Effective Young Modulus Research Articles

Wave propagation in rotating thin‐walled porous blades reinforced with graphene platelets

AbstractIn this study, wave propagation in functionally graded (FG) graphene reinforced porous nanocomposite rotating thin‐walled blades is examined. The porous matrix shows both uniform and nonuniform distribution of graphene platelet alongside the thickness direction. The rule of mixture is used to obtain the effective Young's modulus, based on the Halpin–Tsai micromechanics model along with the mass density as well as Poisson's ratio of the porous blades. Applying the theory of first‐order shear deformation, it is possible to derive the governing motion equations based on Hamilton's principle whose analytical solution results in obtaining wave frequency as well as phase velocity of the rotating thin‐walled porous blades. According to the theory of thin‐walled Timoshenko beam, both lagging and flapping vibration modes have been considered. The impacts of number of layers, graphene platelets together with porous distribution patterns, weight fraction of graphene platelets, geometry of graphene platelets nanofillers as well as porosity coefficient on the wave propagation behaviors of the rotating thin‐walled porous blades are examined for the first time. The results show that the symmetric distribution of porosity with graphene platelets pattern A can predict the highest wave frequency and phase velocity for the composite blades.

Finite element analysis of the influence of porosity and pore geometry on mechanical properties of orthopaedic scaffolds

PurposeScaffolds play a key role in regenerative medicine in the repair of injuries, defects and cancerous changes in long bones. For this reason, scaffolds should meet certain mechanobiological requirements, such as adequate porosity and pore geometry to ensure appropriate osteointegration as well as load transfer. Taking into account the most frequently used cell units, this study attempted to evaluate the porous structures of orthopaedic scaffolds in terms of their strength parameters. Materials and methodsFour pore geometries were selected for analyses: sphere, octagonal prism, cube and triangular prism, all with porosities of 10% up to 60%. Three different material properties were considered: Ti6Al4V alloy, CoCr alloy, 316 L steel. Strength compression simulations were carried out on 144 models, 72 structures of cell units with dimensions of 4 × 4 × 4 mm and 72 structures of scaffolds with a diameter of 16 mm and a height of 15 mm. Effective Young's modulus, as well as 0.2%, offset effective yield strength was estimated. ResultsResearch has shown that scaffolds with bone-like strength properties should be made of Ti6Al4V alloy. The value of 40% turned out to be of the best porosity. The remaining porosities showed much lower or much higher strength parameters and were significantly different from the properties of the bones. ConclusionsThe obtained data allow to indicate the most functional porous structure with Young's modulus similar to that possesses by core bone, while maintaining mechanical strength, allowing for its appropriate use in orthopaedic regenerative medicine.

Elastic stress transfer model and homogenized constitutive equation for the multi-phase geomaterials

Multi-phase geomaterials can be classified as the particulate composites composed of finer matrix and dispersed inclusions. With the extremely nonuniform stress and strain field, prediction of the overall mechanical response from the known mechanical properties and mixed proportion of constituents is a challenging task for multi-phase geomaterials. In this paper, using a concentric composite cylinder as the equivalent representative volume element (RVE), the analytical solutions of stress transfer model are derived from the modified shear-lag analysis. Through the mechanical homogenization of internal stress/strain field, a constitutive equation has been established in the elastic regime, containing a closed-form solution (S-L method) for prediction of effective Young's modulus (EHom). By the comparison with classical models, numerical simulations and experimental results, the homogenized constitutive equation (EHom) has been validated. Meanwhile, parametric studies of proposed solutions have been conducted to discuss the effect of meso-mechanical variables (e.g., mechanical contrast and volume proportion of constituents) on the stress transfer mechanism and the overall mechanical response, providing the useful insights and explanations to previous studies.

