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A surrogate model for dynamical behavior of dielectric elastomer actuators was proposed, the reduced-order framework was based on long short-term memory (LSTM) networks, and the combination of prop...

A design method of the opto-mechanical actuation is proposed. The system is constituted of liquid crystal photo-responsive polymer, and is subject to light-induced isomerization, leading a nematic ...

The jumping motion is adapted by Earth’s creatures to achieve rapid maneuverability and energy-efficient hurdling over uneven terrains or large obstacles. Herein, the continuous photomechanical jumping of polymer monoliths with on-demand height and angle programmability is reported. Upon exposure to actinic light, self-assembled spring-like molecular geometry of azobenzene-functionalized liquid crystalline polymers provide on-demand jumping via snap-through of non-isometric structures. The finite element method simulation quantitatively describes stress–strain responsivity of the experimental jumping. Remarkably, the maximum jumping height reaches 15.5 body length (BL) with the maximum instantaneous velocity of 880 BL s−1. We demonstrate programmable jumping height and angle by varying macroscopic geometry and light intensity profile. Finally, four continuous and directional jumping sequences are demonstrated within 5 s to overcome an obstacle.

Recurrent neural network (RNN)-based accelerated prediction was achieved for the long-term time-dependent behavior of viscoelastic composite laminated Mindlin plates subjected to arbitrary mechanical and hygrothermal loading. Time-integrated constitutive stress-strain relation was simplified via Laplace transform to a linear system to reduce the computational storage. A fast converging smooth finite element method named cell-based smoothed discrete shear gap was employed to enhance the data generation procedure for straining RNNs with a sparse mesh. This technique is applicable under varying hygrothermal conditions for real engineering structure problems with fluctuating temperature and moisture. Hence, accurate RNN-based long-term deformation prediction for laminated structures was realized using the history of environmental temperature and moisture condition.

The cross-deposition of wavy circuits is essential in the mass production of flexible devices. This article clarifies structural limitation in enhancing the maximum stretch ratio of cross-deposited...

A multiscale modeling approach is proposed to account for the interfacial load transfer characteristics of epoxy nanocomposites. The localized stress evolutions in nanocomposites are examined with ...

Considering that the existing C1 absolute nodal coordinate formulation (ANCF) elements must satisfy C1 continuity, herein a four-node plane C0 ANCF element is proposed to overcome current limitatio...

A wavy circuit is one of the structures used in flexible devices, which endure high stretch ratios during operation. In this study, we focus on the importance of the section tilting angle of the wa...

A hierarchical multiscale modeling for analyzing the electromechanical behaviors of carbon nanotube/polymer nanocomposites is presented, considering the matrix damage as well as interfacial debondi...

In the present study, the viscoelastic analysis is investigated for composite laminated plates using a smoothed finite element method called cell/element based smoothed discrete shear gap method. Moreover, the hygrothermal effects is considered on the viscoelastic responses of composite laminated plates. The first-order shear deformation theory is employed due to its simplicity and accuracy. With the help of the convolution theorem in Laplace transformation, the complex stress-strain relationship in integral form is simplified to linear in transformed domain. Therefore, all computing procedures are performed in the transformed domain and then, using inverse techniques (Fast Fourier Transform) to converted back to the real-time domain. The study provides an effective computational tool to analyze the viscoelastic response of laminated composite taking into account the influence of the time and hygrothermal effects.

Wavy pattern circuits are widely used in flexible displays, wearable devices, and biosensor research. In this study, we propose a tilted 2D stretchable wavy circuit design to enhance circuit integr...

This paper presents an asymptotic method-based analysis of composite laminates having interfacial imperfections. In general, imperfect interfaces are simply modeled by introducing a linear, spring-layer model, which empirically assumes that the displacement jumps that occur at the weakened interface are proportional to the transverse shear stresses of interface positions. In this study, we propose a composite plate model derived by using asymptotic expansion that does not make any assumptions, other than the scaling of coordinate systems. Within the framework of the asymptotic analysis, the spring-layer model is introduced to describe the effect of weakened interfaces, which is realized by the separation of domains in the through-the-thickness direction, and the integration of piecewise continuous warping functions. As a result, we newly define a spring parameter that is exactly the same as the stiffness of a spring. Therefore, a set of spring elements are added to the through-the-thickness modeling of the microscopic analysis, and the plate equations derived in the macroscopic problem are the same as those of the perfectly bonded laminates. As a consequence, we also derive the proposed plate model with the mathematical rigor that the previous asymptotic models contain. We provide some numerical results verifying that the proposed method shows good agreement with the elasticity and 3D FEM solutions.

