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Among various intergranular microstructures, pore spaces in SEs play a critical role in Li-metal nucleation in SEs. To realize Li-metal nuclei-free inside the SE, removing pore spaces is essential and a commonly applicable design strategy to all SEs.

Alterations in the intestinal microbial flora are known to cause various diseases, and many people routinely consume probiotics or prebiotics to balance intestinal microorganisms and the growth of beneficial bacteria. In this study, we selected a peptide from fish (tilapia) skin that induces significant changes in the intestinal microflora of mice and reduces the Firmicutes/Bacteroidetes ratio, which is linked to obesity. We attempted to verify the anti-obesity effect of selected fish collagen peptides in a high-fat-diet-based obese mouse model. As anticipated, the collagen peptide co-administered with a high-fat diet significantly inhibited the increase in the Firmicutes/Bacteroidetes ratio. It increased specific bacterial taxa, including Clostridium_sensu_stricto_1, Faecalibaculum, Bacteroides, and Streptococcus, known for their anti-obesity effects. Consequently, alterations in the gut microbiota resulted in the activation of metabolic pathways, such as polysaccharide degradation and essential amino acid synthesis, which are associated with obesity inhibition. In addition, collagen peptide also effectively reduced all obesity signs caused by a high-fat diet, such as abdominal fat accumulation, high blood glucose levels, and weight gain. Ingestion of collagen peptides derived from fish skin induced significant changes in the intestinal microflora and is a potential auxiliary therapeutic agent to suppress the onset of obesity.

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. Topology optimization has been increasingly used in various industrial designs as a numerical tool to optimize the material layout of a structure. However, conventional topology optimization approaches implicitly describe the structural design and require additional post-processing to generate a manufacturable topology with smooth boundaries. To this end, this paper proposes a novel robust topology optimization approach to produce an optimized topology with smooth boundaries directly. A truncated Karhunen–Loeve expansion and a sparse grid collocation method are integrated with the explicit moving morphable components method for uncertainty representation and propagation, respectively. The performance of the proposed method is assessed on three numerical examples of continuum structures under loading and material uncertainties through comparison with several robust topology optimization approaches. Results show that the proposed method is superior to the benchmark methods in terms of the balance among robustness of the objective function, boundary smoothness, and computational efficiency.

Enrichment techniques that employ nonconforming mesh are effective in modeling structures with discontinuities because numerical issues regarding mesh quality are avoided. However, the accurate integration of the bilinear and linear forms on the discretized domain, which is required in the standard Galerkin-based finite element method, is computationally expensive due to the complexity of the enriched basis function. In this paper, we present a fast and accurate alternative method of numerical integration using nonlinear regression enabled by a multi-perceptron feedforward neural network. The relationship between an implicitly represented geometry and the quadrature rule derived from the moment fitting method is predicted by the neural network; the neural network-based regression model circumvents complex computation and significantly reduces the overall online time by avoiding expensive function evaluations. Through the selected numerical examples, we demonstrate the efficiency and accuracy of the current method, as well as the flexibility of the trained network to be used in different contexts.

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 ...

Artificial intelligence and Internet of Things (IoT) technology, which are the core of the 4th industrial revolution, can resolve many problems that optimization of production times in the manufacturing process and reduction of materials required etc. In order to utilize the 4th industrial revolution technology, real-time monitoring technology of metal parts is essential, so technology for embedding sensors and IC chips into parts is essential. Using metal 3d printing technology, it is possible to embed IC chips into metal parts, which was impossible because of the existing high-temperature metal manufacturing process of casting or forging. Here we introduce a novel new method for sensor embedding into SUS316L by hemisphere design to avoid direct laser exposure onto sensors during selective laser melting process. Thermal and microstructural analysis was carried out to characterize the property of inner hemisphere for safe thermal couple embedding into SUS316L.

