Volume Fraction Of Inclusions Research Articles

FEATURES OF THE CONSTRUCTION OF THE STIFFNESS MATRIX OF THE SPATIAL HEXAGONAL FINITE ELEMENT FOR COMPOSITE MATERIAL WITH DISCRETE INCLUSIONS BASED ON THE MOMENT SCHEME

An approach to numerical modeling of the stress-strain state of composite structures with discrete inclusions is presented in the paper. The finite element method is used as the main method, namely its modification – the moment finite-element scheme. The moment scheme, in contrast to the classic scheme of finite elements, allows to avoid such negative properties as not taking in consideration the rigid rotation of the finite element and “false” shear. If both the material of the matrix and the material of the reinforcing inclusions are weakly compressible, then problems arise due to the fact that some elastic constants approach very large values. The Taylor series expansion of the components of the displacement vector, the components of the strain tensor, and the volume change function is used in order to eliminate the mentioned shortcomings, after that, according to the moment scheme, certain sums are removed from these expansions. Homogenization of the material with lamellar inclusions, a small proportion of spherical inclusions, and a large proportion of spherical inclusions is used for modeling the elastic properties of the composite. The chaotic nature of the location of inclusions after homogenization makes it possible to present a non-homogeneous composite material as a homogeneous quasi-isotropic one. The described approaches are used in the construction of the stiffness matrix of the spatial hexagonal finite element. The obtained expressions for the stiffness matrix are done in the software package for calculating structures from composite materials. The calculation of a thick-walled pipe under the action of internal pressure from a composite material with lamellar inclusions, a small proportion of spherical inclusions, and a large proportion of spherical inclusions was carried out using the software package. For different volume fractions of discrete inclusions, the numerical convergence of the results with different finite element meshes has been investigated, which shows great congruence with analytical solutions.

Assessing PAHs-based soot inception models in various laminar non-premixed flame configurations

Accurate soot modeling is challenging due to the complex underlying physical and chemical processes. To improve the fidelity of the soot prediction in inverse coflow flame configurations, an empirical reactive soot inception model with radical involvement was developed in our previous work [Guo et al. Combust Flame 254 (2023) 112,853]. In this study, the model is further assessed by comparing the predictions of polycyclic aromatic hydrocarbons (PAHs) and soot parameters, including volume fraction, number density, and particle size, with measurements in various laminar diffusion flame configurations. These configurations encompass counterflow diffusion flames (CDF), normal coflow diffusion flames (NDF), and inverse coflow diffusion flames (IDF). The empirical reactive inception model is also compared to the reported irreversible and reversible inception models. The results show that the empirical reactive inception model with radical involvement most accurately capture axial soot behavior in IDF configuration, while irreversible and reversible models predict a sustained increase in soot mass, inconsistent with measurements. In CDF configurations, the empirical reactive model and the reported reversible model have better performance than the irreversible inception model, regarding the predictions of spatial distributions of soot and PAHs. Moreover, in NDF configuration, the soot peaks predicted by the reactive and reversible models are in reasonable agreement with measurements within a factor of 2–3. For the soot spatial distribution in NDF, the difference in the predictions is mainly reflected in the flame wings, which is caused by the temperature dependences of the inception rate provided by the different models.

An RBF-based artificial neural network for prediction of dynamic viscosity of MgO/SAE 5W30 oil hybrid nano-lubricant to obtain the best performance of energy systems

Technological progress and complications in microfluidics usage have led researchers to use nanomaterials in different scientific fields. The properties and characteristics of hybrid Nanofluids are more enhanced compared to nanofluids based on single nanoparticles and conventional liquid. Recently, modeling methods have replaced most common statistical methods. Due to the high accuracy of the response and generalizability in various conditions, artificial neural networks (ANNs) to estimate nanofluids’ viscosity and thermal conductivity have become common. Dynamic viscosity (μ) (estimation analyzes one of the key factors in determining the hydrodynamic behavior of nanofluids. In this manuscript, an RBF-ANN is used to simulate the input-output relation of dynamic viscosity of the MgO- SAE 5W30 Oil hybrid nanofluid versus three important parameters, including volume fraction of nanoparticles, temperature, and shear rate. The results show that for this nanofluid, by increasing temperature and shear rate, the dynamic viscosity is decreased. In contrast, the volume fraction of nanoparticles directly affects the output, although this consequence can be neglected. By increasing the temperature from 5° to 55°C, the dynamic viscosity would decrease. Also, changing the shear rate from 50 to 1000 rpm decreases the dynamic viscosity from 400 cP to 25 cP. It is worth mentioning that the obtained trends and deviation of dynamic viscosity for MgO-SAE 5W30 Oil hybrid nanofluid versus temperature, the volume fraction of nanoparticles, and shear rate can be used by the academic community as well as an industrial section to obtain the best performance of energy systems based on this nanofluid.

