Elastic electronics are increasingly prevalent in information storage,smart sensing and health monitoring due to their softness,stretchability and portability.Wearable electronic devices should possess elasticity and ...Elastic electronics are increasingly prevalent in information storage,smart sensing and health monitoring due to their softness,stretchability and portability.Wearable electronic devices should possess elasticity and stretchability that align with biological tissues.Specifically,their materials should be capable of elastic strain up to 50–80%,while the devices themselves must maintain electric stability under strains that accommodate body movements[1].展开更多
The dynamic and static modulus of elasticity （MOE） between bluestained and non-bluestained lumber of Lodgepole pine were tested and analyzed by using three methods of Non-destructive testing （NDT）, Portable Ultras...The dynamic and static modulus of elasticity （MOE） between bluestained and non-bluestained lumber of Lodgepole pine were tested and analyzed by using three methods of Non-destructive testing （NDT）, Portable Ultrasonic Non-destructive Digital Indicating Testing （Pundit）, Metriguard and Fast Fourier Transform （FFT） and the normal bending method. Results showed that the dynamic and static MOE of bluestained wood were higher than those of non-bluestained wood. The significant differences in dynamic MOE and static MOE were found between bulestained and non-bluestained wood, of which, the difference in each of three dynamic MOE （Ep. the ultrasonic wave modulus of elasticity, Ems, the stress wave modulus of elasticity and El, the longitudinal wave modulus of elasticity） between bulestained and non-bluestained wood arrived at the 0.01 significance level, whereas that in the static MOE at the 0.05 significance level. The differences in MOE between bulestained and non-bluestained wood were induced by the variation between sapwood and heartwood and the different densities of bulestained and non-bluestained wood. The correlation between dynamic MOE and static MOE was statistically significant at the 0.01 significance level. Although the dynamic MOE values of Ep, Em, Er were significantly different, there exists a close relationship between them （arriving at the 0.01 correlation level）. Comparative analysis among the three techniques indicated that the accurateness of FFT was higher than that of Pundit and Metriguard. Effect of tree knots on MOE was also investigated. Result showed that the dynamic and static MOE gradually decreased with the increase of knot number, indicating that knot number had significant effect on MOE value.展开更多
The increasing integration of small-scale structures in engineering,particularly in Micro-Electro-Mechanical Systems(MEMS),necessitates advanced modeling approaches to accurately capture their complex mechanical behav...The increasing integration of small-scale structures in engineering,particularly in Micro-Electro-Mechanical Systems(MEMS),necessitates advanced modeling approaches to accurately capture their complex mechanical behavior.Classical continuum theories are inadequate at micro-and nanoscales,particularly concerning size effects,singularities,and phenomena like strain softening or phase transitions.This limitation follows from their lack of intrinsic length scale parameters,crucial for representingmicrostructural features.Theoretical and experimental findings emphasize the critical role of these parameters on small scales.This review thoroughly examines various strain gradient elasticity(SGE)theories commonly employed in literature to capture these size-dependent effects on the elastic response.Given the complexity arising from numerous SGE frameworks available in the literature,including first-and second-order gradient theories,we conduct a comprehensive and comparative analysis of common SGE models.This analysis highlights their unique physical interpretations and compares their effectiveness in modeling the size-dependent behavior of low-dimensional structures.A brief discussion on estimating additional material constants,such as intrinsic length scales,is also included to improve the practical relevance of SGE.Following this theoretical treatment,the review covers analytical and numerical methods for solving the associated higher-order governing differential equations.Finally,we present a detailed overview of strain gradient applications in multiscale andmultiphysics response of solids.Interesting research on exploring the relevance of SGE for reduced-order modeling of complex macrostructures,a universal multiphysics coupling in low-dimensional structures without being restricted to limited material symmetries(as in the case of microstructures),is also presented here for interested readers.Finally,we briefly discuss alternative nonlocal elasticity approaches(integral and integro-differential)for incorporating size effects,and conclude with some potential areas for future research on strain gradients.This review aims to provide a clear understanding of strain gradient theories and their broad applicability beyond classical elasticity.展开更多
Solids in nano-scales hold the promise to exhibit extreme strength and elasticity due to the absence of interior defects and the designability of micro-arrangements.A nano-scaled bulk sample can be produced by diamond...Solids in nano-scales hold the promise to exhibit extreme strength and elasticity due to the absence of interior defects and the designability of micro-arrangements.A nano-scaled bulk sample can be produced by diamond,ice,metallic twins,high entropy alloy(HEA),or cubic boron nitride(cBN).A loading stage capable of 4-DoF movements was designed and built to achieve multi-axial mechanical loading inside a transmission electronic microscope chamber with sub-nanometer loading precision.For single crystal diamond in the shape of nano-needles,we were able to achieve an extreme bending strength of 125 GPa at the tensile side,approaching the theoretical strength of diamond.For ice fibers of sub-micron radius,an extreme elastic strain of 10.9%was acquired,far exceeding the previous record of 0.3%for the elastic strain achievable by ice.For metallic