This work aims to provide a comprehensive review of the continuum models of the phase behaviors of liquid crystal networks (LCNs), novel materials with various engineering applications thanks to their unique composition of polymer and liquid crystal. Two distinct behaviors are primarily considered: soft elasticity and spontaneous deformation found in the material. First, we revisit these characteristic phase behaviors, followed by an introduction of various constitutive models with diverse techniques and fidelities in describing the phase behaviors. We also present finite element models that predict these behaviors, emphasizing the importance of such models in predicting the material’s behavior. By disseminating various models essential to understanding the underlying physics of the behavior, we hope to help researchers and engineers harness the material’s full potential. Finally, we discuss future research directions necessary to advance our understanding of LCNs further and enable more sophisticated and precise control of their properties. Overall, this review provides a comprehensive understanding of the state-of-the-art techniques and models used to analyze the behavior of LCNs and their potential for various engineering applications.

Level set–based optimization for two-dimensional structural configurations with thin members is presented. A structural domain with thin thickness is defined as a narrow band region on the zero-level contour of the level set function. No additional constraints or penalty functional is required to enforce semi-uniformity in member thickness. Design velocity is calculated on the zero level set, not on domain boundaries, and extended to level set grids in the narrow band. For complicated structural layouts, multiple level set functions are employed. The effectiveness of the proposed method is verified by solving optimization problems of bar configurations. Since no thickness constraints are employed, structurally unfavorable distorted joints seen in other literature do not appear in the results.

Recently, topology optimization has drawn interest from both industry and academia as the ideal design method for additive manufacturing. Topology optimization, however, has a high entry barrier as it requires substantial expertise and development effort. The typical numerical methods for topology optimization are tightly coupled with the corresponding computational mechanics method such as a finite element method and the algorithms are intrusive, requiring an extensive understanding. This paper presents a modular paradigm for topology optimization using OpenMDAO, an open-source computational framework for multidisciplinary design optimization. This provides more accessible topology optimization algorithms that can be non-intrusively modified and easily understood, making them suitable as educational and research tools. This also opens up further opportunities to explore topology optimization for multidisciplinary design problems. Two widely used topology optimization methods—the density-based and level-set methods—are formulated in this modular paradigm. It is demonstrated that the modular paradigm enhances the flexibility of the architecture, which is essential for extensibility.

Owing to their tailorable physical properties, periodic cellular structures are considered promising materials for use in various engineering applications. To fully leverage the potential of such structures, it will be necessary to develop a design method that is capable of producing material layouts that are not only intricate but at the same time, readily manufacturable. This paper presents a topology optimization framework for designing well-connected and exact-sized multi-material cellular structures that are to be subjected to temperature change. In this framework, multi-material layouts within designable unit cells are represented using level-set functions and corresponding Boolean operations. The connectivity between exact-sized cells, advantageous in realizing the optimal designs, is guaranteed because of a common length scale assumed between these unit cells and the macrostructure. Increase in the number of degree-of-freedoms and concomitant storage requirements are minimized by applying the Guyan reduction method, in which the secondary degree-of-freedom is condensed out to reduce the size of the discretized model. The design capabilities of the proposed method were investigated using several numerical models. The optimized material layouts show that the presented method can create innovative designs facilitating the thermal expansion to improve the performance and enhance overall layouts’ stiffness in different ways, especially when the design is constituted of multiple materials.

The azobenzene-containing crosslinked liquid crystalline polymer is a potential candidate for a stimuli-responsive soft robot, as it provides contactless actuation without the implementation of any separate component. For facilitating practical applications of this novel material, complicated and predefined motions have been realized by tailoring the chemical structure of the polymer network. However, conventional multiscale mechanical analysis, which utilizes the all-atom molecular dynamics to represent a microscopic model, is unsuitable for handling diverse material design parameters due to excessive computational costs. Hence, a multiscale optomechanical simulation framework, which combines the coarse-grained molecular dynamics (CG MD) and the finite-element (FE) method, is developed in this study. The CG MD simulation satisfactorily reproduces the light-induced phase transition and photosoftening effect on the mechanical properties. In particular, using the mesoscale analysis, the presented methodology can treat diverse morphology parameters (liquid crystal phase, spacer length, and crosslinking density) to observe the associated photodeformations. The photostrain and elastic modulus profiles in terms of photoisomerization ratio are implemented into the continuum-scale governing equation, which is based on the neoclassical elasticity theory. To efficiently reflect the light-induced large rotations of liquid crystal mesogens and the corresponding geometric nonlinearity, a corotational formulation is employed in the FE shell model. We examine the mesostructural-morphology-dependent photobending deformations of the nematic and smectic photoresponsive polymers (PRPs). In addition, the mesoscopic-texture-mediated unique 3D deformations are investigated by modeling the topological defects. This study offers insight into the engineering of PRP materials for designing the mechanical motions of smart actuators.