Mathematical micro–macro modeling of fully coupled nonlinear magneto-elastic reinforced composites

In this paper, integral equation formulations and field-dependent micromechanical modeling of global nonlinear magneto-mechanical behavior of magneto-elastic composites under high strain and magnetic field are elaborated. The modeling is obtained based on an extension of micro–macro transition inclusion problem to nonlinear behavior using field-dependent and highly nonlinear localization tensors. A methodological procedure is elaborated based on newly introduced strain and magnetic field-dependent Green tensors, strain and magnetic field-dependent integral equations linked to tensors of Eshelby and micromechanical approaches. The field-dependent global moduli are predicted based on the Mori–Tanaka approach and self-consistent method. Iterative incremental schemes based on the Newton–Raphson and fixed-point algorithms are examined and established precise semi-analytic equations of the effective magneto-elastic properties of composites that are dependent on the magnetic-strain field for different types of inclusions. A numerical code is elaborated for numerical predictions and the obtained field-dependent effective magneto-elastic coefficients are obtained and presented for various volume fractions of inclusion, types and shapes of the reinforced nonlinear composites.

DISTRIBUTION OF ELECTRIC FIELDS ON THE SURFACE OF INCLUSIONS IN MATRIX COMPOSITE

Expressions are obtained for operators of concentration of electric field strength and displacement on the surface of inclusions in matrix composite depending on shape and volume fraction of inclusions in material. These operators relate the fields on the inclusion surface on the matrix side with the average values of the electric field strength and displacement in the composite sample.

Infection burden and its association with neurite orientation dispersion and density imaging markers in the UK Biobank

BackgroundInfection burden (IB), although linked to neurodegeneration, including Alzheimer’s Disease (AD), has not been examined against neurite orientation, dispersion, and density imaging (NODDI) measures. MethodsAmong 38,803 UK Biobank adults (Age:40–70 years), we tested associations of total IB (IBtotal, 47.5 %) and hospital-treated IB (IBhosp, 9.7 %) with NODDI measures (5–15 years later), including volume fraction of Gaussian isotropic diffusion (ISOVF), intra-cellular volume fraction (ICVF) and orientation dispersion (OD) indices, using multiple linear regression models. ResultsTotal and hospital-treated infection burdens (IBtotal and IBhosp) were associated with increased ISOVF, indicating increased free-water component. IBtotal was positively associated with OD, indicating that at higher IBtotal there was greater fanning of neurites. This was more evident in the lower cardiovascular health group. IBhosp was associated with higher OD, and lower ICVF at higher AD polygenic risk. Together, these findings indicate that both total and hospital-treated infections have effects on NODDI outcomes in the direction of poor brain health. These effects were largely homogeneous across cardiovascular health and AD polygenic risk groups, with some effects shown to be stronger at poor cardiovascular health and/or higher AD risk. ConclusionsTotal and hospital-treated infections were associated with poorer white matter microstructure (higher ISOVF or OD or lower ICVF), with some heterogeneity across cardiovascular health and AD risk. Longitudinal studies with multiple repeats on neuroimaging markers in comparable samples are needed.

