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The shape of a nanochannel significantly affects mass transport. This study provides a new nanochannel model made from a concentric-twin tube (CTT), which can be made by inserting a carbon nanotube (CNT) into another identical CNT. The stable configuration of such a CTT has three subchannels containing different cross-sectional shapes. Molecular dynamic approach is applied to evaluate the transport performances of the confined water in the CTT. Molecular dynamics simulations indicate that the CTT made from (17,17) CNTs is the thinnest nanochannel for water transport. The three subchannels of a CTT have different linear speeds of water and different volume flow rates depending on the CTT's cross-sectional shapes. Based on these characteristics, a fluid nanodevice requiring special transform performances, e.g., sieving the molecules with different sizes in a solution, can be designed from the new nanochannels. [ABSTRACT FROM AUTHOR]

The nonlinear dynamic behavior of a clamped–clamped nanobeam built with boron nitride carbon (BNC) nanotube is investigated as for its potential application in a mass sensor. To make it anisotropic in terms of bending stiffness, the cross section of the tube contains symmetrically two B–N zones and two carbon zones which accommodate 60% of atoms in the whole nanotube. The dynamic behavior of the nanosensor, colliding with a high-speed C 60 at the central part of the beam, is evaluated using molecular dynamics simulations and fast Fourier transform approaches. Results obtained show that the amplitude of vibration of the tube depends on the magnitude (v In) and direction (θ ) of the incident velocity of the C 60 . When v In is higher than a critical value, the beam will be damaged in the collision. The position of the damage on the nanobeam and the critical value depend on θ . If v In is lower than the critical value, the first-order frequency of the vibration at the beam centroid is lower when impacted by a faster C 60 . The second-order frequency depends on the configuration of the beam's central cross section. The intervals of the first-order frequency with respect to θ = 0 ∘ and 90 ∘ are not overlapped. These findings hint that a BNC nanobeam can be used to measure the mass of a molecular under a known incident velocity or an incident velocity of a known molecular via this model. [ABSTRACT FROM AUTHOR]

Fused deposition modelling (FDM) is a technique of additive manufacturing (AM) which is capable of fast construction of plastic prototypes. AM technology has been utilised in orthopaedics and traumatology to fabricate patient-specific models, surgical guides, and implants. However, the layering build-up by FDM usually generates a deleterious rough surface that limits its application to items such as surgical guide and surgical operating guide, because these items require a highly resolved surface quality. The advancement of laser polishing has been offering a cost-effective and fast manufacturing solution for FDM-constructed patient-specific guides and implants. This investigation explores application potential using a contactless laser scanning to improve the surface quality of FDM-fabricated thermoplastics. The results show that a maximum [68%] reduction in surface roughness was achieved at 3 W CO2 laser power, 150 mm/s scan speed, 30 ms scan delay and 0.025 mm line gap. Laser polishing is suitable to treat the surface of polylactic acid (PLA). This study provides data which supports a new approach to the manufacture of AM-fabricated thermoplastics utilising a laser scanning technique to improve the surface quality. [ABSTRACT FROM AUTHOR]

In the paper, an anisotropic Green's function based hybrid finite element was developed for solving fully plane anisotropic elastic materials. In the present hybrid element, the interior displacement and stress fields were approximated by the linear combination of anisotropic Green's functions derived by Lekhnitskii formulation, the element frame fields were constructed by the interpolation of general shape functions widely used in the conventional finite element, and then they are linked by a new double-variable hybrid functional. Because the approximated interior fields exactly satisfied the governing equations related to anisotropic elasticity, all integrals in the present hybrid functional were performed along the element boundary and theoretically arbitrary hybrid polygonal element can be constructed. Finally, the present hybrid polygonal element with four edges was verified by making comparison of numerical results and exact solutions in a cantilever composite beam made with angled lamina. [ABSTRACT FROM AUTHOR]

