Homogeneous Isotropic Material Research Articles

Measurement of surface rectangular defect depth based on laser-excited transmitted surface waves

ABSTRACT In order to study the effect of laser-excited surface waves on the transmission of surface rectangular defects, the transmission information of surface waves is used to achieve the quantitative calculation of defect depth. In this paper, the finite element method is employed to analyse the transmission process of laser-excited surface waves on rectangular defects. Subsequently, the influence of the front and back edges of rectangular defects on the transmission of surface waves is examined, and the formation mechanisms of feature points in the time-domain signals at detection points are elucidated. Ultimately, the calculation formula for defect depth is derived on the basis of the propagation path of each component after transmission. The experimental results are consistent with the simulation results, and the relative error of the surface rectangular defect depth calculation is within 9%. The validation of the proposed method on homogeneous isotropic metallic materials demonstrates the effectiveness and applicability of the proposed method. These results will provide a reliable method for characterising the depth of rectangular defects on surfaces by laser ultrasonic technology.

Optimising structural health monitoring systems: A 2D numerical investigation on impedance matching for FML with integrated sensors

AbstractFibre metal laminates (FML) represent an innovative class of advanced composite materials that integrate the mechanical properties of both metals and fibre‐reinforced composites (FRP). Combining the strength and ductility of metals with the lightweight and high stiffness of FRP and FMLs have emerged as new material compositions for applications in chemical, nuclear, automobile, and aerospace engineering disciplines. Structural health monitoring (SHM) using guided ultrasonic waves (GUW) is the state‐of‐the‐art for non‐destructive testing of thin‐walled structures. When applied to FML, SHM plays a crucial role in monitoring the integrity over time and detecting potential damage such as delamination, fibre breakage, or other structural anomalies. In SHM with GUW, a wave‐field is emitted by actuators. This wave‐field can be affected by damage in the structure, thereby changing its propagation characteristics. Sensors monitor the interaction between damage and GUW, which can be utilized to locate and classify the damage and ascertain the overall health state of the structure. In this study, an advanced integration of measurement hardware, that is, sensors and actuators, within the laminate structure is investigated. Sensor integration into FML allows for improved and more sophisticated monitoring capabilities in comparison to measuring techniques like laser vibrometers, which are limited to measuring displacements on the surface of the structure. However, the integration of sensors and actuators yields the technical difficulty of distorting the wave‐fields and may result in an over‐ or underestimation of the damage. Similar to damage, the distortion of the wave‐field is caused by the changes in acoustic impedance resulting from different material properties. In a previous study, incorporating a functionally graded artificial interphase through acoustic impedance matching between the sensor and host material showed notable and significant outcomes. The current contribution extends the prior graded artificial interphase for an isotropic homogeneous material to an FML structure. This paper presents a comprehensive numerical simulation study on a two‐dimensional model of FML with integrated sensors. The interphases are designed based on impedance matching, which improves signal transmission and reduces disturbing reflections. The conducted investigations hold for several interphase configurations for a wide frequency range. The optimised integration of sensors demonstrates promising results for enhancing the reliability and accuracy of SHM systems. This research serves as a foundation for further experimental validation and the development of advanced sensor‐integrated FML structures with improved monitoring capabilities.

Simple and effective mechanical cloaking

We show theoretically that essentially perfect elastostatic mechanical cloaking of a circular inclusion in a homogeneous surrounding medium can be achieved by means of a simple cloak comprising three concentric annuli, each formed of a homogeneous isotropic linear elastic material of prescribed shear modulus. Importantly, we find that the same combination of annuli will cloak any possible mode of imposed deformation or loading, for any randomly chosen admixture of imposed compression, pure shear and simple shear, without the need to re-design the cloak for different deformation modes. A full range of circular inclusions can be cloaked in this way, from soft to stiff. In consequence, we suggest that an inclusion of any arbitrary shape can also be cloaked, by first enveloping it in a stiff circle, then cloaking the combined structure with three annuli as described. Given that a single inclusion can be fully cloaked in this way, even at near field close to the cloaking perimeter, it also follows that multiple such neutral inclusions arranged with arbitrarily high packing fraction in a surrounding medium can also be cloaked. We confirm this by direct simulation. This indicates a possible route to fabricating composite materials with the same global mechanical response as a counterpart homogeneous material, and with uniform strain and stress fields outwith the cloaked inclusions.