Multi-objective Shape Optimization of Bone Scaffolds: Enhancement of Mechanical Properties and Permeability

Porous scaffolds have recently attracted attention in bone tissue engineering. The implanted scaffolds are supposed to satisfy the mechanical and biological requirements. In this study, two porous structures named MFCC-1 (modified face centered cubic-1) and MFCC-2 (modified face centered cubic-2) are introduced. The proposed porous architectures are evaluated, optimized, and tested to enhance mechanical and biological properties. The geometric parameters of the scaffolds with porosities ranging from 70% to 90% are optimized to find a compromise between the effective Young's modulus and permeability, as well as satisfying the pore size and specific surface area requirements. To optimize the effective Young's modulus and permeability, we integrated a mathematical formulation, finite element analysis, and computational fluid dynamics simulations. For validation, the optimized scaffolds were 3D-printed, tested, and compared with two different orthogonal cylindrical struts (OCS) scaffold architectures. The MFCC designs are preferred to the generic OCS scaffolds from various perspectives: a) the MFCC architecture allows scaffold designs with porosities up to 96%; b) the very porous architecture of MFCC scaffolds allows achieving high permeabilities, which could potentially improve the cell diffusion; c) despite having a higher porosity compared to the OCS scaffolds, MFCC scaffolds improve mechanical performance regarding Young's modulus, stress concentration, and apparent yield strength; d) the proposed structures with different porosities are able to cover all the range of permeability for the human trabecular bones. The optimized MFCC designs have simple architectures and can be easily fabricated and used to improve the quality of load-bearing orthopedic scaffolds. Statement of significancePorous scaffolds are increasingly being studied to repair large bone defects. A scaffold is supposed to withstand mechanical loads and provide an appropriate environment for bone cell growth after implantation. These mechanical and biological requirements are usually contradicting; improving the mechanical performance would require a reduction in porosity and a lower porosity is likely to reduce the biological performance of the scaffold. Various studies have shown that the mechanical and biological performance of bone scaffolds can be improved by internal architecture modification. In this study, we propose two scaffold architectures named MFCC-1 and MFCC-2 and provide an optimization framework to simultaneously optimize their stiffness and permeability to improve their mechanical and biological performances.

Modeling of the Pore Shape Effect on the Effective Young's Modulus of Lotus-Type Porous Materials by a Numerical Homogenization Technique

Lotus-type porous materials (LTPMs) are considered as a new category of engineering materials. They are porous materials characterized by long, straight, unidirectional cylindrical pores, and are obtained via unidirectional solidification from a melt under hydrogen and argon atmospheres. The anisotropic pore morphology of lotus-type materials results in the anisotropy of their mechanical and physical properties. This study aims at investigating the effect of cross-sectional pore shapes on the effective Young's modulus (EYM) of LTPMs. The representative volume element-based finite element homogenization method was used to compute the effective bulk and shear moduli. Subsequently, the EYM was deduced from the effective bulk and shear moduli. The numerical results of the circular pores were validated by comparing them with experimental results. Because the results indicated that the EYM is extremely sensitive to the variation in the pore shapes, a formula for estimating the EYM of LTPMs by considering the pore shapes was developed and validated.

Mechanical properties of glassy polymer nanocomposites via atomistic and continuum models: The role of interphases

The mechanical properties of glassy polymer nanocomposites (PNCs) are investigated via a new hierarchical computational methodology, which combines atomistic molecular dynamics (MD) simulations and homogenization approaches. The homogenization methodology is based on a systematic nano/micro/macro coupling between detailed atomistic MD simulations and a variational approach through the Hill–Mandel lemma. The proposed methodology is applied in model glassy polybutadiene/silica nanocomposites for different nanoparticle (NP) volume fractions. Initially, using MD simulations, the polymer/NP interphase in PNCs is directly examined by probing the density distribution and the stress profile at equilibrium. By using a continuum mechanics based approach, we can compute effective deformation gradients for each atom, allowing us to probe the distribution of the (local) stress and strain fields in the atomistic model. With this new approach, the effective Young modulus and the Poisson ratio of the polymer/NP interphases are directly calculated, exhibiting a higher rigidity compared to the polymer matrix. In the last part of the proposed approach, the mechanical properties at the interphases and the polymer are used together with the homogenization approach to develop a continuum model for predicting the mechanical properties of the PNCs, which are found to be in very good agreement with the effective mechanical properties calculated through atomistic MD simulations.