twin specimens made by nano-welding,a shear strain as large as 364%was recorded parallel to the twin boundary.Cyclic shear loading aligned with the twin boundary would drive an up-and-down sweeping movement of the low-angle grain boundary,as composed by an array of dislocations.The sweep of the grain boundary effectively cleanses the lattice defects and creates a feasible scenario of unlimited cyclic endurance.For a HEA dog-bone specimen in nano-scale,an extreme elastic strain of about 10%was achieved.At this level of mechanical straining,stretch-induced melting for crystalline metals,as envisaged by Lindemann a century ago,was realized.For cBN crystals,a fracture path inclined to the stacking hexagon planes would result in a new failure mechanism of layered decohesion,triggered by the extremely large elastic strain(>7%)along the edge of the submicron-scaled specimen.These results indicate ample room for upgrading the mechanical behaviour of solids in nano-scales.展开更多
The identification of the traction acting on a portion of the surface of an anisotropic solid is very important in structural health monitoring and optimal design of structures. The traction can be determined using in...The identification of the traction acting on a portion of the surface of an anisotropic solid is very important in structural health monitoring and optimal design of structures. The traction can be determined using inverse methods in which displacement or strain measurements are taken at several points on the body. This paper presents an inverse method based on the method of fundamental solutions for the traction identification problem in two-dimensional anisotropic elasticity. The method of fundamental solutions is an efficient boundary-type meshless method widely used for analyzing various problems. Since the problem is linear, the sensitivity analysis is simply performed by solving the corresponding direct problem several times with different loads. The effects of important parameters such as the number of measurement data, the position of the measurement points, the amount of measurement error, and the type of measurement, i.e., displacement or strain, on the results are also investigated. The results obtained show that the presented inverse method is suitable for the problem of traction identification. It can be concluded from the results that the use of strain measurements in the inverse analysis leads to more accurate results than the use of displacement measurements. It is also found that measurement points closer to the boundary with unknown traction provide more reliable solutions. Additionally, it is found that increasing the number of measurement points increases the accuracy of the inverse solution. However, in cases with a large number of measurement points, further increasing the number of measurement data has little effect on the results.展开更多
The precise computation of nanoelectromechanical switches’(NEMS)multi-physical interactions requires advanced numerical models and is a crucial part of the development of micro-and nano-systems.This paper presents a ...The precise computation of nanoelectromechanical switches’(NEMS)multi-physical interactions requires advanced numerical models and is a crucial part of the development of micro-and nano-systems.This paper presents a novel compound numerical method to study the instability of a functionally graded(FG)beam-type NEMS,considering surface elasticity effects as stated by Gurtin-Murdoch theory in an Euler-Bernoulli beam.The presented method is based on a combination of the Method of Adjoints(MoA)together with the Bézier-based multistep technique.By utilizing the MoA,a boundary value problem(BVP)is turned into an initial value problem(IVP).The resulting IVP is then solved by employing a cost-efficient multi-step process.It is demonstrated that the mentioned method can arrive at a high level of accuracy.Furthermore,it is revealed that the stability of the presented methodology is far better than that of other common multi-step methods,such as Adams-Bashforth,particularly at higher step sizes.Finally,the effects of axially functionally graded(FG)properties on the pull-in phenomenon and the main design parameters of NEMS,including the detachment length,are inspected.It was shown that the main parameter of design is the modulus of elasticity of the material,as Silver(Ag),which had better mechanical properties,showed almost a 6%improvement compared to aluminum(Al).However,by applying the correct amount of material with sturdier surface parameters,such as Aluminum(Al),at certain points,the nanobeams’functionality can be improved even further by around 1.5%.展开更多
The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The ...The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The inner surface of the cavity was taken to be traction free and acted upon by a thermal shock to the surface. Laplace transforms techniques were used to obtain the solution by a direct approach.The inverse Laplace transforms was obtained numerically.The temperature,displacement and stress distributions are represented graphically.展开更多
The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so t...The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.展开更多
Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were appli...Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.展开更多
The crystalline and amorphous regions were alternately arranged in the hard elastic polypropylene(PP)films with row-nucleated lamellae.In this work,their structure evolution during stretching and recovery at room temp...The crystalline and amorphous regions were alternately arranged in the hard elastic polypropylene(PP)films with row-nucleated lamellae.In this work,their structure evolution during stretching and recovery at room temperature was followed and the elastic recovery mechanism was discussed by twice cyclic tensile experiment.During the first stretching to 100%,the lamellae crystals are parallel separated and the intercrystallite crazing is formed at the first yield point.Many nano-cavities within the intercrystallite crazing appear when the strain reaches 20%.The strain-hardening process accompanies with the lamellae long period increasing and the intercrystallite crazing enlargement.After the secondary yield point,the lamellae cluster is further separated and more nano-cavities appear.The first and second recovery processes are complete overlap.During recovery,firstly,the energy elasticity provided by nano-cavities surface tension drives the shrinkage of material,and then the entropy elasticity related to amorphous chain relaxation plays a leading role when the strain is smaller than the secondary yield point.The elastic recovery process of hard elastic material is the co-contribution of energy elasticity and entropy elasticity.This work gives a clearer recognition about the source of hard elastic property and the role of amorphous region in material's deformation.展开更多
