ELASTIC EFFECT IN DYNAMIC RESPONSE OF PLASTIC CANTILEVER BEAMS TO IMPACT

A lumped masses-springs model is proposed to analyze the dynamic response of an elastic-plastic cantilever beam resulting from impact. The numerical results are in good agreement with those by finite-element approaches. The simplified model can catch the most essential features of elastic-plastic response of beams; in particular, it demonstrates the effect of elastic deformation on the distribution of bending moment and energy dissipation, and provides valuable quatitative results.

Surface Elastic Effects on Electromechanical Responses of a Piezoelectric Semiconducting Nanobeam

Piezoelectric semiconductors(PSCs)find extensive applications in modern smart electronic devices because of their dual properties of being piezoelectric and semiconductive.With the increasing demand for miniaturization of these devices,the performance of their components needs to be carefully designed and optimized,especially when reduced to nanosize.It has been shown that surface elastic properties play a substantial role in the mechanical performance of nanoscale materials and structures.Building on this understanding,the surface elastic effects,encompassing surface residual stress,surface membrane stiffness,and surface bending stiffness,are comprehensively taken into account to explore the electromechanical responses of a PSC nanobeam.Additionally,the flexoelectric effect on their responses is also systematically studied.The results of this work reveal that surface elastic properties predominantly influence mechanical performance,while the flexoelectric effect plays a more dominant role in electric-related quantities at the nanoscale.Notably,the significance of surface bending rigidity,which was often underestimated in the earlier literature,is demonstrated.Furthermore,owing to the flexoelectric effect,the linear distribution of electric potential and charge carriers along the length transforms into a nonlinear pattern.The distributions of electric potential and charge carriers across the cross section are also evidently impacted.Moreover,the size-dependent responses are evaluated.Our findings may provide valuable insights for optimizing electronic devices based on nanoscale PSCs.

Effects of Initial Defects on Effective Elastic Modulus of Concrete with Mesostructure

An exquisite mesostructure model was presented to predict the effective elastic modulus of concrete,in which concrete is realized as a four-phase composite material consisting of coarse aggregates,mortar matrix,interfacial transition zone(ITZ),and initial defects.With the three-dimensional(3D)finite element(FE)simulation,the highly heterogeneous composite elastic behavior of concrete was modeled,and the predicted results were compared with theoretical estimations for validation.Monte Carlo(MC)simulations were performed with the proposed mesostructure model to investigate the various factors of initial defects influencing the elastic modulus of concrete,such as the shape and concentration(pore volume fraction or crack density)of microspores and microcracks.It is found that the effective elastic modulus of concrete decreases with the increase of initial defects concentration,while the distribution and shape characteristics also exert certain influences due to the stress concentration caused by irregular inclusion shape.

Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

Theoretical prediction of effective elastic constants for new intermetallic compound porous material

Based on microstructure analysis of the new Ti-A1 intermetallic compound porous material, a micromechanics model of heterogeneous Plateau porous structure was established and calculation formulas of elastic constants （including effective elastic modulus, effective shear elastic modulus and effective Poisson ratio） were derived by the energy method for this porous material. Calculation results show that both the effective elastic modulus and effective shear elastic modulus increase with the increase of the relative density while the effective Poisson ratio decreases. Compared with the currently-existing hexagonal honeycomb model and micromechanics model of composite materials, the micromechanics model of heterogeneous Plateau porous structure in this study is more suitable for characterizing the medium-density porous material and more accurate for predicting the effective elastic constants of the medium-density porous material. Moreover, the obtained explicit expressions of the effective elastic constants in term of the relative density rather than the microstructural parameters for the uniform and regular Plateau porous structure are more convenient to engineering application.

