than the reference PV networks at the same nominal network parameters such as density, cross-link density, fiber diameter, and connectivity number. Their response is linear elastic over a broad range of strains, unlike PV networks that exhibit a gradual increase of the tangent stiffness starting from small strains. NCV networks exhibit much smaller Poisson contraction than any network of same nominal parameters. Interestingly, the strength of NCV networks increases continuously with an increasing degree of nonconvexity of the cells. These exceptional properties render this class of networks of interest in a variety of applications, such as tissue scaffolds, nonwovens, and protective clothing.

This paper introduces a method for calculating the deformation displacement of the origami mechanism. The bearing capacity of each face can be analyzed by the relationship between the stress and displacement, which can provide a reference for the origami design. The Miura origami mechanism unit is considered. First, the folding angle of each crease is solved based on the geometric characteristics. The deforming form of the creases is then analyzed, and the bending moment acting on the paper surface is solved. Based on the geometric characteristics and stress forms, the paper surface is modeled as a sheet. Based on the bending theory of a thin plate with small deflection, the complex external load forms are decomposed by Levy's method and the superposition principle, and the expression of the deflection curve during the folding process is obtained. According to the stress and bending moment equations, the relationship between the bending moment and displacement is obtained. Finally, through an application example, the maximum deflection of the paper surface is calculated by matlab , and the deflection diagram of the deformed paper surface is drawn, which verifies the expression of the deflection curve.

We find that the ratio of dielectric permittivity to shear modulus is linearly related to the number of polar groups per polymer chain in polar dielectric elastomers (PDEs). Our discovery is verified via computational modeling and validated by experimental evidences. Based on the finding, we introduce the new concept of dielectric imperfection (DI) and provide some physical insights into understanding it through demonstrating the large nonlinear deformation of PDEs with DIs under electric fields. The results show remarkable DI-induced inhomogeneous deformation and indicate that the size and dielectric permittivity of DIs have a significant impact on the deformation stability of PDEs under electric fields. With this concept, we propose some potential applications of PDEs with DIs.

An innovative bistable energy-absorbing cylindrical shell structure composed of multiple unit cells is presented in this paper. The structural parameters of the single-layer cylindrical shell structure that produces bistable characteristics are expounded both analytically and numerically. The influence of the number of circumferential cells and the size parameters of the cell ligament on the structure’s macroscopic mechanical response was analyzed. A series of cylindrical shell structures with various size parameters were fabricated using a stereolithography apparatus (SLA). Uniaxial loading and unloading experiments were conducted to achieve force–displacement relationships. Deformation of the structural multistable phase transition response was discussed based on experimental and finite element simulation results. The results show that the proposed innovative single-layer cylindrical shell structure will stabilize at two different positions under certain parameters. The multilayer cylindrical shell exhibits different force–displacement response curves under loading and unloading, and these curves enclose a closed area. In addition, this structure can be cyclically loaded and unloaded, thanks to its good stability and reproducibility, making it attractive in applications requiring repetitive energy absorption.

Water-filled containers placed externally on an armored vehicle offer a potentially low cost, light-weight, and simple technique to mitigate near-field explosive blast, although the use of a gap or standoff between the container and target has not been studied. This paper uses experimental testing and numerical simulations to characterize the influence of this container standoff on the mitigation of near-field blast effects. The addition of the container standoff was not found to generally increase the blast mitigation effect provided by water-filled containers on the deformation caused to a steel target plate. While the container standoff was found to enhance the spreading and shadowing blast mitigation mechanisms provided by the water-filled container, this was offset by an increase in blast loading due to the container being closer to the explosive charge. A new mitigation mechanism was identified as the time delay between the initial loading of the steel plate by the blast wave and the subsequent impact of water ejected from the container. The results from this work provide engineers guidance into the design of water-filled containers for near-field blast protection of armored vehicles.

Porous bulk metallic glasses (BMGs) exhibit an excellent combination of superior mechanical properties such as high strength, high resilience, large malleability, and energy absorption capacity. However, a mechanistic understanding of their response under diverse states of stress encountered in practical load-bearing applications is lacking in the literature. In this work, this gap is addressed by performing three-dimensional finite element simulations of porous BMGs subjected to a wide range of tensile and compressive states of stress. A unit cell approach is adopted to investigate the mechanical behavior of a porous BMG having 3% porosity. A parametric study of the effect of stress triaxialities T = 0, ±1/3, ±1, ±2, ±3, and ±∞, which correspond to stress states ranging from pure deviatoric stress to pure hydrostatic stress under tension and compression, is conducted. Apart from the influence of T, the effects of friction parameter, strain-softening parameter and Poisson’s ratio on the mechanics of deformation of porous BMGs are also elucidated. The results are discussed in terms of the simulated stress-strain curves, pore volume fraction evolution, strain to failure, and development of plastic deformation near the pore. The present results have important implications for the design of porous BMG structures.

Electrically driven dielectric elastomers (DEs) suffer from an electromechanical instability (EMI) when the applied potential difference reaches a critical value. A majority of the past investigations address the mechanics of this operational instability by restricting the kinematics to homogeneous deformations. However, a DE membrane comprising both active and inactive electric regions undergoes inhomogeneous deformation, thus necessitating the solution of a complex boundary value problem. This paper reports the numerical and experimental investigation of such DE actuators with a particular emphasis on the EMI in quasistatic mode of actuation. The numerical simulations are performed using an in-house finite element framework developed based on the field theory of deformable dielectrics. Experiments are performed on the commercially available acrylic elastomer (VHB 4910) at varying levels of prestretch and proportions of the active to inactive areas. In particular, two salient features associated with the electromechanical response are addressed: the effect of the flexible boundary constraint and the locus of the dielectric breakdown point. To highlight the influence of the flexible boundary constraint, the estimates of the threshold value of potential difference on the onset of electromechanical instability are compared with the experimental observations and with those obtained using the lumped parameter models reported previously. Additionally, a locus of localized thinning, near the boundary of the active electric region, is identified using the numerical simulations and ascertained through the experimental observations. Finally, an approach based on the Airy stress function is suggested to justify the phenomenon of localized thinning leading to the dielectric breakdown.