Publisher's Note: “Low-strain effective Young's modulus model and validation for multi-layer vocal fold-based silicone specimens with inclusions” [J. Appl. Phys. 131, 054701 (2022)

Publisher's Note: “Low-strain effective Young's modulus model and validation for multi-layer vocal fold-based silicone specimens with inclusions” [J. Appl. Phys. 131, 054701 (2022)

Cylindrical compressible liquid inclusion with surface effects

Liquid-filled microchannels are common in biological tissues, such as blood capillaries and neuronal axons, which may often be regarded as cylindrical compressible liquid inclusions embedded in an infinite elastic matrix. How surface effects influence the elastic field and effective mechanical properties of such liquid inclusions remain elusive, especially when the inclusion size is at micro level wherein surface tension plays a significant role. We present first a theoretical model to analyze the elastic field of a cylindrical compressible liquid inclusion, with surface effects duly accounted for. We then use the solutions of our model, together with the Eshelby approach, to estimate the effective mechanical properties of a composite containing sparsely distributed cylindrical liquid inclusions. Different from previous studies, our model accounts for the nonlinear dependence of the normal vector and curvature of a liquid-solid surface upon surface deformation, achieved by expressing both as first order functions of surface displacement. We then linearize the deformation-induced surface curvature to simplify the problem and get the solution using linearized curvature. Predictions of our model demonstrate that surface effects prevent deformation of the liquid inclusion and increase stress concentration around the inclusion. Further, as the surface energy is increased, the effective Young's modulus of the two-phase composite first increases and then decreases, and the transition point is related to the bulk modulus of liquid; when the surface energy becomes sufficiently large, the effective Poisson ratio becomes negative. These results are useful for understanding and exploring the mechanical behaviors of a wide range of liquid-filled porous biological materials which contain distributed cylindrical pores, e.g., blood vessels, neuronal axons, dentinal tubules and hydrogel pores .

On the free vibrations of FG-GPLRC folded plates using GDQE procedure

The present study theoretically investigates the performance of the generalized differential quadrature element (GDQE) method to obtain the free vibration response of folded plates. The considered folded plate is assumed as a laminated functionally graded composite augmented with graphene platelets (GPLs). This kind of composite is identified as the FG-GPLRC structure. Each lamina is strengthened with randomly oriented and uniformly distributed GPLs. The GPL weight fraction of each layer changes based on several functionally graded (FG) models. The effective Young modulus of each ply is calculated utilizing a second-order correlation homogenization technique called Halpin–Tsai. Based on the GDQE method, the folded plate is split into two plate elements. The motion equations of each element are derived based on the first-order shear deformation theory and utilizing Hamilton’s principle. Equations of motion for each element are solved by employing the conventional GDQ method. After that, the suitable continuity conditions are applied to the common boundaries of the two elements. In this research, the influences of plate dimensions, crank angle, FG patterns, boundary conditions, and GPL weight fraction on the natural frequencies and corresponding mode shapes are examined.