A fully coupled system of generalized thermoelastic theory for semiconductor medium

This study presents a new mathematical framework for analyzing the behavior of semiconductor elastic materials subjected to an external magnetic field. The framework encompasses the interaction between plasma, thermal, and elastic waves. A novel, fully coupled mathematical model that describes the plasma thermoelastic behavior of semiconductor materials is derived. Our new model is applied to obtain the solution to Danilovskaya’s problem, which is formed from an isotropic homogeneous semiconductor material. The Laplace transform is utilized to get the solution in the frequency domain using a direct approach. Numerical methods are employed to calculate the inverse Laplace transform, enabling the determination of the solution in the physical domain. Graphical representations are utilized to depict the numerical outcomes of many physical fields, including temperature, stress, displacement, chemical potential, carrier density, and current carrier distributions. These representations are generated for different values of time and depth of the semiconductor material. Ultimately, we receive a comparison between our model and several earlier fundamental models, which is then graphically represented.

Analytical model for laser-induced transient grating measurements of thermal diffusivity in non-opaque materials

The thermal transport and elastic properties of materials are often measured using the laser-induced transient grating spectroscopy (TGS) technique. The analysis of the TGS signal usually involves fitting well-known expressions, derived assuming the limiting cases of opaque or transparent materials, to the measured data. In this paper, the system of thermoelastic equations is analytically solved for an isotropic homogeneous material assuming finite laser penetration depth, which is an important consideration when the penetration depth is on the order of the acoustic wavelength. The need to use such a solution is discussed and compared to the expression for opaque material. The solution is benchmarked against TGS signal measured on single-crystal silicon with {100} surface orientation and is found to significantly improve the accuracy of the calculated thermal diffusivity as compared to using the expression for opaque material.

A finite element model for investigating the influence of keel design and position on unicompartmental knee replacement cementless tibial component fixation

ObjectivesThe cementless Oxford Unicompartmental Knee Replacement (OUKR) tibial component relies on an interference fit to achieve initial fixation. The behaviour at the implant-bone interface is not fully understood and hence modelling of implants using Finite Element (FE) software is challenging. With a goal of exploring alternative implant designs with lower fracture risk and adequate fixation, this study aims to investigate whether optimisation of FE model parameters could accurately reproduce experimental results of a pull-out test which assesses fixation. Materials and methodsFinite element models of implants with three methods of fixation (standard keel, small keel, and peg) in a bone analogue foam block were created, in which implants were modelled using an analytical rigid definition and the foam block was modelled as a homogenous linear isotropic material. The total interference and elastic slip were varied in these models and optimised by comparing simulated and experimental results of pull-out tests for two (standard and peg) implant geometries. Then the optimised interference and elastic slip were validated by comparing simulated and experimental data of a third (small keel) implant geometry. ResultsThe optimisation of parameters established an interference of 0.16 mm and an elastic slip of 0.20 mm as most suitable for modelling the experimental force–displacement plots during pull-out. This combination of parameters accurately reproduced the experimental results of the small keel geometry. The maximum pull-out forces from the FE models were consistent with experimental data for each implant design. ConclusionsThis study shows that experimental pull-out tests can be accurately modelled using adjusted interference values and non-linear friction and outlines a method for determining these parameters. This study demonstrates that complex problems in modelling implant behaviour can be addressed with relatively simple models. This can potentially lead to the development of implants with reduced risk of failure.

Determination of natural frequencies of non‐uniform aluminum beams coated with functionally graded material

AbstractThe present study comprises a numerical analysis used to find the dimensionless natural frequencies of non‐uniform aluminum beams coated with functionally graded material. The beams have variable width, and their variation is described by exponential and linear functions. While the coating material properties vary with a polynomial function, the lamination theory is used to calculate the overall properties of the functionally graded material coating. The beam is modeled as a modified Timoshenko beam and the gradual transition of the coating material properties as 25 layers of homogeneous isotropic material. In order to find the natural frequencies of the beam, finite element analysis was used, and the numerical results were processed with MATLAB, which were in good agreement with literature values. A parametric study is performed to study the effects of slenderness (L/H), coating thickness (h/H), skewness rate (S) and taper ratio (w2/w1) on the dimensionless natural frequencies. The study showed that tapering and skewing had a limited effect on the natural frequencies in general, however there exists a critical slenderness for every taper ratio and skewness rate where shape variation has a significant effect on the natural frequencies and should be considered.