One way biological creatures exploit their soft tissues and muscles is to quickly adjust to their environments in a flexible manner. Artificial soft material actuators have been inspired by these complex motions and studied to mimic or even exceed these biological systems. A widely adopted soft actuation method is by controlling pressure changes inside a hollow structure through the use of pneumatic systems, where inflating the structure would cause it to deform in different directions depending on its geometrical design. Instead, this work investigated actuation by vaporizing embedded liquid in a soft structure. In particular, ultrasonic waves can be directed to excite the structure that is partially filled with a small amount of ethanol, whereby atomization ejects small droplets of vaporized ethanol into the chamber to inflate the overall structure. As compared to boiling, evaporation by ultrasonic atomization is much faster and occurs at a lower temperature. Furthermore, tethered tubes are unnecessary, since ultrasonic waves can propagate through the structure. Here, soft actuation through ultrasonic atomization was analyzed by comparing the results from both experiments and numerical models. In addition, a soft robotic gripper was designed and fabricated to hold onto various objects.

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.

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.

This paper proposes a new methodology for computing boundary sensitivities in level set topology optimization using the discrete adjoint method. The adjoint equations are constructed using the discretized governing field equations. The objective function is differentiated with respect to the boundary point movement for computing boundary sensitivities using the discrete adjoint equations. For this purpose, we present a novel approach where we perturb the boundary implicitly by locally modifying the level set function around a given boundary point. These local perturbations are combined with the derivatives of the objective function with respect to the volume fractions of individual elements to compute boundary sensitivities. This enables the circumvention of smoothing or interpolation methods typically used in level set topology optimization to compute sensitivities; and improves the accuracy of the sensitivities and the convergence characteristics. We demonstrate the effectiveness of our method in the context of stress minimization and stress constrained topology optimization problems for orthogonal bracket design under multiple load cases.

In a nematic solid, wherein liquid crystal molecules are incorporated into polymeric chains, the chromophore phase is projected onto the polymer conformation, changing the stress-free configuration metric. Stimulated actuation cannot be separated from the structure itself, since the mesoscopic polymer properties dictate the degree and type of shape change. In this research, we focused on self-deforming device programming, inspired by recent optical techniques, to pattern nontrivial alignment textures and induce exotic strain fields on specimens. A finite-element framework incorporating a light-thermo-order coupled constitutive relation and geometric nonlinearities was utilized to compute mechanical deformations for given external stimuli. The distortion of planar strips into various exotic 3D shapes was simulated, and disclination-defect-like liquid crystal texture topographies with different defect strengths produced various many-poled shapes upon irradiation, as observed experimentally. The effects of the boundary conditions and geometric nonlinearities were also examined, exemplifying the need for a comprehensive finite-element-based framework. The same method was applied to textures naturally emerging due to static distortion, and the effects of the prescribed inhomogeneities on the overall deformations, which is the basis of inverse design, were observed. Furthermore, we analyzed the local Poisson-effect-induced instability resulting from inscribing a hedgehog disclination texture onto a solid; the onset of buckling-like deformations was observed energetically, and the relations between this onset and other physical properties were elucidated to enable microstate design while maintaining structural stability. These results will facilitate the development and comprehension of the mechanisms of remotely light-controlled self-assembly and propulsion systems that may soon be realized.