The first purpose of this striking but difficult paper is to revisit the mathematical foundations of Elasticity (EL) and Electromagnetism (EM) by comparing the structure of these two theories and examining with detail...The first purpose of this striking but difficult paper is to revisit the mathematical foundations of Elasticity (EL) and Electromagnetism (EM) by comparing the structure of these two theories and examining with details their known couplings, in particular piezoelectricity and photoelasticity. Despite the strange Helmholtz and Mach-Lippmann analogies existing between them, no classical technique may provide a common setting. However, unexpected arguments discovered independently by the brothers E. and F. Cosserat in 1909 for EL and by H. Weyl in 1918 for EM are leading to construct a new differential sequence called Spencer sequence in the framework of the formal theory of Lie pseudo groups and to introduce it for the conformal group of space-time with 15 parameters. Then, all the previous explicit couplings can be deduced abstractly and one must just go to a laboratory in order to know about the coupling constants on which they are depending, like in the Hooke or Minkowski constitutive relations existing respectively and separately in EL or EM. We finally provide a new combined experimental and theoretical proof of the fact that any 1-form with value in the second order jets (elations) of the conformal group of space-time can be uniquely decomposed into the direct sum of the Ricci tensor and the electromagnetic field. This result questions the mathematical foundations of both General Relativity (GR) and Gauge Theory (GT). In particular, the Einstein operator (6 terms) must be thus replaced by the adjoint of the Ricci operator (4 terms only) in the study of gravitational waves.展开更多
In this paper, a method of transforming volume integrals to boundary integrals is given for complicated loadings such as a i(y)x i and b i(x)y i . In the present method the volume in...In this paper, a method of transforming volume integrals to boundary integrals is given for complicated loadings such as a i(y)x i and b i(x)y i . In the present method the volume integrals are approximately transformed to boundary integrals.展开更多
In this paper,the choice and parametrisation of finite deformation polyconvex isotropic hyperelastic models to describe the behaviour of a class of defect-free monocrystalline metal materials at the molecular level is...In this paper,the choice and parametrisation of finite deformation polyconvex isotropic hyperelastic models to describe the behaviour of a class of defect-free monocrystalline metal materials at the molecular level is examined.The article discusses some physical,mathematical and numerical demands which in our opinion should be fulfilled by elasticity models to be useful.A set of molecular numerical tests for aluminium and tungsten providing data for the fitting of a hyperelastic model was performed,and an algorithm for parametrisation is discussed.The proposed models with optimised parameters are superior to those used in non-linear mechanics of crystals.展开更多
A three-dimensional(3D)asymptotic theory is reformulated for the static analysis of simply-supported,isotropic and orthotropic single-layered nanoplates and graphene sheets(GSs),in which Eringen’s nonlocal elasticity...A three-dimensional(3D)asymptotic theory is reformulated for the static analysis of simply-supported,isotropic and orthotropic single-layered nanoplates and graphene sheets(GSs),in which Eringen’s nonlocal elasticity theory is used to capture the small length scale effect on the static behaviors of these.The perturbation method is used to expand the 3D nonlocal elasticity problems as a series of two-dimensional(2D)nonlocal plate problems,the governing equations of which for various order problems retain the same differential operators as those of the nonlocal classical plate theory(CST),although with different nonhomogeneous terms.Expanding the primary field variables of each order as the double Fourier series functions in the in-plane directions,we can obtain the Navier solutions of the leading-order problem,and the higher-order modifications can then be determined in a hierarchic and consistent manner.Some benchmark solutions for the static analysis of isotropic and orthotropic nanoplates and GSs subjected to sinusoidally and uniformly distributed loads are given to demonstrate the performance of the 3D nonlocal asymptotic theory.展开更多
Non-local plane elasticity problems are discussed in the context of Λ-fractional linear elasticity theory. Adapting the Λ-fractional derivative along with the Λ-fractional space, where geometry and mechanics are va...Non-local plane elasticity problems are discussed in the context of Λ-fractional linear elasticity theory. Adapting the Λ-fractional derivative along with the Λ-fractional space, where geometry and mechanics are valid in the conventional way, non-local plane elasticity problems are solved with the help of biharmonic functions. Then, the results are transferred into the initial plane.Applications are presented to homogeneous and the fractional beam bending problem.展开更多