Wave propagation of the viscoelastic FG-GPLRPC microplate via sinusoidal shear deformation theory (SSDT) and modified coupled stress theory (MCST)

This is the first research on the wave propagation analysis of the viscoelastic functionally graded graphene platelet reinforced piezoelectric composite (FG-GPLRPC) microplate exposed to the electromagnetic field. Uniform distribution (UD) and two types of functionally graded distribution patterns of GPL reinforcements are considered. Kelvin Voigt’s model is engaged in providing the realistic material property of the viscoelastic system. The viscoelastic FG-GPLRPC microplate is embedded in the orthotropic Visco Pasternak foundation. Halpin–Tsai micromechanics model and the rule of mixture (ROM) is applied to formulate the effective Young's modulus, density, and Poisson's ratio of viscoelastic FG-GPLRPC microplate. Governing equations are derived using nonlocal modified coupled stress theory (MCST) and sinusoidal shear deformation theory (SSDT). After validating the results, the influence of different parameters, including three pattern types of functionally graded distributions of GPLs, the weight fraction of GPLs, various foundation models, magnetic field, the geometrical aspect ratio of the system, and damping coefficient, are carried out. The results illustrate that adding 1% weight fraction of GPLs leads to an increment of 28.57% in the dimensionless phase velocity of the structure. It is hoped that the results of this study will be useful in improving the design of smart systems.

Exploring the mechanical properties of nanometer-thick elastic films through micro-drop impinging on large-area suspended graphene.

In this work, the dependence of effective Young's modulus on the thickness of suspended graphene was confirmed through a drop impingement method. Large area suspended graphene (LSG) layers with a diameter of up to 400 μm and a nanometer thickness were prepared through transferring chemical vapor deposition grown graphene from copper substrates. 4, 8, and 12-layer LSG samples were found to be crumpled yet defect-free. The mechanical properties of LSG were first studied by observing its interaction with impinging droplets from an ink-jet nozzle. First, the effective Young's modulus was calculated by fitting the instant deformation captured by high speed photography within microseconds. Next, droplets deposited on LSG caused deformation and generated wrinkles and the effective Young's modulus was calculated from the number of wrinkles. The above methods yielded effective Young's modulus values ranging from 0.3 to 3.4 TPa. The results from these methods all indicated that the effective Young's modulus increases with the decreasing thickness or size of suspended graphene layers. Moreover, the crumpled LSG yields higher effective Young's modulus than ideal flat graphene. These comprehensive results from complementary methodologies with precise LSG thickness control down to the nanometer scale provide good evidence to resolve the debate on the thickness dependence of mechanical strength for LSG.

Elastic and plastic mechanical properties of nanoparticle-based silica aerogels and xerogels

This paper reports and analyzes, for the first time, the effective Young's modulus and hardness of nanoparticle-based silica aerogels and xerogels with porosity ranging from 46 to 81%. Pure silica aerogel and xerogel monoliths were synthesized by (i) gelation of aqueous suspensions of silica nanoparticles on omniphobic substrates (PTFE or perfluorocarbon liquids), (ii) aging, (iii) drying at ambient temperature and pressure, and (iv) calcination. The aging and calcination conditions were varied to elucidate their effect on the mechanical properties of the monoliths. Both the effective Young's modulus and the hardness of the mesoporous slabs were measured by nanoindentation and were found to obey a power law as a function of the effective density. No effect of the synthetic conditions or structural parameters other than porosity were observed. Interestingly, the effective hardness was linearly proportional to the effective Young's modulus. The elastic properties of the present nanoparticle-based materials were compared with those of the molecular precursor-based silica aerogels and xerogels reported in the literature. A single relationship was proposed that can be used to estimate the effective Young's modulus of nanoparticle-based and molecular precursor-based silica aerogels and xerogels with porosity between 0 and 98% and Young's modulus between ∼10−4 and 70 GPa. Deposition of an alumina coating was also demonstrated as a way to increase the hardness of these mesoporous monoliths by a factor 2–13 for porosity of 40–73%. The experimental results and the accompanying analysis broaden the understanding of structure-property relationships in mesoporous silica and will help in the design and fabrication of mesoporous silica components.