Effective mechanical properties of frozen hydrogel with ice inclusions

Hydrogel exhibits attractive mechanical properties that can be regulated to be extremely tough, strong and resilient, adhesive and fatigue-resistant, thus enabling diverse applications ranging from tissue engineering scaffolds, flexible devices, to soft machines. As a liquid-filled porous material composed of polymer networks and water, the hydrogel freezes at subzero temperatures into a new material composed of polymer matrix and ice inclusions: the frozen hydrogel displays dramatically altered mechanical properties, which can significantly affect its safety and reliability in practical applications. In this study, based upon the theory of homogenization, we predicted the effective mechanical properties (e.g., Young's modulus, shear modulus, bulk modulus and Poisson ratio) of a frozen hydrogel with periodically distributed longitudinal ice inclusions. We firstly estimated its longitudinal Young's modulus, longitudinal Poisson ratio and plane strain bulk modulus using the self-consistent method, and then its longitudinal and transverse shear modulus using the generalized self-consistent method; further, the results were employed to calculate its transverse Young's modulus and transverse Poisson ratio. We validated the theoretical predictions against both finite element (FE) simulation and experimental measurement results, with good agreement achieved. We found that the estimated transverse Poisson ratio ranges from 0.3 to 0.53 and, at low volume fraction of ice inclusions, exhibits a value larger than 0.5 that exceeds the Poisson ratios of both the polymer matrix and the ice inclusion (typically 0.33–0.35). Compared with other homogenization methods (e.g., the rule of mixtures, the Halpin-Tsai equations, and the Mori-Tanaka method), the present approach is more accurate in predicting the effective mechanical properties (in particular, the transverse Poisson ratio) of frozen hydrogel. Our study provides theoretical support for the practical applications of frozen liquid-saturated porous materials such as hydrogel.

Effective elastic properties of one-dimensional hexagonal quasicrystal composites with spring-type imperfect interfaces

Considering the spring-type imperfect interfaces, the effective elastic properties of one-dimensional (1D) hexagonal quasicrystal (QC) are investigated systematically. The spring-type imperfect interface between QC matrix and inclusion is an ultra-thin, soft and weakly conductive interface. The Mori–Tanaka method is presented to determine the effective elastic constants of phonon, phason and phonon–phason coupling field. The numerical results are provided to show that the existence of imperfect interfaces reduces the effective elastic constants to some extent. It indicates that the interface plays an important role in the elastic properties of QC composites. Besides, the effective elastic constants are also subject to the aspect ratio and the volume fraction of inclusions.

Improved antioxidant activity and delivery of peppermint oil Pickering emulsion stabilized by resveratrol-grafted zein covalent conjugate/quaternary ammonium chitosan nanoparticles

Novel nanoparticles (Z-R/H) were successfully fabricated by a resveratrol-grafted zein covalent conjugate (Z-R) combined with quaternary ammonium chitosan (HTCC), which were used as stabilizers to prepare peppermint oil (PO) Pickering emulsions with antioxidant activity. HTCC effectively adjusted wettability of Z-R conjugate, and three-phase contact angle of Z-R/H3:1 was moderate (95.01°). The influencing factors of Pickering emulsion formation, including volume fraction of PO, concentration of Z-R/H, and mass ratio of Z-R to HTCC, were evaluated by droplet size, ζ-potential, microscopic observation, and stability index analysis. Pickering emulsions stabilized by Z-R/H3:1 showed excellent physical stability under heat treatment. Z-R/H nanoparticles adsorbed on the oil-water interface yielded a dense filling layer as a physical barrier to improve the emulsion stability, which was validated by confocal laser-scanning microscopy. After 4 weeks of storage, retention rate of PO in Pickering emulsion stabilized by Z-R/H3:1 remained high (72.1 %). Electronic nose analysis showed that Z-R/H3:1-stabilized emulsion effectively prevented volatilization of PO aroma components. Additionally, PO and Z-R/H nanoparticles provided an additive antioxidant effect of Pickering emulsions against DPPH and ABTS free radicals. In summary, these novel Z-R/H nanoparticle offer promising applications as a stabilizer with great potential in preparing functional Pickering emulsions to improve essential oil delivery.

From stress concentrations between inclusions to probability of breakage: A two-dimensional peridynamic study of particle-embedded materials.

Particle-embedded materials consist of a dispersed phase of particles in a sticking matrix. We used a bond-based peridynamics method to investigate their elastic properties, rupture, and probability of failure. We performed an extensive two-dimensional parametric study where particles are disk-shaped inclusions diluted into a pore-filling matrix. Both particle and matrix are considered to be brittle elastic with a perfectly bonded interface. The inclusion volume fraction φ and the inclusion matrix toughness ratio β (β≥1) were varied from 0.254-0.754 (jamming point) and 1.5-100.0, respectively. A total of 5000 uniaxial tensile tests up to failure were performed. We showed that the Halpin-Tsai model fits well all Young elastic moduli even for nearly in-contact particles. The stress distribution strongly depends on φ and β. As the highest stresses (at the origin of crack nucleation) occur between neighboring particles, we analyzed the average stress in gaps. We found that, regardless of the particle volume fraction, the yield stress is a power law of a grain-scaled stress concentration factor. We also investigated the probability of failure of the samples. We found that whatever φ and β, this probability follows a classical Weibull law. Finally, we showed that Weibull modulus, normalized by its value for infinitely rigid particles, is inversely proportional to a function of the stress concentration factor.