Topology and orientation optimization of multi-material hinge-free composite compliant mechanisms under multiple design-dependent loadings

Compliant mechanisms with multiple input loads and output ports are commonly applied in micro-electromechanical systems (MEMS), while compliant mechanisms under design-dependent pressure loadings (such as pneumatic or hydraulic) can generate smooth and compatible deformations. Combining these two types of problems, we propose the design problem of compliant mechanisms under multiple design-dependent loadings. To potentially improve the structural performances, fiber-reinforced composite materials are introduced, and multi-material topology optimization and material orientation optimization are considered simultaneously, which enables the materials to be anisotropic and heterogeneous. Since compliant mechanisms utilize elastic deformation to transmit input forces or displacements to output forces or displacements, anisotropic and heterogeneous material can increase the freedoms in displacement and force transmissions compared to conventional homogeneous isotropic material. The topology optimization is implemented via an extended moving iso-surface threshold (MIST) method for multi-material, in which a novel element-based searching scheme is employed for tracking multiple fluid–structure interfaces. The orientation optimization is achieved via an analytical solution derived for fully anisotropic materials and multi-input-multi-output compliant mechanisms. Numerical examples are presented to show the validity of the present MIST method to design multi-material hinge-free compliant mechanisms under multiple design-dependent loadings.

Predicting the temperature field of thermal cloaks in homogeneous isotropic multilayer materials based on deep learning

Thermal cloaks can realize thermal manipulation and have been widely applied in the engineering field. Traditional methods, like the finite element method (FEM) and finite difference method, obtain the temperature of the thermal cloak with time-consuming. A deep learning model is proposed to predict the temperature field in homogeneous isotropic multilayer materials. The FEM is applied to solve the thermal cloak and the training data are obtained. The layer's properties, including different layers, thickness, relative thermal conductivities and distribution modes, of the thermal control or manipulative ability for temperature and heat diffusion are also investigated. The deep learning mode is developed by mapping the parameters layout to the temperature field as an image-to-image regression task and the relationship between the layer's properties and the cloaking performances is intelligently established. The temperature field of the arbitrary layout composite can be acquired almost with no time cost. The temperature field with the largest node numbers of medium temperature by the FEM and the deep learning model, is exhibited and compared. Furthermore, we extend the surrogate model to different cases with different boundary conditions, which can still achieve good prediction results. Owing to the high efficiency and complete independence from the mesh densities, the proposed method offers a novel and robust technique for predicting the temperature field and suggestion for the design of the thermal cloak.

An efficient approach for free vibration analysis of functionally graded sandwich beams of variable cross-section

In this research paper, a powerful numerical method is implemented to examine the free vibration analysis of functionally graded (FG) sandwich beams of variable cross-section. The core of the beam is considered to be made from homogenous isotropic material and the faces of the sandwich beam are considered to be made of FG materials. The effect of the shear strain is considered in the formulations based on the first-order shear deformation theory (FSDT). The governing canonical equations for the dynamic response of FG sandwich beams are derived with the aid of the canonically conjugate momentums for the first time. To solve these equations numerically the Complementary Functions Method (CFM) is implemented. The free vibration behavior of the symmetric and asymmetric FG sandwich beams is investigated for different boundary conditions. The presented efficient numerical method is validated with the available literature. Moreover, detailed parametric studies are conducted to demonstrate the influence of layers, geometric constants, material volume fraction indexes, and beam slenderness on the natural frequencies of FG sandwich beams.

Controllable Deformations of Unconstrained Ideal Nematic Elastomers

We establish that, for ideal unconstrained uniaxial nematic elastomers described by a homogeneous isotropic strain-energy density function, the only smooth deformations that can be controlled by the application of surface tractions only and are universal in the sense that they are independent of the strain-energy density are those for which the deformation gradient is constant and the liquid crystal director is either aligned uniformly or oriented randomly in Cartesian coordinates. This result generalizes the classical Ericksen’s theorem for nonlinear homogeneous isotropic hyperelastic materials. While Ericksen’s theorem is directly applicable to liquid crystal elastomers in an isotropic phase where the director is oriented randomly, in a nematic phase, the constitutive strain-energy density must account also for the liquid crystal orientation which leads to significant differences in the analysis compared to the purely elastic counterpart.

Load identification in a plate-beam lattice from interior dynamic data

We consider the inverse problem of determining transverse dynamic loads acting on a clamped plate stiffened by two sets of orthogonal beams. Under the assumption of infinitesimal deformation, in the sense that linear elasticity applies, homogeneous isotropic material and negligible beam torsional stiffness, we show that the measurement of the transverse response of the system in an open subset of the mid-plane, and for an arbitrarily small interval of time, is sufficient for the unique determination of the spatial component of the load. The uniqueness result holds for multiple asynchronous loads and suggests a reconstruction procedure, which is used for a numerical validation of the method.