The hygroelasticity of oxygen-functionalized graphene (GO)-epoxy nanocomposites is studied. Two different transversely isotropic nanocomposite molecular models are constructed: with uniformly distributed and interface-concentrated water molecules, respectively. The stress-strain curves and coefficients of moisture expansion (CMEs) are determined according to moisture content. The degradation of the GO/epoxy interface due to the infiltrated moisture is characterized by interfacial decohesion tests. The micromechanics model is used to derive new closed-form solutions for the effective elastic stiffness and CME of multi-phase composites with interfacial imperfections. Regardless of the moisture distribution, the overall hygroelastic behavior of nanocomposites clearly degrades upon moisture absorption.

The mechanical behavior of the nano-sized structure is estimated by the bridging method considering the surface effect. As the Kirchhoff plate theory and homogenization theory using asymptotic expa...

Structural failure of the polycrystalline material is influenced by the interaction between the crystal and their boundaries. Specifically, a ductile material such as copper exhibit the different mechanisms of failure depending on the direction of the crack propagation within the grain boundary. Such directional anisotropy is often studied based on Rice’s criteria, which has the analytic solution in the grain boundary with [110] rotation of the axis. In this work, we expand the study of such intergranular directionality to a propagation within [100] grain boundary. This work introduces the inherent bias found in the intergranular fracture of [100] grain boundaries, using molecular dynamics simulations. Later, such observation is shown to agree with the relative crack propagation velocities, and cohesive energies obtained at the crack tip vicinity. These anisotropic trends are lastly correlated with the detailed atomistic movements observed during structural failures. These findings are to be used in improving the simulation capability and predictability of crack propagation.

A fracture of the active particle such as silicon anode results in a potential degradation in lithium-ion batteries with charge/discharge cycle. The massive volume expansion during the lithiation generates large stress which induces the cracking on its surface. We propose the finite element model to have a deep insight into the diffusion-induced stress with fracture process for crystalline silicon nanowires. This model is constructed based on the large deformation theory and cohesive zone model that can describe the failure of Si nanowires. At the beginning of lithiation, high compressive hoop stress is generated on its surface. However, further lithiation, the hoop stress near the surface become less compressive and tensile, which is associated with the “push out effect” as a result of the volume expansion of lithiated material near the phase boundary. When the diffusion induced tensile stress exceeds the fracture threshold, a crack is initiated on the surface and propagates continuously to the center of the silicon nanowire. This crack follows the phase boundary rapidly, but the crack growth speed decreases due to the neighboring compressive hoop stress generated near the phase boundary. From the observation of failure mechanism in Si, we characterize a critical size of Si nanowire, below which fracture can be averted, and we suggest a safe state of charge (safe SOC) depending on its radial size during lithiation.

Ni-rich layered oxides have been identified as promising candidates for commercial cathodes in Li-ion batteries. However, the commercialization has been hindered by severe cyclic degradation and mechanical failure induced by severe phase transformations and fractures. To resolve these challenges by understanding their fundamental mechanisms, we present mechanics-based multiscale investigations to elucidate the fundamental mechanisms of mechanical failure including deformations and fractures. We have also suggested a practical solution to the failure, which involves enhancing electronic interactions between transition metal layers. The methodological framework for our investigations was developed from first-principles atomic calculations, electronic structure, thermodynamics and kinetics for combined phase transformation, phase field modeling, finite element methodology for mechanical deformation, and phase field crack modeling. Our practical solution addresses the electronic interactions that can be strengthened when O ions are reduced by substituting strongly oxidizing elements such as Ti. Our multiscale framework shows that the reduced O ions are responsible for higher fracture toughness, reduced volume changes, stable deformation, mitigated stress generation, and suppressed fractures. Thus, this study proposes a practical solution for the improvement and design of Ni-rich layered oxide cathode materials. Furthermore, the mechanics-based multiscale methodology employed herein could be applied to a number of other solid-state energy materials suffering from mechanical failures.