Retrieving the Intrinsic Microwave Permittivity and Permeability of Ni-Zn Ferrites

Mixing rules may be extremely useful for predicting the properties of composite materials and coatings. The paper is devoted to the study of the applicability of the mixing rules to permittivity and permeability and the possibility of retrieving the intrinsic properties of inclusions. Magnetically soft Ni-Zn ferrites are chosen as the object of the study due to their low permittivity and the negligible influence of the skin effect. Due to this, the microwave properties of bulk ferrites may be measured by standard techniques. It is suggested to perform the analysis of the microwave properties of composites filled with Ni-Zn ferrite powder in terms of the normalized inverse susceptibility defined as the volume fraction of inclusions divided by the effective dielectric or magnetic susceptibility of the composite. The measured properties of the bulk ferrite are compared with those obtained by mixing rules from composite materials. The experimental evidence for difference between the mixing rules for permittivity and permeability of a composite, which was previously predicted only theoretically, is obtained. The reason for the difference is considered to be the effect of non-ideal electrical contacts between neighboring inclusions. It is also experimentally shown that the measured permeability of the bulk material may differ from the retrieved one. The measured static permeability is 1400 and the retrieved one is 12. The reason for the discrepancy is the difference between the domain structures and demagnetizing fields of particles and bulk ferrite.

Predicting effective thermal conductivity of fibrous and particulate composite materials using convolutional neural network

Thermal insulation composite materials, such as aerogels and cellular foams, typically exhibit great performance such as low thermal conductivity and complex microstructures at the nanometer or micrometer scale. However, traditional micromechanics-based methods like homogenization and finite element analysis may not accurately predict their effective thermal conductivity due to a limited understanding of microscopic heat transfer mechanisms and the vast amounts of multi-scale microstructural data. In this paper, the effective thermal conductivity of composite materials is predicted using a convolutional neural network (CNN). To model the microstructure of the composites, digital images are generated using the Quartet Structure Generation Set (QSGS) method and the Random Generation-Growth Method (RGGM). The Lattice Boltzmann Method (LBM) is then used to predict the effective thermal conductivities. The CNN model is trained and validated using the microstructural images as input data and the conductivities predicted by LBM as output data. Subsequently, Parametric studies are conducted to investigate the material characteristics, including volume fraction and microstructural anisotropy. Additionally, the CNN predictions are compared with the results of experiments, analytical models, and computational methods. Finally, the proposed CNN model is utilized to predict the thermal conductivity of materials with novel microstructures that are not included in the training set. By capturing the scattering characteristics of heterogeneous materials through artificial intelligence, the CNN model predicts thermal conductivity more efficiently than traditional methods. This highlights the potential of machine learning to advance materials science and accelerate development of materials with desired properties.

Hybrid influences of interphase and grain-size on material responses of CNT-reinforced metal matrix composites

In this investigation, a theoretical model is developed to consider the coupled influence of interphase and grain-size of metal on the nonlinear response of CNT-reinforced MMCs. A multiscale theoretical framework based on the energy-based effective strain method and the field fluctuation method is established. The second-order stress moment and dislocation density model are also adopted to predict the entire grain-size dependent stress-strain relations. The energy-based effective strain method is proposed to better exhibit the energy stored in the three-phase composites by replaced average-strain. The microstructure variables include volume fraction, moduli of interphase, geometrical size factor, aspect ratio of CNTs, and grain size in metal matrix. The accuracy of the present predictions is verified by some available experimental data. As a result, the proposed model can be used to define the mechanical behavior and make an optimum design of CNT reinforced MMCs as well as advanced engineering composites.