We investigated the optical and thermal actuation behavior of densely cross-linked photoresponsive polymer (PRP) and polymer nanocomposites containing gold nanoparticles (PRP/Au) using all-atom molecular dynamics (MD) simulations. The modeled molecular structures contain a large number of photoreactive mesogens with linear orientation. Flexible side chains are interconnected through covalent bonds under periodic boundary conditions. A switchable dihedral potential was applied on a diazene moiety to describe the photochemical trans-to-cis isomerization. To quantify the photoinduced molecular reorientation and its effect on the macroscopic actuation of the neat PRP and PRP/Au materials, we characterized the photostrain and other material properties including elastic stiffness and thermal stability according to the photoisomerization ratio of the reactive groups. We particularly examined the effect of nanoparticle size on the photothermal actuation by varying the diameter of the nanofiller (10-20 Å) under the same volume fraction of 1.62%. The results indicated that the insertion of the gold nanoparticles enlarges the photostrain of the material while enhancing its mechanical stiffness and thermal stability. When the diameter of the nanoparticle reaches a size similar to or smaller than the length of the mesogen, the interfacial energy between the nanofiller and the surrounding polymer matrix does not significantly affect the alignment of the mesogens, but rather the adsorption energy at the interface generates a stable interphase layer. Hence, these improvements were more effective as the size of the gold nanoparticle decreased. The present findings suggest a wider analysis of the nanofiller-reinforced PRP composites and could be a guide for the mechanical design of the PRP actuator system.

At elevated temperature environments, elastic structures experience a change of the stress-free state of the body that can strongly influence the optimal topology of the structure. This work presents level-set based topology optimization of structures undergoing large deformations due to thermal and mechanical loads. The nonlinear analysis model is constructed by multiplicatively decomposing thermal and mechanical effects and introducing an intermediate stress-free state between the undeformed and deformed coordinates. By incorporating the thermoelastic nonlinearity into the level-set topology optimization scheme, wider design spaces can be explored with the consideration of both mechanical and thermal loads. Four numerical examples are presented that demonstrate how temperature changes affect the optimal design of large-deforming structures. In particular, we show how optimization can manipulate the material layout in order to create a counteracting effect between thermal and mechanical loads, even up to a degree that buckling and snap-through are suppressed. Hence the consideration of large deformations in conjunction with thermoelasticity opens many new possibilities for controlling and manipulating the thermo-mechanical response via topology optimization.

Topology optimization is one of the widely known branches among the structural optimization, and it distinguishes itself by a large design domain and versatility. It can determine the optimal design out of an infinite number of configurations, thereby drawing interest from both industry and academia with regards to its applicability to additive manufacturing. However, its implementation is often a daunting task for engineers in practice. One of the issues is the programming effort required whenever the implementation requires any changes, ranging from subtle tweaks to drastic changes in the problem definition, and the derivative computation must be correspondingly updated after any change. The implementation, therefore, is not only time-consuming but also repetitive and susceptible to human-induced errors. In this regard, topology optimization implementations stand to benefit from reusability, ease of restructuring, and modularity. In this work, we propose OpenMDAO, a computational framework for multidisciplinary design optimization (MDO), as a generic platform for topology optimization. Two widely used topology optimization techniquesâ€"density-based and level-setâ€"are implemented as a demonstration. These techniques are implemented in a decomposed manner, with the aid of the modular architecture of OpenMDAO as well as state-of-the-art numerical methods. Variations on the density-based topology optimization approach are shown to demonstrate the modularity and automation for derivative computation that OpenMDAO provides.

Azobenzene liquid-crystal networks (LCNs) are well known for their photo-deformation, shrinking in UV light, and reverting to their original shape in visible light. Such reversible deformation is due to trans-cis photoisomerization of the azobenzene monomer, which disturbs well-aligned order of nematic LCN. In order to predict the photo-strain of azobenzene LCNs in multiple conditions (light intensity, polarization angle, and temperature), we propose using a density functional theory (DFT)-based modeling approach, which integrates stimulated Raman adiabatic passage calculations (STIRAP), non-linear Beer's law, and polymer physics. The model predicts that as the azobenzene ratio increases, the penetration depth of photo strain decreases, whereas the shrinkage ratio of the LCN in the unit cell increases. We identify that this opposite tendency of change is the reason why there is bending limit during the photo bending of azobenzene LCN films when increasing the ratio of the azobenzene monomer, which was also measured in experimental data.