Mori-Tanaka-based statistical methodology to compute the effective Young modulus of polymer matrix nano-composites considering the experimental quantification of nanotubes dispersion and alignment degree

This paper presents a Mori-Tanaka-based statistical methodology to predict the effective Young modulus of carbon nanotubes (CNTs)-reinforced composites considering three variables: weight content, reinforcement dispersion and orientation. Last two variables are quantified by two parameters, namely, free-path distance between nano-reinforcements and orientation angle regarding the loading direction. To validate the present methodology, samples of multi-walled CNTs (MWCNTs)-reinforced polyvinyl alcohol (PVA)-matrix composite were manufactured by mixing solution. The MWCNT/PVA Young modulus was measured by nano-indentation, while the MWCNTs Young modulus was quantified by micro-Raman spectroscopy. Both stretched and unstretched composite specimens were fabricated. Transmission electron microscopy (TEM) and in-plane image analysis were used to obtain fitting coefficients of log-normal frequency distribution functions for the free-path distance and orientation angle. It was evidenced that numerical results fit well to measured values of effective Young modulus of MWCNTs and MWCNT/PVA, with exception of some particular cases where significant differences were found. Microstructural heterogeneities, cluster formation, polymer chains alignment, errors associated with the dispersion, orientation and mechanical characterization procedures, as well as idealization and statistical errors, were identified as possible causes of these differences. Finally, using the proposed methodology and the dispersion and orientation distribution functions experimentally obtained, the effective Young modulus is estimated for three kinds of thermoplastic matrices (polyvinyl alcohol, polyethylene ketone, and ultra-high molecular weight polyethylene) with different kinds of nanotubes (single wall, double wall, and multi-walled), at different weight contents, finding the superior mechanical performance for double-walled CNTs-reinforced composites and the lower one for multi-walled CNTs-reinforced ones.

Correlation of cell mechanics with the resistance to malignant transformation in naked mole rat fibroblasts.

Naked mole rats (NMRs) demonstrate exceptional longevity and resistance to cancer. Using a biochemical approach, it was previously shown that the treatment of mouse fibroblast cells with RasV12 oncogene and SV40 Large T antigen (viral oncoprotein) led to malignant transformations of cells. In contrast, NMR fibroblasts were resistant to malignant transformations upon this treatment. Here we demonstrate that atomic force microscopy (AFM) can provide information which is in agreement with the above finding, and further, adds unique information about the physical properties of cells that is impossible to obtain by other existing techniques. AFM indentation data were collected from individual cells and subsequently processed through the brush model to obtain information about the mechanics of the cell body (absolute values of the effective Young's moduli). Furthermore, information about the physical properties of the pericellular layer surrounding the cells was obtained. We found a statistically significant decrease in the rigidity of mouse cells after the treatment, whereas there was no significant change found in the rigidity of NMR cells upon the treatment. We also found that the treatment caused a substantial increase in a long part of the pericellular layer in NMR cells only (the long brush was defined as having a size of >10 microns). The mouse cells and smaller brush did not show statistically significant changes upon treatment. The observed change in cell mechanics is in agreement with the frequently observed decrease in cell rigidity during progression towards cancer. The change in the pericellular layer due to the malignant transformation of fibroblast cells has practically not been studied, though it was shown that the removal of part of the pericellular layer of NMR fibroblasts made the cells susceptible to malignant transformation. Although it is plausible to speculate that the observed increase in the long part of the brush layer of NMR cells might help cells to resist malignant transformations, the significance of the observed change in the pericellular layer is yet to be understood. As of now, we can conclude that changes in cell mechanics might be used as an indication of the resistance of NMR cells to malignant transformations.