A new computational model by integrating the boundary element method and the compactly supported radial basis functions (CSRBF) is developed for three-dimensional (3D) linear elasticity with the presence of body forces. The corresponding displacement and stress particular solution kernels across the supported radius in the CSRBF are obtained for inhomogeneous term interpolation. Subsequently, the classical dual reciprocity boundary element method, in which the domain integrals due to the presence of body forces are transferred into equivalent boundary integrals, is formulated by introducing locally supported displacement and stress particular solution kernels for solving the inhomogeneous 3D linear elastic system. Finally, several examples are presented to demonstrate the accuracy and efficiency of the present method. [ABSTRACT FROM AUTHOR]

An optimization model is presented for obtaining optimal layout of multiple bi-modulus materials systems under multiple load cases (MLC). In the optimization model, the objective function is the linearly weighted structural compliance under MLC. The bi-modulus materials in a finite element are replaced by isotropic materials according to the stress state of that element. The equivalent mechanical properties of an element are expressed as the power-law function of the volume fractions (design variables) and moduli of the solid phases. Numerical experiments are presented to verify the validity and efficiency of the present algorithm. The effects of factors including the bi-modulus behavior of materials, the load directions and the weighting schemes of MLC are also investigated numerically. [ABSTRACT FROM AUTHOR]

Band structures are investigated in two-dimensional phononic crystals (PC) composed of a periodic S-shaped slot in an air matrix with a square lattice. Dispersion relations, pressure fields and transmission spectra are calculated using the finite element method and Bloch theorem. Numerical results show that the proposed PC can yield complete and large band gaps at lower frequency ranges compared with that of the Jerusalem slots in Li et al. (Phys B 456:261-266, ) under the same parameter setting of the lattice and outline of the inclusions. The transmission spectrum is verified to be reasonably consistent with the band gaps along the $$\Gamma X$$ direction. By analysing the pressure fields of several modes, the resonance modes of cavities within the S-shaped slot structure are found to result in the low-frequency band gaps. The effects of the geometrical parameters on the upper and lower edges of the first and second complete band gap are further studied. Numerical results show that the bandwidth of the first and second band gaps can be modulated over an extremely large frequency range by the geometrical parameters. The properties of the proposed PC have potential for implementation in structures and devices of noise and vibration control, such as noise filters and waveguides. [ABSTRACT FROM AUTHOR]

In this paper, a new type of hybrid fundamental solution-based finite element method (HFS-FEM) is developed for analyzing plane piezoelectric problems with defects by employing fundamental solutions (or Green's functions) as internal interpolation functions. The hybrid method is formulated based on two independent assumptions: an intra-element field covering the element domain and an inter-element frame field along the element boundary. Both general elements and a special element with a central elliptical hole or crack are developed in this work. The fundamental solutions of piezoelectricity derived from the elegant Stroh formalism are employed to approximate the intra-element displacement field of the elements, while the polynomial shape functions used in traditional FEM are utilized to interpolate the frame field. By using Stroh formalism, the computation and implementation of the method are considerably simplified in comparison with methods using Lekhnitskii's formalism. The special-purpose hole element developed in this work can be used efficiently to model defects such as voids or cracks embedded in piezoelectric materials. Numerical examples are presented to assess the performance of the new method by comparing it with analytical or numerical results from the literature. [ABSTRACT FROM AUTHOR]

A bone cell population dynamics model for cortical bone remodeling under mechanical stimulus is developed in this paper. The external experiments extracted from the literature which have not been used in the creation of the model are used to test the validity of the model. Not only can the model compare reasonably well with these experimental results such as the increase percentage of final values of bone mineral content (BMC) and bone fracture energy (BFE) among different loading schemes (which proves the validity of the model), but also predict the realtime development pattern of BMC and BFE, as well as the dynamics of osteoblasts (OBA), osteoclasts (OCA), nitric oxide (NO) and prostaglandin E (PGE) for each loading scheme, which can hardly be monitored through experiment. In conclusion, the model is the first of its kind that is able to provide an insight into the quantitative mechanism of bone remodeling at cellular level by which bone cells are activated by mechanical stimulus in order to start resorption/formation of bone mass. More importantly, this model has laid a solid foundation based on which future work such as systemic control theory analysis of bone remodeling under mechanical stimulus can be investigated. The to-be identified control mechanism will help to develop effective drugs and combined nonpharmacological therapies to combat bone loss pathologies. Also this deeper understanding of how mechanical forces quantitatively interact with skeletal tissue is essential for the generation of bone tissue for tissue replacement purposes in tissue engineering. [ABSTRACT FROM AUTHOR]