We propose an efficient simulation-based methodology to characterize the quasi-static (experimental low strain rate) yield stress of an amorphous thermoset polymer, which has generally been considered a limitation of molecular dynamics (MD) simulations owing to the extremely short time steps involved. In an effort to overcome this limitation, the temperature-accelerated method – in which temperature is treated as being equivalent to time in deformation kinetics – is employed to explore the experimental strain rate conditions. The mechanical tensile behavior of a highly crosslinked polymer is then investigated with MD simulations by considering different strain rates and temperatures below the glass transition temperature. The derived yield stress represents the time- and temperature-dependent characteristics, showing that the yield stress decreases with increasing temperature and decreasing strain rate. Changeable vertical and horizontal shift factors are introduced for the first time to reflect nonlinear characteristics of the yield stress across a broad range of strain rates and to quantify the correlation between increasing temperatures and decreasing strain rates. With the proposed method, the Eyring plot, which describes the rate effect on yield from quasi-static to high-rate conditions, is predicted from MD simulations, and agrees well with macroscopic experimental results. From the constructed Eyring plot, the experimentally validated quasi-static stress-strain response is also estimated by using linear elastic model and Ludwick's hardening model. The proposed method provides new avenues for the design of glassy polymers using only fully atomistic MD simulations, thus overcoming the existing temporal scale limitations.

A molecular dynamics (MD) simulation is performed on the coalescence kinetics and mechanical behavior of a thermally sintered nanoporous copper (Cu) nanoparticulate system. To investigate the effect of particle size and sintering temperature on the coalescence of the nanoparticulate system, particles with sizes of 4, 5, and 6 nm are sintered at temperatures of 300, 500, and 700 K. To determine the thermal sintering process at elevated temperatures and ambient pressure, bulk periodic nanoparticle unit cells consisting of a finite number of nanoparticles are equilibrated through isothermal–isobaric ensemble simulations. In thermally sintered configurations, uniaxial tension/compression and shearing simulations are applied at a constant strain rate to derive stress–strain curves. It is found that stacking faults are actively generated in smaller nanoparticles even at a low sintering temperature, while local amorphization and surface and grain boundary diffusion are rather prominent in larger nanoparticles. Even at the same sintering temperature, the density of the sintered nanoparticle increases as the size of the nanoparticle decreases. In elastic moduli, the same particle size dependency is observed, while no obvious difference is observed in tension and compression. On the other hand, the yield strengths of the sintered nanoparticles in tension are larger than those in compression. The asymmetric yield strength of the sintered systems is clarified by addressing the surface stress and surface equilibrium strain of atoms on the surface of nanopores by the evolution of atomic virial stress in tension and compression.

Because of its nonlinearity and path-dependency, analysis of the elasto-plastic behavior of the finite element (FE) model is computationally expensive. By directly learning sequential data, modeling plasticity via deep learning has shown successful performance in immediately predicting the path-dependent response. However, large-scale elasto-plastic FE models still have challenges in that they require numerous degrees of freedom and are accompanied by high-dimensional data. This study proposes a practical framework for the surrogate modeling of a large-scale elasto-plastic FE model by combining long short-term memory (LSTM) neural networks with proper orthogonal decomposition (POD). First, displacement, plastic strain magnitude, and von Mises stress are generated using commercial FE analysis software, and then, the high-dimensional data are reduced to low-dimensional POD coefficient data before being used for training. With the drastically reduced data, a neural network architecture can be introduced in the form of individual and ensemble structures to achieve accurate and robust prediction. As the proposed POD-LSTM surrogate model operates on the structural level, POD-LSTM surrogate models are constructed and implemented for each of the three large-scale elasto-plastic FE models. In all three examples, the proposed POD-LSTM surrogate models were found to be efficient and accurate for predicting elasto-plastic responses.

To overcome inaccurate prediction of yield surface evolution arising from the general use of classical yield functions, a method to formulate data-driven yield functions is established, using machine learning technique operating on the multi-axial yield data that exhibit the unique multi-axial hardening behavior of amorphous polymers. A scheme to generate sufficient data for multi-axial hardening responses is proposed, using molecular dynamics simulations, considering their timescale limitations, on quantitative estimations of mechanical responses. Based on the mined data-driven yield function, a constitutive model is constructed, and the corresponding multi-axial stress evolutions are compared with those of classical models. To examine the possibility of yield function mining by symbolic regression, the development of the classical yield functions von–Mises, Drucker–Prager, Tresca, Mohr–Coulomb, and paraboloidal yield functions was reproduced by using the proposed approach. Additional simulations were undertaken to characterize the influence of noise in the yield data set on the chosen functions.