Finite Element Modelling of Prestressed Concrete Piles in Soft Soils, Case Study: Northern Jakarta, Indonesia

Jakarta is faced with limited land resources due to its position as the capital city of Indonesia. Therefore, numerous high-rise buildings are being constructed to solve this problem and provide accommodations for a large number of Jakarta residents. Studies have shown that prestressed concrete piles (spun piles) are commonly used as the foundations of high-rise buildings in metropolitan cities across Indonesia, especially in the Northern Jakarta Coastal area, which is predominant with deep soft soils deposit. To further assess and verify the ultimate capacity of the pile, a static loading test was conducted. However, not all results from the field test produced ideal, accurate, precise, and reliable load-settlement curve (until failure) results. Therefore, this study aims to determine the soil properties for the analysis of prestressed concrete spun piles with a diameter of 600 mm in the Northern Jakarta coastal area based on the standard penetration test values (SPT-N). It is a case study of a well-documented static pile load test using the kentledge system. Back analyses were performed by the finite element method to obtain the extrapolated load-settlement curve. Furthermore, the effect of interface strength between pile and soil on the load-settlement curve was also investigated. The results showed that a reduction of interface strength leads to a smaller load–settlement curve. In addition, several geotechnical engineering parameters of soil, such as the undrained shear strength and effective young's modulus, were established using data from an in-situ soil site investigation and empirical correlations with SPT-N.

Micro-cantilever beam experiments and modeling in porous polycrystalline UO2

Understanding the impact of microstructure on the thermo-mechanical behavior of oxide nuclear fuels is vital to predicting their performance through multiscale models . Evaluating the mechanical properties at the sub-grain length scale is key to developing these multiscale models. In this work, 3D finite element (FE) models were constructed to simulate the micrometer-scale bending of micro-cantilever beams fabricated using porous polycrystalline uranium dioxide (UO 2 ) and tested at room temperature. The results showed that the porosity and elastic anisotropy of individual grains can play a significant role in determining the effective mechanical properties of the material deduced from the tests. Specifically, the porosity had a non-negligible effect, given that the pore size was of the same order of magnitude as the dimensions of the micro-beams. Correlations between load-deflection data, pore location, and elastic properties (effective Young's modulus) were investigated using UO 2 micro-beam FE models, where pore clusters were included and placed at different locations along the length of the beam. Results indicated that the presence of pore clusters near the substrate, i.e., the clamp of the micro-cantilever beam, has the strongest effect on the load-deflection behavior, with the porosity leading to a reduction of stiffness that is the largest for any location of the pore clusters. Furthermore, it was also found that pore clusters located towards the middle of the span and close to the end of the beam have a comparatively small effect on the load-deflection behavior. Therefore, it is concluded that accurate estimates of Young's modulus can be obtained from micro-cantilever experiments after accounting for porosity on the one third of the beam length close to the clamp. This, in turn, provides an avenue to improve microscale experiments and their analysis in porous, anisotropic elastic materials.

How Does In Situ Stress Rotate Within a Fault Zone? Insights From Explicit Modeling of the Frictional, Fractured Rock Mass

AbstractWe quantitatively investigate the spatial stress variations within the fault zone rock mass by explicitly incorporating macroscopic fractures into a 2D multilayer model. Based on elastic crack theory, we first derive a unified constitutive law for frictional fractures, featuring elastic and plastic shear deformation and shear‐induced dilatancy. To honor the varying degrees of damage across fault zones, the multilayer model is composed of varying densities of randomly oriented frictional fractures from layer to layer. Under the boundary conditions specific to fault zones, the global mechanical response of each layer is quantitatively related to the local fracture deformation. We show that the major principal stress always rotates toward a limiting angle of 45° with respect to the fault plane and that the differential stress invariantly decreases with increasing fracture density. Approaching the fault core, the mean stress can either increase or decrease, depending on whether the fault strikes at a high (>45°) or low (<45°) angle to the regional major principal stress. Accumulated damage also results in the decrease and increase of the effective Young's modulus and Poisson's ratio of the fractured rock mass, respectively. Both the fracture properties and pore pressure affect the stress variations by modulating the fracture‐associated deformation and the relative proportion of the elastic and plastic components. Our model illuminates the systematic variations of in situ stresses and effective elastic properties within the damage zone of a mature fault.