The reflection and transmission properties of thermo-elastic waves at five possible interfaces between two different strain gradient thermo-elastic solids are investigated based on the generalized thermo-elastic theor...The reflection and transmission properties of thermo-elastic waves at five possible interfaces between two different strain gradient thermo-elastic solids are investigated based on the generalized thermo-elastic theory without energy dissipation （the GN theory）. First, the function of free energy density is postulated and the constitutive relations are defined. Then, the temperature field and the displacement field are obtained from the motion equation in the form of displacement and the thermal transport equation without energy dissipation in the strain gradient thermo-elastic solid. Finally, the five types of thermo-elastic interracial conditions are used to calculate the amplitude ratios of the reflection and transmission waves with respect to the incident wave. Further, the reflection and transmission coefficients in terms of energy flux ratio are calculated and the numerical results are validated by the energy conservation along the normal direction. It is found that there are five types of dispersive waves, namely the coupled longitudinal wave （the CP wave）, the coupled thermal wave （the CT wave）, the shear wave, and two evanescent waves （the coupled SP wave and SS wave）, that become the surface waves at an interface. The mechanical interfacial conditions mainly influence the coupled CP waves, SV waves, and surface waves, while the thermal interracial conditions mainly influence the coupled CT waves.展开更多
Rotation is antisymmetric and therefore is not a coherent element of the classical elastic theory, which is characterized by symmetry. A new theory of linear elasticity is developed from the concept of asymmetric stra...Rotation is antisymmetric and therefore is not a coherent element of the classical elastic theory, which is characterized by symmetry. A new theory of linear elasticity is developed from the concept of asymmetric strain, which is defined as the transpose of the deformation gradient tensor to involve rotation as well as symmetric strain. The new theory basically differs from the prevailing micropolar theory or couple stress theory in that it maintains the same basis as the classical theory of linear elasticity and does not need extra concepts, such as “microrotation” and “couple stresses”. The constitutive relation of the new theory, the three-parameter Hooke’s law, comes from the theorem about isotropic asymmetric linear elastic materials. Concise differential equations of translational motion are derived consequently giving the same velocity formula for P-wave and a different one for S-wave. Differential equations of rotational motion are derived with the introduction of spin, which has an intrinsic connection with rotation. According to the new theory, S-wave essentially has rotation as large as deviatoric strain and should be referred to as “shear wave” in the context of asymmetric strain. There are nine partial differential equations for the deformation harmony condition in the new theory;these are given with the first spatial differentiations of asymmetric strain. Formulas for rotation energy, in addition to those for (symmetric) strain energy, are derived to form a complete set of formulas for the total mechanical energy.展开更多
In the present paper, the spectrums of off-diagonal infinite-dimensional Hamiltonian operators are studied. At first, we prove that the spectrum, the continuous-spectrum, and the union of the point-spectrum and residu...In the present paper, the spectrums of off-diagonal infinite-dimensional Hamiltonian operators are studied. At first, we prove that the spectrum, the continuous-spectrum, and the union of the point-spectrum and residual- spectrum of the operators are symmetric with respect to real axis and imaginary axis. Then for the purpose of reducing the dimension of the studied problems, the spectrums of the operators are expressed by the spectrums of the product of two self-adjoint operators in state spac,3. At last, the above-mentioned results are applied to plane elasticity problems, which shows the practicability of the results.展开更多
The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value problem of planar linear elasticity. The optimal error est...The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value problem of planar linear elasticity. The optimal error estimates are obtained by using some novel approaches and techniques. The method proposed in this article is robust in the sense that the convergence estimates in the energy and L^2-norms are independent-of the Lame parameter λ.展开更多
Uniaxial Compressive Strength (UCS) and modulus of elasticity (E) are the most important rock parameters required and determined for rock mechanical studies in most civil and mining projects. In this study, two mathem...Uniaxial Compressive Strength (UCS) and modulus of elasticity (E) are the most important rock parameters required and determined for rock mechanical studies in most civil and mining projects. In this study, two mathematical methods, regression analysis and Artificial Neural Networks (ANNs), were used to predict the uniaxial compressive strength and modulus of elasticity. The P-wave velocity, the point load index, the Schmidt hammer rebound number and porosity were used as inputs for both meth-ods. The regression equations show that the relationship between P-wave velocity, point load index, Schmidt hammer rebound number and the porosity input sets with uniaxial compressive strength and modulus of elasticity under conditions of linear rela-tions obtained coefficients of determination of (R2) of 0.64 and 0.56, respectively. ANNs were used to improve the regression re-sults. The generalized regression and feed forward neural networks with two outputs (UCS and E) improved the coefficients of determination to more acceptable levels of 0.86 and 0.92 for UCS and to 0.77 and 0.82 for E. The results show that the proposed ANN methods could be applied as a new acceptable method for the prediction of uniaxial compressive strength and modulus of elasticity of intact rocks.展开更多
基金supported by generous grants from the Natural Science Foundation of Zhejiang Province(LR24E030003)Zhejiang Province Qianjiang Talent Program(ZJ-QJRC-2020-32).