In this paper, a new type of hybrid finite element method (FEM), hybrid fundamental-solution-based FEM (HFS-FEM), is developed for analyzing plane piezoelectric problems by employing fundamental solutions (Green's functions) as internal interpolation functions. A modified variational functional used in the proposed model is first constructed, and then the assumed intra-element displacement fields satisfying a priori the governing equations of the problem are constructed by using a linear combination of fundamental solutions at a number of source points located outside the element domain. To ensure continuity of fields over inter-element boundaries, conventional shape functions are employed to construct the independent element frame displacement fields defined over the element boundary. The proposed methodology is assessed by several examples with different boundary conditions and is also used to investigate the phenomenon of stress concentration in infinite piezoelectric medium containing a hole under remote loading. The numerical results show that the proposed algorithm has good performance in numerical accuracy and mesh distortion insensitivity compared with analytical solutions and those from ABAQUS. In addition, some new insights on the stress concentration have been clarified and presented in the paper. [ABSTRACT FROM AUTHOR]

Abstract: A novel hybrid graded element model is developed in this paper for investigating thermal behavior of functionally graded materials (FGMs). The model can handle a spatially varying material property field of FGMs. In the proposed approach, a new variational functional is first constructed for generating corresponding finite element model. Then, a graded element is formulated based on two sets of independent temperature fields. One is known as intra-element temperature field defined within the element domain; the other is the so-called frame field defined on the element boundary only. The intra-element temperature field is constructed using the linear combination of fundamental solutions, while the independent frame field is separately used as the boundary interpolation functions of the element to ensure the field continuity over the inter-element boundary. Due to the properties of fundamental solutions, the domain integrals appearing in the variational functional can be converted into boundary integrals which can significantly simplify the calculation of generalized element stiffness matrix. The proposed model can simulate the graded material properties naturally due to the use of the graded element in the finite element (FE) model. Moreover, it inherits all the advantages of the hybrid Trefftz finite element method (HT-FEM) over the conventional FEM and boundary element method (BEM). Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show a good numerical accuracy. [Copyright &y& Elsevier]

Abstract: Carbon nanotube fibers can be fabricated by the chemical vapor deposition spinning process. They are promising for a wide range of applications such as the building blocks of high-performance composite materials and micro-electrochemical sensors. Mechanical twisting is an effective means of enhancing the mechanical properties of carbon nanotube fibers during fabrication or by post processing. However, the effects of twisting on the mechanical properties remain an unsolved issue. In this paper, we present a two-scale damage mechanics model to quantitatively investigate the effects of twisting on the mechanical properties of carbon nanotube fibers. The numerical results demonstrate that the developed damage mechanics model can effectively describe the elastic and the plastic-like behaviors of carbon nanotube fibers during the tension process. A definite range of twisting which can effectively enhance the mechanical properties of carbon nanotube fiber is given. The results can be used to guide the mechanical twisting of carbon nanotube fibers to improve their properties and help optimize the mechanical performance of carbon nanotube-based materials. [Copyright &y& Elsevier]

Special hole elements are presented for analyzing the stress behavior of an isotropic elastic solid containing an elliptical hole. The special hole elements are constructed using the special fundamental solutions for an infinite domain containing a single elliptical hole, which are derived based on complex conformal mapping and Cauchy integrals. During the construction of the special elements, the interior displacement and stress fields are assumed to be the combination of fundamental solutions at a number of source points, and the frame displacement field defined over the element boundary is independently approximated with conventional shape functions. The hybrid finite element model is formulated based on a hybrid functional that provides a link between the two assumed independent fields. Because the fundamental solutions used exactly satisfy both the traction-free boundary conditions of the elliptical hole under consideration and the governing equations of the problems of interest, all integrals can be converted into integrals along the element boundary and there is no need to model the elliptical hole boundary. Thus, the mesh effort near the elliptical hole is significantly reduced. Finally, the numerical model is verified through three examples, and the numerical results obtained for the prediction of stress concentration factors caused by elliptical holes are extremely accurate. [ABSTRACT FROM AUTHOR]