Quantifying Patient-Specific in vivo Coronary Plaque Material Properties for Accurate Stress/Strain Calculations: An IVUS-Based Multi-Patient Study.

Introduction: Mechanical forces are closely associated with plaque progression and rupture. Precise quantifications of biomechanical conditions using in vivo image-based computational models depend heavily on the accurate estimation of patient-specific plaque mechanical properties. Currently, mechanical experiments are commonly performed on ex vivo cardiovascular tissues to determine plaque material properties. Patient-specific in vivo coronary material properties are scarce in the existing literature.Methods: In vivo Cine intravascular ultrasound and virtual histology intravascular ultrasound (IVUS) slices were acquired at 20 plaque sites from 13 patients. A three-dimensional thin-slice structure-only model was constructed for each slice to obtain patient-specific in vivo material parameter values following an iterative scheme. Effective Young's modulus (YM) was calculated to indicate plaque stiffness for easy comparison purposes. IVUS-based 3D thin-slice models using in vivo and ex vivo material properties were constructed to investigate their impacts on plaque wall stress/strain (PWS/PWSn) calculations.Results: The average YM values in the axial and circumferential directions for the 20 plaque slices were 599.5 and 1,042.8 kPa, respectively, 36.1% lower than those from published ex vivo data. The YM values in the circumferential direction of the softest and stiffest plaques were 103.4 and 2,317.3 kPa, respectively. The relative difference of mean PWSn on lumen using the in vivo and ex vivo material properties could be as high as 431%, while the relative difference of mean PWS was much lower, about 3.07% on average.Conclusion: There is a large inter-patient and intra-patient variability in the in vivo plaque material properties. In vivo material properties have a great impact on plaque stress/strain calculations. In vivo plaque material properties have a greater impact on strain calculations. Large-scale-patient studies are needed to further verify our findings.

3D‐multilayer simulation of microstructure and mechanical properties of porous materials by selective sintering

AbstractThis work presents multilayer phase‐field simulation of selective sintering process and the calculation of effective mechanical properties and residual stress of the microstructure using the finite element method. The dependence of the effective properties and residual stress on the process parameters, such as beam power and scan speed, are analyzed. Significant partial melting of powders is observed for large beam power and low scan speed, which results in low porosity of the microstructure. Nonlinear relationship between the effective mechanical properties and process parameters is observed. The increasing rate of effective mechanical properties decreases with increasing beam power, while increases with decreasing scan speed. The dependence of effective Young's modulus and Poisson's ratio on porosity are well established using power law models. Stress concentrations are found at the necking region of powders and the intensity increases with the level of partial melting, which results in increasing residual stress in the microstructure. The numerical results reveal quantitatively the process‐microstructure‐property relation, which implies the feasibility of the subsequent data‐driven approach.

Out‐of‐Plane Tension of Thin Two‐Layered Plates of Cubic Crystals

Herein, the theoretical analysis of out‐of‐plane tension of a thin rectangular two‐layered plate of cubic crystals with the same orientation is provided. The dependences of effective Young's modulus and effective Poisson's ratio of the plate on Poisson's ratios of layers, the ratio of Young's moduli, and the thickness ratio are obtained. It is shown that when the ratios between Young's moduli and ratios between Poisson's ratios of the layers are equal, effective Young's modulus and effective Poisson's ratio coincide with Reuss'es means. The rules of mixtures are not fulfilled in the absence of equality of these ratios. In this case, effective Young's modulus can exceed not only Reuss'es mean but also Voigt's mean. It is demonstrated that effective Young's modulus can be larger than Young's moduli of both layers in two‐layered plates of nonauxetic−nonauxetic and auxetic−auxetic type. It is established that the behavior of effective Poisson's ratio of nonauxetic−nonauxetic plates can vary depending on the ratio of the layer thicknesses. At the same time, effective Poisson's ratio of plates from pairs of auxetics cannot be less than Poisson's ratios of both initial auxetic layers.