文摘Elastic electronics are increasingly prevalent in information storage,smart sensing and health monitoring due to their softness,stretchability and portability.Wearable electronic devices should possess elasticity and stretchability that align with biological tissues.Specifically,their materials should be capable of elastic strain up to 50–80%,while the devices themselves must maintain electric stability under strains that accommodate body movements[1].
基金This paper was supported by "Wood-inorganic Res-toration Material" in "Technique Introduction and Innovation of Bio-macromolecule New Material" of Introducing Overseas Advanced Forest Technology Innovation Program of China ("948" Innovation Pro-ject, Number: 2006-4-C03)
文摘The dynamic and static modulus of elasticity （MOE） between bluestained and non-bluestained lumber of Lodgepole pine were tested and analyzed by using three methods of Non-destructive testing （NDT）, Portable Ultrasonic Non-destructive Digital Indicating Testing （Pundit）, Metriguard and Fast Fourier Transform （FFT） and the normal bending method. Results showed that the dynamic and static MOE of bluestained wood were higher than those of non-bluestained wood. The significant differences in dynamic MOE and static MOE were found between bulestained and non-bluestained wood, of which, the difference in each of three dynamic MOE （Ep. the ultrasonic wave modulus of elasticity, Ems, the stress wave modulus of elasticity and El, the longitudinal wave modulus of elasticity） between bulestained and non-bluestained wood arrived at the 0.01 significance level, whereas that in the static MOE at the 0.05 significance level. The differences in MOE between bulestained and non-bluestained wood were induced by the variation between sapwood and heartwood and the different densities of bulestained and non-bluestained wood. The correlation between dynamic MOE and static MOE was statistically significant at the 0.01 significance level. Although the dynamic MOE values of Ep, Em, Er were significantly different, there exists a close relationship between them （arriving at the 0.01 correlation level）. Comparative analysis among the three techniques indicated that the accurateness of FFT was higher than that of Pundit and Metriguard. Effect of tree knots on MOE was also investigated. Result showed that the dynamic and static MOE gradually decreased with the increase of knot number, indicating that knot number had significant effect on MOE value.
基金support from the Anusandhan National Research Foundation(ANRF),erstwhile Science and Engineering Research Board(SERB),India,under the startup research grant program(SRG/2022/000566).
文摘The increasing integration of small-scale structures in engineering,particularly in Micro-Electro-Mechanical Systems(MEMS),necessitates advanced modeling approaches to accurately capture their complex mechanical behavior.Classical continuum theories are inadequate at micro-and nanoscales,particularly concerning size effects,singularities,and phenomena like strain softening or phase transitions.This limitation follows from their lack of intrinsic length scale parameters,crucial for representingmicrostructural features.Theoretical and experimental findings emphasize the critical role of these parameters on small scales.This review thoroughly examines various strain gradient elasticity(SGE)theories commonly employed in literature to capture these size-dependent effects on the elastic response.Given the complexity arising from numerous SGE frameworks available in the literature,including first-and second-order gradient theories,we conduct a comprehensive and comparative analysis of common SGE models.This analysis highlights their unique physical interpretations and compares their effectiveness in modeling the size-dependent behavior of low-dimensional structures.A brief discussion on estimating additional material constants,such as intrinsic length scales,is also included to improve the practical relevance of SGE.Following this theoretical treatment,the review covers analytical and numerical methods for solving the associated higher-order governing differential equations.Finally,we present a detailed overview of strain gradient applications in multiscale andmultiphysics response of solids.Interesting research on exploring the relevance of SGE for reduced-order modeling of complex macrostructures,a universal multiphysics coupling in low-dimensional structures without being restricted to limited material symmetries(as in the case of microstructures),is also presented here for interested readers.Finally,we briefly discuss alternative nonlocal elasticity approaches(integral and integro-differential)for incorporating size effects,and conclude with some potential areas for future research on strain gradients.This review aims to provide a clear understanding of strain gradient theories and their broad applicability beyond classical elasticity.