Numerical simulation of an electromagnetic squeezing hybrid nanofluid flow through permeable plates with sensor monitoring system

The primary aim of this study is to examine the effect of squeezing hybrid nanofluids copper and magnetite with water flow across a horizontal surface under the impact of magnetic and radiative effects, which has extensive applications in the field of biomedical engineering and nanotechnology. Additionally, a microcantilever sensor is placed between the horizontal surfaces to surveil the flow behaviors. The equations pertaining to momentum and energy are reconstructed into a set of ordinary differential equations (ODEs). These ODEs are subsequently solved through a numerical approach, wherein the bvp4c solver from MATLAB is utilized. This solver employs a collocation technique for the numerical solution. As a result, the solutions acquired for velocity and temperature are graphically displayed for different parameters, including volume fraction of nanoparticles, squeezing flow index parameter (b), magnetic parameter (M), permeable velocity parameter (f0), radiation parameter R, and Prandtl number (Pr). It has been observed that increasing the magnetic effect as well as the volume fraction of nanoparticles strengthens the flow effect. In contrast, increasing the squeezing and permeable velocity parameter impedes the flow. When there is an increase in a permeable velocity parameter, the temperature shoots up, and the cooling effect is spotted in the temperature profile, when the Prandtl number and magnetic and squeezing parameters are raised. This investigation upholds the significance of drag reduction, flow instabilities, fluid structure interactions, and heat transfer effectiveness by virtue of wall shear stress, squeezing flow index parameter, various hybrid nanofluids, and Nusselt number, respectively. A considerable comparative study has been made for the validation of current results.

A mean-field micromechanical incremental approach for brittle damage in particulate microstructures under monotonic loading, using a piecewise uniform damage field

In this work, a mean-field micromechanical approach is proposed to determine the effective behaviour of a microstructure where damage occurs in one phase. Our approach fits into the framework of generalised standard materials proposed by Germain et al. (1983) by defining an incremental potential in the spirit of Lahellec and Suquet (2007), made up of two potentials: the free energy and the dissipation, given in this work by Lorentz and Andrieux (2003). It results in the definition of an elastic nonlinear problem at each time increment but, due to the damage evolution, this incremental potential is non convex. The proposed incremental approach also deviates from Lahellec and Suquet (2007) by considering in the damaged phase two sub-phases characterised by two damage states at the beginning of each time step. Next, this elastic nonlinear problem is regularised by introducing a linear comparison composite whose features are optimised by taking inspiration from the Full Optimised Second Order approach of Ponte-Castañeda (2016). However, the reduction of the number of degrees of freedom of the problem is realised by considering an isotropic linear comparison medium.The abilities of the proposed approach are assessed through a particular case. The composite is made up of two elastic phases : the matrix and the inclusions. The inclusions are subjected to a monotonous increasing swelling while the boundary of the RVE is stress free. For this problem, the resulting solution is given by closed-form expressions. These analytical developments are then used to obtain the effective response of the composite whose dependency on physical parameters (volume fraction of inclusions, toughness of the matrix, elastic contrast ...) is then analysed. The analysis is essentially based on an energy balance between the relaxed stored elastic energy and the dissipated energy. Explicit expressions of the critical values of the unique loading parameter (swelling of the inclusions) related to the onset of damage and the failure of the matrix phase are also given. The theoretical effective response compares well with the results of full fields calculations.

Influence of trace rare earth elements on very high cycle fatigue behavior of hot rolled bearing steel

In this study, the effect of trace rare earth (RE) elements on the fatigue property of bearing steel in very high cycle fatigue regime was investigated. For this purpose, ultrasonic tension–compression fatigue tests were conducted on specimens extracted from hot rolled bearing steels with and without RE addition. Crack propagation behavior within the characteristic “fish-eye” (FiE) area and the non-inclusion induced fatigue failure were analyzed after the fatigue test. Results showed that the addition of trace RE can modify inclusions to varying degrees. Further, it significantly reduces the volume fraction of inclusions as well as the number of large inclusions. Consequently, the fatigue life of bearing steel is more than doubled based on the 10% and 50% failure probabilities. During the propagation of cracks within the FiE area, the microstructure and intrinsic defects in bearing steel exhibit high sensitivity to the instantaneous driving force for crack propagation. The discontinuity in their size may result in abnormally slow crack propagation. For the non-inclusion induced fatigue failure of bearing steel, microcracks preferentially form at the junction of lath interfaces or at the enclosed area of martensite laths/plates which tend to grow along the interfaces perpendicular to the loading direction.