The cis profile of azobenzene is a key factor in predicting the photodeformation of the nematic azobenzene liquid crystal network (LCN). An ab initio based method for predicting the photoisomerization profile of azobenzene is developed by coupling the stimulated Raman adiabatic passage (STIRAP) method with non-linear Beers law, and compared with experimental data. Using this combined method, we calculate the photoisomerization profile of azobenzene with various light input conditions. We identify the cis profile of the nematic LCN structure evolves into a step-like decaying shape when the direction of polarized light is parallel to the nematic direction.

This study investigates the asymmetric surface effect on nanosprings composed of Si/SiGe bilayer thin films. The misfit strain between Si and SiGe layers is known to be the driving force whereby the deformation into the nanospring shape occurs. The crystalline orientation and width-to-thickness ratio are the main factors that determine the deformed equilibrium configuration. In addition, as the thickness decreases to dozens of nanometers or less, the effect of the surface on the equilibrium configuration of the thin film is magnified. The diamond cubic crystal structure, unlike the face-centered or body-centered cubic structures, has asymmetric surface properties. Owing to the asymmetry, Si/SiGe bilayers with odd numbers of atomic layers have different surface configurations than those with even numbers of atomic layers. Finite element analysis with the surface effect has been performed to investigate the surface effect on the equilibrium configuration. It is observed that both size and surface configuration affect the equilibrium configuration of bilayer Si/SiGe nanosprings. An unexpected spring shape was observed when the film aligned in the 〈100〉 direction, which is unlikely if the surface effect is neglected.

By the chemical cross-linking of rigid molecules, liquid crystal polymer (LCP) has been envisaged as a novel heterogeneous material due to the fact that various optical and geometric states of the liquid crystalline (LC) phases are projected onto the polymeric constituents. The phase behavior, which refers to the macroscopic shape change of LCP under thermotropic phase change, is a compelling example of such optical-mechanical coupling. In this study, the photomechanical behavior, which broadly refers to the thermal- or light-induced actuation of smectic solids, is investigated using three-dimensional nonlinear finite element analysis (FEA). First, the various phases of LC are considered as well as their relation to polymeric conformation defined by the strain energy of the smectic polymer; a comprehensive constitutive equation that bridges the strong, optomechanical coupling is then derived. Such photomechanical coupling is incorporated in the FEA considering geometric nonlinearity, which is vital to understanding the large-scale light-induced bending behavior of the smectic solid.To demonstrate the simulation capability of the present model, numerous examples of photomechanical deformations are investigated parametrically, either by changing the operating conditions such as stimuli (postsynthesis) or the intrinsic properties (presynthesis). When compared to nematic solids, distinguished behaviors due to smectic substances are found herein and discussed through experiments. The quasisoftness that bidirectionally couples microscopic variables to mechanical behavior is also explained, while considering the effect of nonlinearity. In addition to providing a comprehensive measure that could deepen the knowledge of photomechanical coupling, the use of the proposed finite element framework offers an insight into the design of light-responsive actuating systems made of smectic solids.

A liquid crystal network whose chromophores are functionalized by photochromic dye exhibits light-induced mechanical behaviour. As a result, the micro-scaled thermotropic traits of the network and the macroscopic phase behaviour are both influenced as light alternates the shape of the dyes. In this paper, we present an analysis of this photomechanical behaviour based on the proposed multiscale framework, which incorporates the molecular details of microstate evolution into a continuum-based understanding. The effects of trans-to-cis photoisomerization driven by actinic light irradiation are first examined using molecular dynamics simulations and are compared against the predictions of the classical dilution model; this reveals certain characteristics of mesogenic interaction upon isomerization, followed by changes in the polymeric structure. We then upscale the thermotropic phase-related information with the aid of a nonlinear finite element analysis; macroscopic deflection with respect to the wide ranges of temperature and actinic light intensity are thereby examined, which reveals that the classical model underestimates the true deformation. This work therefore provides measures for analysing photomechanics in general by bridging the gap between the micro- and macro-scales.