We report on responses of hydrated and dehydrated cortical bone tissues to mechanical loading applied by a Vickers indenter. The Vickers indentations were imaged in two- and three-dimensions (2D and 3D) using confocal laser scanning microscopy (CLSM) to understand mechanical behavior of bone tissues. Serial optical sections of indentation patterns of dry and wet bones were collected using CLSM. The indention surface structures were mapped using topographical CLSM imaging. The observation of CLSM shows the fundamental indentation responses for both the hydrated and dehydrated bone tissues were plastic deformation. No visible fracture was observed in the Vickers indentation patterns in the wet bone tissue, while non-propagating lamellar microcracks occurred in the dry bone tissue. This indicates that drying resulted in increased brittleness of the bone tissue. The Vickers hardness values of dry bone tissue were significantly higher than those of wet bone tissue at any applied loads (analysis of variation, ANOVA, p < 0.05). The resolution limits of confocal microscopy were also discussed for bone tissue scanning. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid graded element model for the transient heat conduction problem in functionally graded materials (FGMs). First, a Laplace transform approach is used to handle the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, a hybrid graded element is formulated based on the obtained fundamental solution and a frame field. As a result, the graded properties of FGMs are naturally reflected by using the fundamental solution to interpolate the intra-element field. Further, Stefest's algorithm is employed to convert the results in Laplace space back into the time-space domain. Finally, the performance of the proposed method is assessed by several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

The present paper develops a new type of hybrid finite element model with regular and special fundamental solutions (also known as Green's functions) as internal interpolation functions for analyzing plane elastic problems in structures weakened by circular holes. A variational functional used in the proposed model is first constructed, and then, the assumed intra-element displacement fields satisfying a priori the governing partial differential equations of the problem under consideration is constructed using a linear combination of fundamental solutions at a number of source points outside the element domain, as was done in the method of fundamental solutions. To ensure continuity of fields over inter-element boundaries, conventional shape functions are employed to construct the independent element frame displacement fields defined over the element boundary. The linkage of these two independent fields and the element stiffness equations in terms of nodal displacements are enforced by the minimization of the proposed variational functional. Special-purpose Green's functions associated with circular holes are used to construct a special circular hole element to effectively handle stress concentration problems without complicated local mesh refinement or mesh regeneration around the hole. The practical efficiency of the proposed element model is assessed via several numerical examples. [ABSTRACT FROM AUTHOR]

The low-order polynomial-distributed eigenstrain formulation of the boundary integral equation (BIE) and the corresponding definition of the Eshelby tensors are proposed for the elliptical inhomogeneities in two-dimensional elastic media. Taking the results of the traditional subdomain boundary element method (BEM) as the control, the effectiveness of the present algorithm is verified for the elastic media with a single elliptical inhomogeneity. With the present computational model and algorithm, significant improvements are achieved in terms of the efficiency as compared with the traditional BEM and the accuracy as compared with the constant eigenstrain formulation of the BIE. [ABSTRACT FROM AUTHOR]

ABSTRACT: A new type of hybrid finite element formulation with fundamental solutions as internal interpolation functions, named as HFS-FEM, is presented in this paper and used for solving two dimensional heat conduction problems in single and multi-layer materials. In the proposed approach, a new variational functional is firstly constructed for the proposed HFS-FE model and the related existence of extremum is presented. Then, the assumed internal potential field constructed by the linear combination of fundamental solutions at points outside the elemental domain under consideration is used as the internal interpolation function, which analytically satisfies the governing equation within each element. As a result, the domain integrals in the variational functional formulation can be converted into the boundary integrals which can significantly simplify the calculation of the element stiffness matrix. The independent frame field is also introduced to guarantee the inter-element continuity and the stationary condition of the new variational functional is used to obtain the final stiffness equations. The proposed method inherits the advantages of the hybrid Trefftz finite element method (HT-FEM) over the conventional finite element method (FEM) and boundary element method (BEM), and avoids the difficulty in selecting appropriate terms of T-complete functions used in HT-FEM, as the fundamental solutions contain usually one term only, rather than a series containing infinitely many terms. Further, the fundamental solutions of a problem are, in general, easier to derive than the T-complete functions of that problem. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show good numerical accuracy and remarkable insensitivity to mesh distortion. [Copyright &y& Elsevier]