We propose a new model for predicting the trans-cis-trans reorientation (TCTR)-based photodeformation of the azobenzene-doped liquid-crystal polymer (azo-LCP). The model was validated through the results of a bi-directional photobending experiment performed at various temperatures and mole ratios of the azobenzene monomer within the azo-LCP. Through both numerical and experimental investigations, we found that the photobending curvature of the azo-LCP shows a maximum point at certain temperatures, but only shows a proportional relationship with the azobenzene mole ratio within the azo-LCP. We confirmed that this tendency is caused by the change in the polymeric constraint with the temperature and the low light propagation in azo-LCP.

In this paper, a new analysis method based on the conventional Lo-Christensen-Wu theory (LCW) is proposed to accurately and efficiently predict the thermo-mechanical behavior of laminated composite and sandwich plates. The main objective herein is to systematically modify the strain energy of the conventional LCW theory. To this end, the independent transverse shear stresses are obtained from the fifth-order zigzag model, whereas the displacement fields based on conventional LCW are employed to amplify the benefits of numerical efficiency. The relationships between the two independent fields are systematically derived via the mixed variational theorem (MVT) and the least-square approximation of the mean displacement. The resulting strain energy is referred to as the enhanced Lo-Christensen-Wu theory via the mixed variational theorem (ELCWM). The ELCWM offers the same computational advantage as the conventional LCW while improving upon the accuracy of the local distributions of thermo-mechanical response via a post-processing procedure. To demonstrate the accuracy and efficiency of the proposed theory, the numerical results obtained herein are compared with exact solutions and with data available in the literature.

A new method based on the C0-type efficient higher-order zigzag theory (EHOZT) is proposed for the efficient and accurate thermomechanical analysis of laminated composite plates. In this method, the transverse shear strain energy is modified according to the mixed variational theorem (MVT). The transverse stress field is defined by the arbitrary m-th order zigzag model including the transverse normal strain effect to improve the accuracy, while the displacement field is obtained from the C0-type EHOZT to amplify the benefits of the numerical efficiency. The transverse displacement field is assumed to be a smooth parabolic distribution to consider the transverse normal strain effect, which has a significant role in predicting the thermal deformation. Derivative components of the transverse displacement field are eliminated from the in-plane displacement field of the C0-type EHOZT by the transverse shear stress condition. The resulting strain energy expressions are collectively referred to as the C0-type EHOZT via the MVT. The proposed theory has the computational advantage of utilizing the C0-continuity condition for finite element implementation while allowing local distributions of the transverse stress to be improved via the recovery procedure. The obtained displacements and stress distributions were compared with data available in the literature for validation.

In this study, we develop the methodology to predict the fatigue crack growth of the thermoset polymer nanocomposites, based on multiscale approach. The experimentally observed microscopic energy dissipating mechanisms (nanoparticulate debonding, the subsequent plastic yield of nanovoids, and localized shear banding) are reflected in the proposed methodology. The predicted results show satisfactory agreements with respect to experimental data. In addition, the extrinsic crack closure effects are considered, and their influences on the fatigue crack propagation are investigated. The achievement of this study is expected to elucidate the complex phenomenon of fatigue crack growth as well as provide high efficiency with satisfactory predictions.

A multiscale modeling approach is proposed to characterize the interfacial behavior and the interphase properties of epoxy nanocomposites. The interfacial characteristics between the filler and matrix are investigated using molecular dynamics (MD) and molecular mechanics (MM) simulations. With increasing crosslink conversions, the interfacial adhesion between the filler and matrix is reduced which is attributed to the changes of inherent non-bond interaction characteristics at the interface, resulting in retarded reinforcing effect on the stiffness and thermal stability of epoxy nanocomposites. Moreover, to understand the structural change in the interphase region of nanocomposites with crosslinking, the radial density profile, the local crosslinks distribution, and the free volume at the filler surface are further examined. The results of structural features consistently demonstrate that the structural conformation of the interphase is substantially influenced by the reduction of interfacial communication with increasing crosslink conversion. In order to take into account the variations of interfacial compliance and the thermomechanical property of the interphase region, the effective interphase concept is implemented. Further, the micromechanics-based multi-inclusion model provides a reasonable prediction for the thermomechanical property of composites using the effective interphase concept.