文摘Solids in nano-scales hold the promise to exhibit extreme strength and elasticity due to the absence of interior defects and the designability of micro-arrangements.A nano-scaled bulk sample can be produced by diamond,ice,metallic twins,high entropy alloy(HEA),or cubic boron nitride(cBN).A loading stage capable of 4-DoF movements was designed and built to achieve multi-axial mechanical loading inside a transmission electronic microscope chamber with sub-nanometer loading precision.For single crystal diamond in the shape of nano-needles,we were able to achieve an extreme bending strength of 125 GPa at the tensile side,approaching the theoretical strength of diamond.For ice fibers of sub-micron radius,an extreme elastic strain of 10.9%was acquired,far exceeding the previous record of 0.3%for the elastic strain achievable by ice.For metallic twin specimens made by nano-welding,a shear strain as large as 364%was recorded parallel to the twin boundary.Cyclic shear loading aligned with the twin boundary would drive an up-and-down sweeping movement of the low-angle grain boundary,as composed by an array of dislocations.The sweep of the grain boundary effectively cleanses the lattice defects and creates a feasible scenario of unlimited cyclic endurance.For a HEA dog-bone specimen in nano-scale,an extreme elastic strain of about 10%was achieved.At this level of mechanical straining,stretch-induced melting for crystalline metals,as envisaged by Lindemann a century ago,was realized.For cBN crystals,a fracture path inclined to the stacking hexagon planes would result in a new failure mechanism of layered decohesion,triggered by the extremely large elastic strain(>7%)along the edge of the submicron-scaled specimen.These results indicate ample room for upgrading the mechanical behaviour of solids in nano-scales.
基金funded by Vice Chancellor of Research at Shiraz University(grant 3GFU2M1820).
文摘The identification of the traction acting on a portion of the surface of an anisotropic solid is very important in structural health monitoring and optimal design of structures. The traction can be determined using inverse methods in which displacement or strain measurements are taken at several points on the body. This paper presents an inverse method based on the method of fundamental solutions for the traction identification problem in two-dimensional anisotropic elasticity. The method of fundamental solutions is an efficient boundary-type meshless method widely used for analyzing various problems. Since the problem is linear, the sensitivity analysis is simply performed by solving the corresponding direct problem several times with different loads. The effects of important parameters such as the number of measurement data, the position of the measurement points, the amount of measurement error, and the type of measurement, i.e., displacement or strain, on the results are also investigated. The results obtained show that the presented inverse method is suitable for the problem of traction identification. It can be concluded from the results that the use of strain measurements in the inverse analysis leads to more accurate results than the use of displacement measurements. It is also found that measurement points closer to the boundary with unknown traction provide more reliable solutions. Additionally, it is found that increasing the number of measurement points increases the accuracy of the inverse solution. However, in cases with a large number of measurement points, further increasing the number of measurement data has little effect on the results.
文摘The precise computation of nanoelectromechanical switches’(NEMS)multi-physical interactions requires advanced numerical models and is a crucial part of the development of micro-and nano-systems.This paper presents a novel compound numerical method to study the instability of a functionally graded(FG)beam-type NEMS,considering surface elasticity effects as stated by Gurtin-Murdoch theory in an Euler-Bernoulli beam.The presented method is based on a combination of the Method of Adjoints(MoA)together with the Bézier-based multistep technique.By utilizing the MoA,a boundary value problem(BVP)is turned into an initial value problem(IVP).The resulting IVP is then solved by employing a cost-efficient multi-step process.It is demonstrated that the mentioned method can arrive at a high level of accuracy.Furthermore,it is revealed that the stability of the presented methodology is far better than that of other common multi-step methods,such as Adams-Bashforth,particularly at higher step sizes.Finally,the effects of axially functionally graded(FG)properties on the pull-in phenomenon and the main design parameters of NEMS,including the detachment length,are inspected.It was shown that the main parameter of design is the modulus of elasticity of the material,as Silver(Ag),which had better mechanical properties,showed almost a 6%improvement compared to aluminum(Al).However,by applying the correct amount of material with sturdier surface parameters,such as Aluminum(Al),at certain points,the nanobeams’functionality can be improved even further by around 1.5%.
文摘The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The inner surface of the cavity was taken to be traction free and acted upon by a thermal shock to the surface. Laplace transforms techniques were used to obtain the solution by a direct approach.The inverse Laplace transforms was obtained numerically.The temperature,displacement and stress distributions are represented graphically.
文摘The fracture theory of cubic quasicrystal was developed. The exact analytic solution of a Mode Ⅲ Griffith crack in the material was obtained by using the Fourier transform and dual integral equations theory, and so the displacement and stress fields, the stress intensity factor and strain energy release rate were determined. The results show that the stress intensity factor is independent of material constants, and the strain energy release rate is dependent on all material constants. These provide important information for studying the deformation and fracture of the new solid material.