Pyroelectric effect and piezoelectric properties of composites based on ferroelectric copolymer of poly(vinylidene fluoride-trifluoroethylene) and deuterated triglycine sulfate

In this work, composite films of a copolymer of vinylidene fluoride with trifluoroethylene P(VDF-TrFE) comprising microcrystals of deuterated triglycine sulfate (DTGS) were produced. The pyroelectric properties of the composite samples were studied by the dynamic method. Pyroelectric measurements indicated an extreme dependence of the pyroelectric coefficient on the concentration of DTGS inclusions in the composite. Piezoelectric modules were macroscopically measured in static mode. The measured piezoelectric moduli d 31 and d 33 show ambiguous dependences on the volume fraction of DTGS inclusions.

Numerical estimation via remeshing and analytical modeling of nonlinear elastic composites comprising a large volume fraction of randomly distributed spherical particles or voids

We investigate numerically via finite element (FE) simulations and analytically the nonlinear behavior of a soft matrix comprising a large volume fraction (up to 55%) of monodisperse spherical inclusions, which can be either rigid particles or voids. To address the issue of severe mesh distortion at large strains, we employ a successive remeshing and solution mapping technique that allows us to achieve a large macroscopic deformation, with the maximum attained stretch being at least two to three times when compared to that without remeshing. A general algorithm allowing to read complex arbitrary particle geometries is proposed and implemented allowing to remesh a finitely strained domain with randomly distributed inclusions of arbitrary shape. The present simulation results for a neo-Hookean elastic matrix filled with rigid particles show that the nonlinear stress–stretch uniaxial tension response can be well approximated by a neo-Hookean material with an effective shear modulus that depends on the volume fraction of the inclusions. Additionally, a study of the number of particles demonstrates that sixty four monodisperse spheres is a good compromise to reach accurate results for large deformations and maintain a reasonable CPU-time. The FE data serve as a powerful assessment tool for analytical homogenization models. Newly developed and existing models for small and large strains are proposed and assessed, respectively, for both rigid particles and voids. These results fill the gap for large volume fractions of inclusions and serve as a reference for the homogenization of the microstructures of interest.

An Optimization Framework for Enhancing Cycle Life of Composite Positive Electrodes in Lithium-Ion Batteries via Composition Ratio Optimization

Lithium-ion batteries still require improvement, and design optimization is an important method that can improve battery performance. This study proposes a novel optimization framework to maximize the cycle life of the positive composite electrode by optimizing the composition ratio of active material (AM), conductive additives, and binder. As the composition of the constituents affects the electrochemical and degradation parameters associated with cell performance and side reactions, the relationship between the AM, conductive additives, and binder material was considered. A fundamental physics-based electrochemical cell model with side reactions was developed to predict the performance and cycle life of a battery. The developed optimization framework was used to maximize battery performances, including volume fraction, capacity, discharge energy (DE), and accumulated discharge energy (ADE). The obtained results verified that the maximum values of the aforementioned features continuously changed with different composition ratios and cycle numbers. Although the maximum difference in capacity or discharge energy changed depending on the sample compositions, the differences between maximum and minimum capacities were up to 22%; this was significant only by changing the composition of the composite electrode. The developed optimization framework can effectively maximize the cycle life and be easily incorporated into real-time applications.

Slurry preparation for semi-solid metal direct writing by a novel approach of mixed powder remelting

Extrusion-based metal direct writing is a promising metal additive manufacturing technology due to its high efficiency and low cost. However, fabricating parts with high integrity and complex geometry remains challenging. The most critical factor is the unavailable of semi-solid slurries with uniform and nearly spherical solid particles, resulting in uncontrollable extrusion and printing. Currently, mixed powder remelting (MPR) is reported to preset the features of the solid phases, including volume fraction, morphology, and size distribution. Specifically, the semi-solid slurries of hypoeutectic AlSi alloys were obtained by preheating and shearing the mixed powder composed of eutectic AlSi alloy powder and pure aluminum powder. Their microstructural characteristics and rheological behavior were investigated, demonstrating the microstructure tailoring (controllable solid fraction and size distribution, high shape factor of about 0.9) and the reduced viscosity fluctuation by a factor of 7 compared with traditional processes. MPR shows unparalleled advantages for further engineering applications of metal direct writing.