Effective elastic thickness of the lithosphere from joint inversion in western China and its implications

The western China lies in the convergence zone between Eurasian and Indian plates.It is an ideal place to study the lithosphere dynamics and tectonic evolutions on the continental Earth.The lithospheric strength is a key factor in controlling the lithosphere dynamics and deformations.The effective elastic thickness(T_(e))of the lithosphere can be used to address the lithospheric strength.Previous researchers only used one of the admittance or coherence methods to investigate the T_(e) in the western China.Moreover,most of them ignored the internal loads of the lithosphere during the T_(e) calculation,which can produce large biases in the T_(e) estimations.To provide more reliable T_(e) estimations,we used a new joint inversion method that integrated both admittance and coherence techniques to compute the T_(e) in this study,with the WGM2012 gravity data,the ETOPO1 topographic data,and the Moho depths from the CRUST1.0 model.The internal loads are considered and investigated using the load ratio(F).Our results show that the joint inversion method can yield reliable T_(e) and F values.Based on the analysis of T_(e) and F distributions,we suggest(1)the northern Tibetan Plateau could be the front edge of the plate collision of Eurasian and Indian plates;(2)the southern and part of central Tibetan Plateau have a strong lithospheric mantle related to the rigid underthrusting Indian plate;(3)the southeastern Tibetan Plateau may be experiencing the delamination of lithosphere and upwelling of asthenosphere.

THE GENERAL SOLUTION OF SECOND ORDER EFFECTS IN ELASTIC HALF-SPACE ACTED UPON BY A NON-UNIFORM SHEAR LOAD

This paper is a continuation of [1]. A closed form solution to the second order elasticity problem, when an isotropic compressible elastic half-space undergoes a deformation owing to a non-uniformly distributed shear load, is presented. The method of integral transform is employed to determine the solutions.

THE ILLUSTRATION CALCULATIONS OF SECOND ORDER EFFECTS IN ELASTIC HALF-SPACE ACTED UPON BY A NON-UNIFORM SHEAR LOAD

This paper is a continuation of [1]. An example is discussed in derail to illustrate the second order effects. Numerical calculations for the second order elastic material for the z-direction displacement and the stress t(rz) are carried out. It is found that the second order effect is to reduce z-direction displacement and to decrease t(rz)inside the circle but to increase its value outside the circle.

EFFECTIVE ELASTIC MODULI OF AN INHOMOGENEOUS MEDIUM WITH CRACKS

In the present paper, the effective elastic moduli of an inhomogeneous medium with cracks are derived and obtained by taking into account its microstructural properties which involve the shape, size and distribution of cracks and the interaction between cracks. Numerical results for the periodic microstructure of different dimensions are presented. From the results obtained, it can be found that the distribution of cracks has a significant effect on the effective elastic moduli of the material.

EFFECTIVE ELASTIC MODULI OF INHOMOGENEOUS SOLIDS BY EMBEDDED CELL MODEL

An embedded cell model is presented to obtain the effective elastic moduli for three-dimensional two-phase composites which is an exact analytic formula without any simplified approximation and can be expressed in an explicit form. For the different cells such as spherical inclusions and cracks surrounded by sphere and oblate ellipsoidal matrix, the effective elastic moduli are evaluated and the results are compared with those from various micromechanics models. These results show that the present model is direct, simple and efficient to deal with three-dimensional two-phase composites.

Effective Elastic Thickness of the Lithosphere in the Mariana Subduction Zone and Surrounding Regions and Its Implications for Their Tectonics

To understand the rheology,structure,and tectonics of the lithosphere in the Mariana subduction zone and surrounding regions,we calculated the effective elastic thickness of the lithosphere(Te)in these areas using the improved moving window admittance technique(MWAT)method.We find that smaller data grid spacing can better reflect Te variations in the subduction zone.The Te of the study region ranges from 0 to 47 km.The Te is reduced from 40 km on the seaward side of the outer-rise region to 1-2 km along the trench axis.The lithospheric breaking distance from the trench axis ranges from 0 to 250 km.We suggest that the intermediate Te values in seamounts and high Te values on the seaward side of the outer-rise region respectively reflect the‘fossil’rheological state and current lithospheric strength of the Pacific plate.The faulting induced by the downward bending of subducting plate not only ruptures the lithosphere but also contributes to the mantle serpentinization,significantly reducing the lithospheric strength.The largest breaking distance of the Ogasawara Plateau may be due to the increase in the mass load of the subducting plate in the Ogasawara Plateau and the significant horizontal bending force in the plate caused by the resistance of seamounts to subduction.Furthermore,a good positive correlation exists between the breaking distance and subduction dip angle along the trench axis.We suggest that the subducting plate with a larger breaking distance is likely to form a larger subduction angle.