文摘Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.
基金supported by the National Natural Science Foundation of China(Nos.51773044 and 51603047)Research and Development Plan for Key Areas in Guangdong Province(No.2019B090914002)+1 种基金Guangdong Province Science and Technology Plan Project(No.2016A010103030)the PhD Start-up Fund of Natural Science Foundation of Guangdong Province,China(No.2016A030310344).
文摘The crystalline and amorphous regions were alternately arranged in the hard elastic polypropylene(PP)films with row-nucleated lamellae.In this work,their structure evolution during stretching and recovery at room temperature was followed and the elastic recovery mechanism was discussed by twice cyclic tensile experiment.During the first stretching to 100%,the lamellae crystals are parallel separated and the intercrystallite crazing is formed at the first yield point.Many nano-cavities within the intercrystallite crazing appear when the strain reaches 20%.The strain-hardening process accompanies with the lamellae long period increasing and the intercrystallite crazing enlargement.After the secondary yield point,the lamellae cluster is further separated and more nano-cavities appear.The first and second recovery processes are complete overlap.During recovery,firstly,the energy elasticity provided by nano-cavities surface tension drives the shrinkage of material,and then the entropy elasticity related to amorphous chain relaxation plays a leading role when the strain is smaller than the secondary yield point.The elastic recovery process of hard elastic material is the co-contribution of energy elasticity and entropy elasticity.This work gives a clearer recognition about the source of hard elastic property and the role of amorphous region in material's deformation.
文摘The first purpose of this striking but difficult paper is to revisit the mathematical foundations of Elasticity (EL) and Electromagnetism (EM) by comparing the structure of these two theories and examining with details their known couplings, in particular piezoelectricity and photoelasticity. Despite the strange Helmholtz and Mach-Lippmann analogies existing between them, no classical technique may provide a common setting. However, unexpected arguments discovered independently by the brothers E. and F. Cosserat in 1909 for EL and by H. Weyl in 1918 for EM are leading to construct a new differential sequence called Spencer sequence in the framework of the formal theory of Lie pseudo groups and to introduce it for the conformal group of space-time with 15 parameters. Then, all the previous explicit couplings can be deduced abstractly and one must just go to a laboratory in order to know about the coupling constants on which they are depending, like in the Hooke or Minkowski constitutive relations existing respectively and separately in EL or EM. We finally provide a new combined experimental and theoretical proof of the fact that any 1-form with value in the second order jets (elations) of the conformal group of space-time can be uniquely decomposed into the direct sum of the Ricci tensor and the electromagnetic field. This result questions the mathematical foundations of both General Relativity (GR) and Gauge Theory (GT). In particular, the Einstein operator (6 terms) must be thus replaced by the adjoint of the Ricci operator (4 terms only) in the study of gravitational waves.
文摘In this paper, a method of transforming volume integrals to boundary integrals is given for complicated loadings such as a i(y)x i and b i(x)y i . In the present method the volume integrals are approximately transformed to boundary integrals.
文摘In this paper,the choice and parametrisation of finite deformation polyconvex isotropic hyperelastic models to describe the behaviour of a class of defect-free monocrystalline metal materials at the molecular level is examined.The article discusses some physical,mathematical and numerical demands which in our opinion should be fulfilled by elasticity models to be useful.A set of molecular numerical tests for aluminium and tungsten providing data for the fitting of a hyperelastic model was performed,and an algorithm for parametrisation is discussed.The proposed models with optimised parameters are superior to those used in non-linear mechanics of crystals.
文摘A three-dimensional(3D)asymptotic theory is reformulated for the static analysis of simply-supported,isotropic and orthotropic single-layered nanoplates and graphene sheets(GSs),in which Eringen’s nonlocal elasticity theory is used to capture the small length scale effect on the static behaviors of these.The perturbation method is used to expand the 3D nonlocal elasticity problems as a series of two-dimensional(2D)nonlocal plate problems,the governing equations of which for various order problems retain the same differential operators as those of the nonlocal classical plate theory(CST),although with different nonhomogeneous terms.Expanding the primary field variables of each order as the double Fourier series functions in the in-plane directions,we can obtain the Navier solutions of the leading-order problem,and the higher-order modifications can then be determined in a hierarchic and consistent manner.Some benchmark solutions for the static analysis of isotropic and orthotropic nanoplates and GSs subjected to sinusoidally and uniformly distributed loads are given to demonstrate the performance of the 3D nonlocal asymptotic theory.
文摘Non-local plane elasticity problems are discussed in the context of Λ-fractional linear elasticity theory. Adapting the Λ-fractional derivative along with the Λ-fractional space, where geometry and mechanics are valid in the conventional way, non-local plane elasticity problems are solved with the help of biharmonic functions. Then, the results are transferred into the initial plane.Applications are presented to homogeneous and the fractional beam bending problem.