This paper presents an efficient interpolation-based parametric reduced order model with component mode synthesis. The off-line sampling of a large-scale structural dynamic system containing many parameters requires many computations to investigate the parameter-dependency of a dynamical system. Therefore, we introduce a dynamic substructuring scheme to execute off-line sampling in the subdomain level. In addition, we suggest discriminating the interpolation of the subsystem depending on the characteristics of each substructural mode. We synthesize the substructures, and we then construct a two-level, semi-parametrized ROM by reducing the degrees of freedom of the interface in the on-line stage. We then demonstrate the efficiency and accuracy of the present method by computing the relative eigenvalue errors and the transient responses of the system with random values for the parameters, and we conduct the design optimization of large-scale systems under dynamic loading conditions. A comparison of the present method with the full order model and a conventional reduced order model indicates that the present method is useful in carrying out an efficient analysis and design optimization for various large-scale structural dynamic systems.

Phase transformations in most electrodes used for electrochemical energy storages follow the conserved dynamics of combined one- and two-phase reactions, which leads to complicated charge–discharge processes with various voltage plateaus; this could affect an electrochemical performance as a generic phenomenon in electrochemical system. In order to fully describe the combined-phase reactions from the atomic scale to the mesoscale, we propose a multiscale-based phase transformation model that also considers electrochemical states and mechanical deformations. This model predicts the miscibility gap, spinodal region, voltage profile, phase transformation, and stress generations of the combined-phase electrodes in the electrochemical reactions. We apply this multiscale model to high-rate cathode material Li x FePO 4 to fundamentally understand the experimental phase transformation behaviors (Yamada et al., 2006). This model is applicable to various electrodes for phase behaviors too complex to be detected experimentally due to combined-phase reactions.

Carbon fiber reinforced plastic (CFRP) laminated composites, called bi-stable composites, are applied as soft morphing host structural component. These bi-stable composites have two cylindrical stable states which have parallel direction between fiber direction of composites and principle curvature of bi-stable shape. Their final curvature can be tailored by the initial curvature. However, the cross-ply composites have twisted shape in a certain negative initial curvature. These twisted shapes also have bi-stability. Herein, the reasons for the twisted shapes are discussed from a mechanical perspective. In addition, the twisted shape was simulated by a developed analytical model considering the discussed mechanical mechanism. The simulation results show that the CFRP laminated composites have two kinds of bi-stable states (conventional shape or twisted shape) and a mono-stable state with respect to the negative initial curvature. These analytical results were verified by comparing them with those obtained by finite element analysis (FEA).

Sequential multiscale analysis was performed to investigate the effect of temperature on the mechanical properties and fatigue behaviors of a polymeric material. With increasing temperature, a nonlinear degradation of the elastic and plastic properties were clearly observed, which arose from the phase transition of polymer molecules. The influence of the temperature on the acceleration of crack growth rate was also evaluated via the plastically dissipated energy-based finite element analysis. Continuous curves of the Paris-regime crack growth rate were constructed by representing the Paris coefficients as a function of temperature. The predicted crack growth rates in the present study match well with the published experimental data on polyamide 66. The proposed framework provides an accurate estimation of the mechanical properties and fatigue crack growth rate of polymers, with a reduced reliance on experiments.

Based on the results of molecular dynamics (MD) simulations and a mean-field micromechanics model, we report on some positive contributions of the oxygen functional groups in single-layer graphene oxide (GO) to the mechanical and interfacial properties of polyethylene (PE)/graphene nanocomposites. As the epoxide and hydroxyl group degrade the mechanical properties of single-layer graphene, clear degradations in the longitudinal Young's and in-plane shear moduli are observed when the deformation of graphene is involved in the loading of the nanocomposite unit cells. However, a significant improvement in the longitudinal shear modulus of nanocomposites is predicted. By comparing the MD simulation results with double-inclusion (D-I) model predictions, contributions of the interphase zone and the interfacial stiffening effect to the elasticity of nanocomposites are again confirmed. Finally, we demonstrate a novel evolution of the out-of-plane normal stress and longitudinal shear stress in single-layer GO arising from its interaction with the surrounding PE matrix via atomic virial stress.