Effective Elastic Thickness of Southeast Part ofArctic Ocean-Eurasia Continent-PacificOcean Geoscience Transect

The effective lithospheric elastic thickness of the continent is an important parameter for examination of the large-scale structure and analyses of the mechanism of isostatic compensation within the plate, and a parameter standing for the strength of the lithosphere. The Te values along Quanzhou-Heishui, the southeast section of the Arctic Ocean-Eurasian Continent-Pacific Ocean geoscience transect, are estimated by using the coherence technique developed by Forsyth. Studies of the feature of the coherence between gravity and topography suggest that at short wavelengths (6. 6-100 km) for each data box that is used to estimate Te, the plate is strong enough to support topographic loads and gravity and topography are uncorrelated. At long wavelengths where the plate is deflected by surface and subsurface loads are compensated by the flexure model. Sichuan land-stone with low heat-flow values has high Te values whereas in Ninghua, Datian, land-stone with high heat-flow values has low Te values, which reflects a correlation, low heat-flow values corresponding to high Te values and high heat-flow values corresponding to low Te values. Te values can be divided into two sections: northwest high section and southeast low section. There is roughly a positive correlation between crustal thickness and effective elastic thickness of the lithosphere.

GREEN’S FUNCTION AND EFFECTIVE ELASTIC STIFFNESS TENSOR FOR ARBITRARY AGGREGATES OF CUBIC CRYSTALS

A closed but approximate formula of Green’s function for an arbitrary aggregate of cubic crystallites is given to derive the e?ective elastic sti?ness tensor of the polycrystal. This formula, which includes three elastic constants of single cubic crystal and ?ve texture coe?cients, accounts for the e?ects of the orientation distribution function (ODF) up to terms linear in the tex- ture coe?cients. Thus it is expected that our formula would be applicable to arbitrary aggregates with weak texture or to materials such as aluminum whose single crystal has weak anisotropy. Three examples are presented to compare predictions from our formula with those from Nishioka and Lothe’s formula and Synge’s contour integral through numerical integration. As an applica- tion of Green’s function, we brie?y describe the procedure of deriving the e?ective elastic sti?ness tensor for an orthorhombic aggregate of cubic crystallites. The comparison of the computational results given by the ?nite element method and our e?ective elastic sti?ness tensor is made by an example.

A New Simulation of Track Structure of Low-Energy Electrons in Liquid Water:Considering the Condensed-Phase Effect on Electron Elastic Scattering

A new Monte Carlo simulation of the track structure of low-energy electrons （〈10keV） in liquid water is presented. The feature of the simulation is taken into consideration of the condensed-phase effect of liquid water on electron elastic scattering with the use of the Champion model, while the dielectric response formalism incorporating the optical-data model developed by Emfietzoglou et al. is applied for calculating the electron inelastic scattering. The spatial distributions of energy deposition and inelastic scattering events of low-energy electrons with different primary energies in liquid water are calculated and compared with other theoretical evaluations. The present work shows that the condensed-phase effect of liquid water on electron elastic scattering may be of the influence on the fraction of absorbed energy and distribution of inelastic scattering events at lower primary energies, which also indicate potential effects on the DNA damage induced by low-energy electrons.