基金supported by HeiLongJiang Natural Science Fund(No.B2015019)the National Natural Science Foundation of China(No.10972029)Basic Business Special in Heilongjiang Province Department of Education(135109232)
文摘The reflection and transmission properties of thermo-elastic waves at five possible interfaces between two different strain gradient thermo-elastic solids are investigated based on the generalized thermo-elastic theory without energy dissipation （the GN theory）. First, the function of free energy density is postulated and the constitutive relations are defined. Then, the temperature field and the displacement field are obtained from the motion equation in the form of displacement and the thermal transport equation without energy dissipation in the strain gradient thermo-elastic solid. Finally, the five types of thermo-elastic interracial conditions are used to calculate the amplitude ratios of the reflection and transmission waves with respect to the incident wave. Further, the reflection and transmission coefficients in terms of energy flux ratio are calculated and the numerical results are validated by the energy conservation along the normal direction. It is found that there are five types of dispersive waves, namely the coupled longitudinal wave （the CP wave）, the coupled thermal wave （the CT wave）, the shear wave, and two evanescent waves （the coupled SP wave and SS wave）, that become the surface waves at an interface. The mechanical interfacial conditions mainly influence the coupled CP waves, SV waves, and surface waves, while the thermal interracial conditions mainly influence the coupled CT waves.
文摘Rotation is antisymmetric and therefore is not a coherent element of the classical elastic theory, which is characterized by symmetry. A new theory of linear elasticity is developed from the concept of asymmetric strain, which is defined as the transpose of the deformation gradient tensor to involve rotation as well as symmetric strain. The new theory basically differs from the prevailing micropolar theory or couple stress theory in that it maintains the same basis as the classical theory of linear elasticity and does not need extra concepts, such as “microrotation” and “couple stresses”. The constitutive relation of the new theory, the three-parameter Hooke’s law, comes from the theorem about isotropic asymmetric linear elastic materials. Concise differential equations of translational motion are derived consequently giving the same velocity formula for P-wave and a different one for S-wave. Differential equations of rotational motion are derived with the introduction of spin, which has an intrinsic connection with rotation. According to the new theory, S-wave essentially has rotation as large as deviatoric strain and should be referred to as “shear wave” in the context of asymmetric strain. There are nine partial differential equations for the deformation harmony condition in the new theory;these are given with the first spatial differentiations of asymmetric strain. Formulas for rotation energy, in addition to those for (symmetric) strain energy, are derived to form a complete set of formulas for the total mechanical energy.
基金supported by the National Natural Science Foundation of China under Grant No.10562002the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20070126002+1 种基金the Natural Science Foundation of Inner Mongolia under Grant No.200508010103the Inner Mongolia University Scientific Research Starting Foundation for Talented Scholars under Grant No.207066
文摘In the present paper, the spectrums of off-diagonal infinite-dimensional Hamiltonian operators are studied. At first, we prove that the spectrum, the continuous-spectrum, and the union of the point-spectrum and residual- spectrum of the operators are symmetric with respect to real axis and imaginary axis. Then for the purpose of reducing the dimension of the studied problems, the spectrums of the operators are expressed by the spectrums of the product of two self-adjoint operators in state spac,3. At last, the above-mentioned results are applied to plane elasticity problems, which shows the practicability of the results.
基金The research is supported by NSF of China (10371113 10471133)
文摘The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value problem of planar linear elasticity. The optimal error estimates are obtained by using some novel approaches and techniques. The method proposed in this article is robust in the sense that the convergence estimates in the energy and L^2-norms are independent-of the Lame parameter λ.
文摘Uniaxial Compressive Strength (UCS) and modulus of elasticity (E) are the most important rock parameters required and determined for rock mechanical studies in most civil and mining projects. In this study, two mathematical methods, regression analysis and Artificial Neural Networks (ANNs), were used to predict the uniaxial compressive strength and modulus of elasticity. The P-wave velocity, the point load index, the Schmidt hammer rebound number and porosity were used as inputs for both meth-ods. The regression equations show that the relationship between P-wave velocity, point load index, Schmidt hammer rebound number and the porosity input sets with uniaxial compressive strength and modulus of elasticity under conditions of linear rela-tions obtained coefficients of determination of (R2) of 0.64 and 0.56, respectively. ANNs were used to improve the regression re-sults. The generalized regression and feed forward neural networks with two outputs (UCS and E) improved the coefficients of determination to more acceptable levels of 0.86 and 0.92 for UCS and to 0.77 and 0.82 for E. The results show that the proposed ANN methods could be applied as a new acceptable method for the prediction of uniaxial compressive strength and modulus of elasticity of intact rocks.