This article describes a novel design for a smart soft composite structure, capable of four actuating modes, with three different types of scaffold structures, and two shape memory alloy wires embedded above and below the scaffold structures. Each component is combined with polydimethylsiloxane (PDMS) so it has the advantage of a soft morphing motion. Actuating modes, consisting of symmetric, anti-symmetric, asymmetric, and torsional motion, and the associated end edge displacement and twisting angle, were measured according to different ply combinations, which were symmetric, anti-symmetric, and asymmetric. The 60-mm actuator is capable of end edge displacement up to 67 mm and twisting up to 85° in a bend-twist coupled motion. In the torsion-only motion, without bending, 108.4° deformation was achieved. Next, a finite element method (FEM) model, based on the Lagoudas shape memory alloy (SMA) model, is presented to predict the actuating performance of the actuator according to the scaffold stacking sequence. Using the FEM model, end edge displacement and twisting angle are compared with experimental data in the four modes of actuation. The actuating trajectory expected from the FEM model is compared with the experimental data.

A statistical multiscale homogenization strategy of polymer nanocomposites is proposed to account for the inherent uncertainties of molecular dynamics (MD) simulations. The proposed statistical multiscale homogenization scheme includes a discrete MD simulation system, a continuum theory of micromechanics of Eshelby's solution and two-scale homogenization, and Monte-Carlo simulations. The means and standard deviations of the elastic properties of the nanocomposites are quantified and discussed through statistical analyses that show the interphase effect. The elastic properties of the matrix, interphase, and composites are assumed to follow a lognormal distribution. An iterative inverse algorithm for obtaining the probability density distribution of the interphase is proposed and validated.

In this study, a multiscale approach was constructed for the multi-axial plastic deformations of epoxy polymers to develop a macroscopic constitutive model at a quasi-static strain rate (consistent with laboratory tests) without any experiments. The 3-dimensional constitutive model was fully characterized, considering the effects of strain rate, temperature, hydrostatic pressure, and crosslinking density. The quasi-static yield stress was predicted by conducting molecular dynamics simulations based on the Argon theory and internal stress law established by thermomechanical properties. For the proper description of nonlinear dependences of the obtained yield stresses on the strain rate and temperature, which have not been considered in previous studies, a cooperative model was adopted as a link between the simulations and experiments. Taking into account characteristic quasi-static yield behavior, one-dimensional quasi-static constitutive equations were derived by developing hardening laws considering strain rate dependences of the yield strain and yield stress established at the quasi-static level. Finite element analysis was then performed on these equations considering the influence of temperature, hydrostatic pressure, and crosslinking density by implementing a continuum model based on the paraboloidal yield function. Finite element simulations included a 1-element patch test conducted for one-dimensional loading paths and open-hole test performed for both the validation and practical use of the model describing the structural behavior of the studied polymer under combined loading. The results of open-hole simulations revealed that the proposed multiscale framework successfully considered the microscopic structural characteristics of amorphous polymers in establishing elasto-plastic finite element models.

Silicon (Si) is one of the most promising anodes for next-generation lithium (Li)-ion batteries because of its high capacity. However, the commercial uses of Si anodes are hindered by extremely poor cycling stability caused by huge volume expansion during charging and discharging processes as well as by a change in material properties according to Li concentration. Given these reasons, we propose the multiscale analysis of Si nanowire anode using a diffusion-induced stress model with Li concentration effects, such as softening of mechanical modulus and enhancement of Li diffusion. From the geometry context, the diffusion-induced stress model exhibits stress relaxation during the lithiation and optimal condition of the Si nanowire. We then construct an approximated stress criteria equation for the safe operation of Si nanowire of various sizes and shapes. Our multiscale analysis predicts the various types of Si nanowire, including holecaped Si nanowires, which are beneficial to mechanical stability. This study provides insights into the physics of Li-Si compound behaviors and introduces the possibility of developing Si-based anodes with mechanical stability.

An efficient higher-order plate theory for viscoelastic materials is developed to predict the time-dependent mechanical behaviors of composite laminates. In-plane displacement fields are constructed by superimposing a cubic varying displacement field on a linear zig-zag varying field. Time-dependent relaxation moduli have the form of Prony series, which can be determined by the master curve based on experimental data. The constitutive equation of linear viscoelastic materials in the form of the Boltzmann superposition integral is simplified by the convolution theorem of the Laplace transform to avoid direct integration as well as to improve both computational accuracy and efficiency. By using the equivalent linear elastic stress–strain relationship in the corresponding Laplace domain, the transverse shear stress-free conditions at the top and bottom surfaces and the transverse shear stress continuity conditions at the interfaces between layers are satisfied conveniently. Finally, the viscoelastic responses in the time domain are obtained through various numerical inverse Laplace transforms. To validate the present theory, the numerical results for graphite/epoxy GY70/339 material are obtained and compared with the solutions of elastic composite laminated plates.