Lithospheric strength of the Anatolian plateau and implications for strong earthquake activity in Turkey

On February 6, 2023, the doublet earthquake including two main shocks with magnitudes M_(W)7.8 and M_(W)7.5, occurred near the western side of the East Anatolian Fault at the southeast boundary of the Anatolian Plateau in Turkey. Based on the WGM2012 Bouguer gravity anomaly data and the Etopo1topography data, this study first introduced a joint inversion of admittance and coherence functions and used the Bayesian optimal parameter estimation method to obtain the effective elastic thickness Teand loading ratio F of the lithosphere for various tectonic units in the Anatolian Plateau. Secondly, we discussed the characteristics and influencing factors of the lithospheric mechanical strength and analyzed its relationship with seismic activity. The lithospheric mechanical strength of the Anatolian Plateau showed clear lateral heterogeneity and a "weak-strong-weak" spatial pattern from east to west,reflecting various tectonic processes. At last, the strong seismic activity was found where the lithospheric strength was low in the Anatolian Plate. We also incorporated GPS strain rate and other results to investigate the tectonic background and primary causes of the M_(W)7.8 and M_(W)7.5 doublet earthquakes in Turkey. The results have a good insight into urban safety design in the Turkish region, including postdisaster rehabilitation, earthquake hazard assessment, and loss reduction.

Multitaper spectral method to estimate the elastic thickness of South China: Implications for intracontinental deformation

The effective elastic thickness （Te） represents the thickness of the elastic layer or the flexural rigidity of the lithosphere, the equivalent of which can be calculated from the spectral analysis of gravity and topographic data. Studies of Te have profound influence on intracontinental deformation, and coupling of the tectonic blocks. In this paper, we use the multitaper spectral estimation method to calculate the coherence between Bouguer gravity and topography data, and to obtain the Te map of South China. Through the process of correction, we discuss the relationships of Te versus heat flow, and Te versus seismicity. The results show that Te distribution of South China is affected by three factors：the original age, which controls the basic feature;the Mesozoic evolution, which affects the Te distribution;and the neotectonic movement, which shaped the final distribution. The crust age has a positive correlation with the first-order Te distribution;thus the Yangtze Craton has a relatively higher Te （about 50 km） whereas the Te in Cathaysia block is only 10e20 km. By analysis and comparison among the tectonic models of South China, the Te distribution can be well explained using the flat-subduction model. As is typical with neotectonics, the region with a higher heat flow is related with a lower Te. The seismicity does not have a clear relationship with Te, but the strong seismicity could cause a low Te. Seismogenic layer （Ts） has a similar trend as Te in the craton, whereas in other areas the relationship is complex.

Three-dimensional admittance analysis of lithospheric elastic thickness over the Louisville Ridge

Using bathymetry and altimetric gravity anomalies, a 1°×9 1° lithospheric effective elastic thickness（Te） model over the Louisville Ridge and its adjacent regions is calculated using the moving window admittance technique. For comparison, three bathymetry models are used： general bathymetric charts of the oceans, SIO V15.1,and BAT_VGG. The results show that BAT_VGG is more suitable for calculating T e than the other two models. T e along the Louisville Ridge was re-evaluated. The southeast of the ridge has a medium Te of 10–20 km, while Te increases dramatically seaward of the Tonga-Kermadec trench as a result of the collision of the Pacific and IndoAustralian plates.

Topology and Shape Optimization of 2-D and 3-D Micro-ArchitecturedThermoelastic Metamaterials Using a Parametric Level Set Method

2-D and 3-D micro-architectured multiphase thermoelastic metamaterials are designed and analyzed using a parametric level set method for topology optimization and the finite element method.An asymptotic homogenization approach is employed to obtain the effective thermoelastic properties of the multiphase metamaterials.Theε-constraint multi-objective optimization method is adopted in the formulation.The coefficient of thermal expansion(CTE)and Poisson’s ratio(PR)are chosen as two objective functions,with the CTE optimized and the PR treated as a constraint.The optimization problems are solved by using the method of moving asymptotes.Effective isotropic and anisotropic CTEs and stiffness constants are obtained for the topologically optimized metamaterials with prescribed values of PR under the constraints of specified effective bulk modulus,volume fractions and material symmetry.Two solid materials along with one additional void phase are involved in each of the 2-D and 3-D optimal design examples.The numerical results reveal that the newly proposed approach can integrate shape and topology optimizations and lead to optimal microstructures with distinct topological boundaries.The current method can topologically optimize metamaterials with a positive,negative or zero CTE and a positive,negative or zero Poisson’s ratio.

C^1 natural element method for strain gradient linear elasticity and its application to microstructures

C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.