In this study, body segment parameters of Korean adults were estimated using the three-dimensional (3D) body scan data from the SizeKorea database. Mass-inertial parameters and segment dimensions of 40 male subjects and 40 female subjects (18–59 years old) were estimated using a 16-segment model under the assumption that each segment has a constant density distribution after reconstructing the scan data. Therefore, several sets of linear regression functions based on gender, stature, and weight were established, which provided a convenient method for estimating body segment parameters of Korean adults. The obtained mass ratios of body segments were compared with those for Russians reported by Zatsiorsky and Seluyanov (1983) and for those for Chinese and Germans reported by Shan and Bohn (2003) , in which the same 16-segment model was used. In addition, the results were compared with the Korean data results reported by Jung, 1993 , Lim, 1994 , and Park et al. (1999) . These comparisons revealed that Asians have larger head mass ratios and smaller lower limb mass ratios than Caucasians, while the differences in the head mass ratios between males and females from the same ethnic groups were not significant. Females were found to have larger mass ratios for the lower torso and smaller mass ratios for the upper torso, middle torso, upper arm, forearm, foot, and hand, as compared to males from the same ethnic groups. In addition, the data obtained by different researchers were compared, thereby showing high reproducibility of our method. Relevance to industry The obtained segment parameters can be used to define digital human models and applied to the fields of ergonomics and biomechanics, such as for workspace design, furniture design, vehicle interior design, and human movement analysis.

As a polymeric system incorporating rigid molecules within its structure, the liquid-crystal network (LCN) has been envisaged as a novel heterogeneous material. Under the influence of external stimuli, the orientational order of the liquid-crystalline phase becomes dilute and overall anisotropy is hence decreased; the actinic light absorbed by photochromic molecules, for example, induces the geometric isomerization and subsequently yields internal stress within the local network. In this study we investigate light- and temperature-induced spontaneous deformations of the LCN structure via a three-dimensional finite element model that incorporates geometric nonlinearity with a photomechanical constitutive model. We first examine the bending behavior and its nonlinearity and then parametrically study the various behaviors that stem from different origins ranging from the microscale to the macroscale: (i) the geometry of the LCN film, (ii) the macroscopic global order, (iii) the distorted mesogenic orientation due to the Fredericks distortion, and (iv) defect-induced instability. These interrelated behaviors demonstrate both the simulation capability and the necessity of the presenting framework. By employing a nonlinear consideration along with a microscopic shape parameter $r$ the present approach facilitates further understanding of photomechanical physics such as the deconvolution of various stimuli and the deformed shape obtained due to snap-through instability. Furthermore, this study may offer insight into the design of light-sensitive actuation systems by deepening our knowledge and providing an efficient measure.

The opto-mechanical properties of a photo-responsive nematic polymer network (PRPN) are investigated using molecular dynamics simulation. For the implementation of the trans-to-cis isomerization of azo compounds, a switchable potential formalism for the N = N bond is applied to the crosslinked PRPN unit cell model. During the light switch-on and heating-up simulations at a wide range of temperatures, the scalar orientational order parameter for the mesogenic side group molecules, the effective photo-induced strain of the bulk polymer network, and the opto-mechanical properties are characterized. The correlation between the microstate which belongs to the molecular location and the macroscopically observed photostrain is identified according to the isomerization ratio of the diazene groups.

We investigate length and boundary effects on the equilibrium strain of a ⟨100⟩ copper nanorod with {100} or {110} surfaces. Unlike a nanowire, a free-edged nanorod has finite length and has two more surfaces at both tip and root. Although the area of these two edge surfaces is generally much smaller than that of side surfaces, the effect of the edge surfaces should not be ignored in the equilibrium configuration of a nanorod. In this letter, an analytical model to estimate the equilibrium strain of the nanorod is proposed, and molecular statics simulations are performed to prove the proposed model. As the length of a nanorod increases, the equilibrium strain increases and converges to that of a nanowire. As for the boundary effect, we compare the equilibrium strain of a clamped nanorod with that of a free-edged nanorod.