A system identification method has been proposed to validate finite element models of complex structures using measured modal data. Finite element method is used for the system identification as well as the structural analysis. In perturbation methods, the perturbed system is expressed as a combination of the baseline structure and the related perturbations. The changes in dynamic responses are applied to determine the structural modifications so that the equilibrium may be satisfied in the perturbed system. In practical applications, the dynamic measurements are carried out on a limited number of accessible nodes and associated degrees of freedom. The equilibrium equation is, in principle, expressed in terms of the measured (master, primary) and unmeasured (slave, secondary) degrees of freedom. Only the specified degrees of freedom are included in the equation formulation for identification and the unspecified degrees of freedom are eliminated through the iterative improved reduction scheme. A large number of system parameters are included as the unknown variables in the system identification of large-scaled structures. The identification problem with large number of system parameters requires a large amount of computation time and resources. In the present study, a hierarchical clustering algorithm is applied to reduce the number of system parameters effectively. Numerical examples demonstrate that the proposed method greatly improves the accuracy and efficiency in the inverse problem of identification.

A diffusion induced stress (DIS) model based on the finite element method was used to analyze mechanical stress within a multiscale framework for silicon nanowire anodes designed for use in Li-ion batteries. With a prelithiated nanowire, the mechanical moduli of lithium silicide and the migration energy barriers of lithium were calculated by density functional theory method, while the diffusion constants for lithium silicide were obtained using kinetic Monte Carlo simulations. Unlike previous DIS analyses, this multiscale approach reveals a decreasing hoop stress with increasing lithium concentration. Furthermore, an increase in the diffusion coefficient with Li concentration was also found to be a much more significant factor than the reduction in the mechanical moduli, causing a prelithiated silicon anode to experience lower stress levels than pristine silicon. On the basis of this finding, it is concluded that prelithiation reduces the loss in cycling performance that typically occurs due largely to an excess of induced stress.

The thermal and mechanical behaviors of bent GaN nanowires are investigated using molecular dynamics (MD) simulations. The nanowires considered have an axial orientation along the [0 0 0 1] crystalline direction and hexagonal cross sections with diameters of 2.91 and 3.55 nm. A phase transformation from wurtzite to a tetragonal structure occurs near the surfaces of the nanowires in the bending process. The thermal conductivity is evaluated using an analytical model. This model is based on the same atomistic potential used in the MD calculations and uses configurational information from the MD calculations as input. The method is 50 times more computationally efficient compared with the Green–Kubo method. It is found that the thermal conductivity decreases by 35% and 25%, respectively, for nanowires 2.91 and 3.55 nm in diameter during the phase transformation in the bending process. In contrast, the thermal conductivity does not change during unloading and is found to be independent of the bending angle. The overall trend in thermal and mechanical responses of the nanowire with a diameter of 3.55 nm is similar to that for the nanowire with a diameter of 2.91 nm. Results also show that the phase transformation due to bending cannot be reversed by simple unloading. The finding points out a mechanism for altering the structure and thermal conductivity of GaN nanowires through transverse mechanical loading.

Lithium alloys with metallic or semi-metallic elements are attractive candidate materials for the next-generation high-capacity rechargeable Li-ion battery anodes, due to their large specific and volumetric capacities. The key challenge in the application of these materials has been the very large volume changes, and the associated stress buildup and failure during insertion and extraction of lithium. While such stress buildup bears resemblance to the process of thermo-stress development, a phenomenon relatively well-understood, the physics involved in these alloy-based electrodes is much more complex in nature, more challenging to address, and richer in the variety of influencing factors. The reasons not only lie in the fact that the mechanical deformations are much larger, but also arise from the fact that the processes entail interactions among mass diffusion, chemical reactions, non-linear plastic flow and material property evolutions. In this paper, we present a review of some of the fundamental issues and the latest research related to the mechanical reliability of such alloy-based anode materials, with a focus on Li/Si, a material with the highest known theoretical energy storage capacity. The review primarily concerns continuum-level analyses, with relevant experimental data and atomistic-level results as input.