A nonlinear finite element analysis was carried out to investigate the viscoplastic deformation of solder joints in a ball grid array (BGA) package under temperature cycling. The effects of constraint on printed circuit board (PCB) and stiffness of substrate on the deformation behavior of the solder joints were also studied. A relative damage stress was adopted to analyze the potential failure sites in the solder joints. The results indicated that high inelastic strain and strain energy density were developed in the joints close to the package center. On the other hand, high constraint and high relative damage stress were associated with the joint closest to the edge of the silicon chip which was regarded as the most susceptible failure site if cavitation instability is the dominant failure mechanism. Increasing the external constraint on PCB causes a slight increase in stress triaxiality $$ \left( {\sigma _m /\sigma _{eq} } \right) $$ and relative damage stress in the joint closest to the edge of the silicon die. The relative damage stress is not sensitive to the Young's modulus of the substrate. [ABSTRACT FROM AUTHOR]

Fused filament fabrication (FFF) stands out as one of the most widely used additive manufacturing (AM) techniques, attracting considerable attention in recent years. Despite the remarkable strides witnessed in FFF-based AM technology, challenges persist in fabricating robust, high-performance, and functional components for demanding real-world applications. In comparison to polymer/continuous carbon fiber-reinforced polymer (CCFRP) composites produced using conventional processing methods, those fabricated via FFF technology often exhibit inherent weaknesses in their mechanical properties, including reduced strength and anisotropic behavior. These deficiencies stem from inherent imperfections such as voids and poor interfacial adhesion, a consequence of the layer-by-layer deposition nature coupled with the dual-phase composition of composite materials. While traditional remedies such as process refinement, in situ processing, and post-processing techniques have been pursued, there remain limitations in their effectiveness. This paper begins with an overview of the categories of voids and interfaces encountered in FFF-fabricated polymer/CCFRP composites. Subsequently, the existing improvement strategies are reviewed, and the focus shifts to an in-depth exploration of material modification approaches. This encompasses both matrix material modification and carbon fiber (CF) surface enhancements, examining their influence on void formation, interface quality, and overall performance of printed parts. Finally, the prospects for future research directions in material modification of three-dimensional (3D) printed polymers and CCFRP composites are highlighted. [ABSTRACT FROM AUTHOR]

For a two-dimensional piezoelectric plate, the thermoelectroelastic Green's functions for bimaterials subjected to a temperature discontinuity are presented by way of Stroh formalism. The study shows that the thermoelectroelastic Green's functions for bimaterials are composed of a particular solution and a corrective solution. All the solutions have their singularities, located at the point applied by the dislocation, as well as some image singularities, located at both the lower and the upper half-plane. Using the proposed thermoelectroelastic Green's functions, the problem of a crack of arbitrary orientation near a bimaterial interface between dissimilar thermopiezoelectric material is analysed, and a system of singular integral equations for the unknown temperature discontinuity, defined on the crack faces, is obtained. The stress and electric displacement (SED) intensity factors and strain energy density factor can be, then, evaluated by a numerical solution at the singular integral equations. As a consequence, the direction of crack growth can be estimated by way of strain energy density theory. Numerical results for the fracture angle are obtained to illustrate the application of the proposed formulation. [ABSTRACT FROM AUTHOR]

In the fabrication of a thermally driven rotary nanomotor with the dimension of a few nanometers, fabrication and control precision may have great influence on rotor's stability of rotational frequency (SRF). To investigate effects of uncertainty of some major factors including temperature, tube length, axial distance between tubes, diameter of tubes and the inward radial deviation (IRD) of atoms in stators on the frequency's stability, theoretical analysis integrating with numerical experiments are carried out. From the results obtained via molecular dynamics simulation, some key points are illustrated for future fabrication of the thermal driven rotary nanomotor. [ABSTRACT FROM AUTHOR]