At high guest (lithium) atom concentrations, the diffusion of host (e.g., silicon) atoms may become significant in amorphous Li-alloy-based solid electrodes. The effect of this diffusion mechanism on stress development is in addition to guest atom diffusion, stress-induced enhancement of guest atom diffusion and plasticity. The effect of the diffusive migration of host atoms in amorphous Li-alloy-based electrodes is investigated using a continuum model. A mixed-form finite element framework is developed to simulate the full coupling between stress development and interdiffusion. This framework overcomes the challenges associated with the numerical evaluation of the hydrostatic stress gradient. The analysis focuses on the relative importance of the mechanical driving force and chemical driving force for host migration. Calculations show that host migration can cause stress reductions of up to ∼20% in Li–Si electrodes at stress levels below the yield threshold of the material. Analyses also show that the long-term steady state of stress distribution is independent of the host diffusivity and the thermodynamic factor of diffusion which quantifies the tendency of the two species of atoms to chemically mix, even though the transient behavior (in particular, the peak stresses during charging being important quantities) does depend on the thermodynamic factor and the host diffusivity. The diffusion of Si (host) introduces a time scale which, along with the time scale for Li (guest) diffusion, controls the diffusional response of electrodes.

A hierarchical multiscale modeling approach to characterize the elastic and plastic behavior of carbon nanotube (CNT)-reinforced polymer nanocomposites is proposed via molecular dynamics simulations and a continuum nonlinear micromechanics based on the secant moduli method. Even though the importance of the densified interphase zone formed between the CNT and polymer matrix has been demonstrated by many related studies for elastic properties, studies on how to identify the behavior and contribution of the interfacial condition and interphase zone in the overall elastoplastic behavior of nanocomposites is still an open issue. Different from conventional micromechanics approaches that homogenize overall elastoplastic behavior of heterogeneous structures from known behaviors of its constituent phases, the present study focuses on the identification of local elastoplastic behavior of the interphase region from the known elastoplastic behavior of nanocomposites through a hierarchical domain decomposition method. Firstly, the overall elastoplastic behavior of the CNT-reinforced nanocomposites is obtained from molecular dynamics (MD) simulations which are based on an ab initio force field. Due to a weak van der Waals interaction between the pristine CNT and the matrix polymer, the elastoplastic behavior of the nanocomposites clearly shows a weakened interface condition, while the matrix molecular structure in the vicinity of the CNT confirms the existence of the interphase zone. In upper level analysis, an effective matrix concept is adopted, and its elastoplastic behavior is inversely identified by equating the MD simulation result to a two-phase nonlinear micromechanics model that can consider imperfect interfacial condition. Then, the effective matrix domain is again decomposed into the interphase and pure matrix polymer regions in lower level analysis, and the elastoplastic behavior of the interphase is again identified through the same method. Using the constitutive relation of the interphase obtained from the proposed multiscale model, the overall elastoplastic behavior of the nanocomposites is obtained and compared with some available experimental results and an additional MD simulation result to validate the applicability and physical rigorousness of the proposed nonlinear multiscale approach.

The elastic properties of nano-sized structures are size-dependent. To capture this phenomenon, atomistic-level calculation is generally required. The size-dependent mechanical property is due to the reconstruction of atomic bonding at surfaces. Honeycomb structures in the nanoscale level have excellent functionality due to the very high ratio of the surface area to volume. Such structures have been manufactured in practice above submicron scale so that the atomistic simulations are not tractable to evaluate their performance because the repeated computation of micro/submicro-scale in atomistic simulations requires too much computational time and resources. In this study, to overcome the limitation in atomistic simulations, a continuum finite element analysis is carried out by introducing the surface elasticity. The surface elastic property for very simple structure is once identified by using the molecular dynamic (MD) simulations, and then the numerical homogenization method in the continuum level is applied to nano-sized periodic structures including honeycomb structures. The obtained homogenized stiffness over the representative volume element (RVE) is used to predict the global behaviors of the honeycomb structures. The present sequential multiscale analysis provides the reliable prediction of size-dependent elastic properties, and is very useful to design the patterns of the nano-sized honeycomb structures. The bending stiffness and shear stiffness of patterned honeycomb structures are highly size- and height-dependent.