Ventcel-type Transmission Conditions for the Scattering of a Time-harmonic Wave Problem with Accuracy up to Order $3$

This work deals with the asymptotic behaviour of the electric field in the transverse magnetic (TM) mode, propagating in a bidimensional heterogeneous medium, composed by a homogeneous linear dielectric isotropic material surrounded by a thin layer of thickness $\varepsilon$ (destined to tend to $0$) and embedded in an ambient medium. Using the tools of multiscale analysis, an asymptotic expansion of the solution $u^{\varepsilon}$ to the Helmholtz problem with respect to the thickness $\varepsilon$ is derived. As a consequence, Ventcel-type transmission conditions on the limit interface $\Gamma$ are obtained modelling the effect of the thin layer with accuracy up to $O(\varepsilon^{3})$. A particular choice of the interface $\Gamma$ leads to a well-posed Ventcel's problem.

Development of a tensile relaxation modulus test for identifying the tensile relaxation spectrum of asphalt binder

The tensile properties of asphalt binder such as strength, ductility, and stress-relaxation (relaxation) modulus are not only closely related to binder performance, but the modulus is also a necessary input for accurate material characterisation, modelling, and simulation. The linear behaviour of a homogeneous isotropic material can be fully characterised by both the tensile and shear relaxation moduli or their corresponding relaxation spectra. The shear properties of asphalt binders are often studied through dynamic shear tests. However, its tensile relaxation modulus and spectrum are seldom determined. Instead, they are often derived from the shear relaxation modulus with a prescribed Poisson ratio. However, it remains a question whether the ratio is material-, time- or even loading-independent. A tensile relaxation test is thus developed for determining the tensile relaxation modulus and spectrum directly. The continuous tensile relaxation spectrum is numerically derived based on the integral equation that connects the modulus to the spectrum. Spectrum regularisation and L-curve are used for solving the overfitting issue of the ill-posed equations. Two binders are used to evaluate the experimental method and the computational approach. The data suggest that the Poisson ratio may not be regarded as a constant for different asphalt binders. Hence, it is necessary to characterise asphalt binders using the tensile relaxation spectrum. Cross-checking between tensile and shear test data and between experimental relaxation moduli and the back-calculated ones from the tensile relaxation spectra indicate that the developed methods are robust and reliable.

Investigation on the effect of interface properties on compressive failure behavior of 3D woven composites through micromechanics-based multiscale damage model

In this paper, the effect of interface properties on the compressive failure behavior of 3D woven composites (3DWC) is investigated by incorporating a micromechanics-based multiscale damage model (MMDM). The correlation between the mesoscopic stress of yarns and microscopic stress of constituents is established by defining a stress amplification factor. With the microscopic stresses, the fiber breakage and matrix failure can be separately evaluated at the microscale, without assuming the yarns as transversely isotropic homogeneous materials. Especially, the interfacial debonding between yarns and matrix is also a dominant damage mode within 3DWC. Given that there is still a lack of studies on the influence of interfacial properties on the compressive failure behavior of 3DWC, it is meaningful to perform numerical parametric studies to reveal how the interface properties contribute to the damage mechanisms of 3DWC under compressions. The predicted results indicate that with the increase of interface strengths and fracture toughness, the compressive resistance of 3DWC can be significantly improved, resulting in higher strength and failure strain. Additionally, the studied 3DWCs with weak, medium and strong interfaces exhibit different damage development processes.

ALLDMD Dissipation Energy Analysis by the Method Extended Finite Elements of a 2D Cracked Structure of an Elastic Linear Isotropic Homogeneous Material

The analysis of the crack parameters of a material is an important effect for characterizing the state of stress. Nowadays, materials occupy a very necessary place in modern industry for the study of the life of such structure. This article deals numerically the evolution of (ALLDMD) dissipation energy for an initial rectilinear crack of α=0°. Furthermore, the second case study is based on a crack inclined by the orientation angle α=15°, 30°, and 45°. The X-FEM extended finite element method was used. In addition, the linear elastic isotropic homogeneous material was applied. Thus, the 4-node quadratic CPS4R elements were used. The crack is then modeled numerically using the ABAQUS finite element calculation code. Characterization parameters such as ALLDMD dissipation energy and von Mises stress were calculated. In addition, the results obtained concerning the numerical simulation were compared and discussed between the different mesh approximate total size TGA=1, 2 and 3mm. A good correspondence was obtained between the different comparison results concerning the evolution of the Von Mises stress in all the modeling cases of our work.

Determination of the Primary Excitation Spectra in XPS and AES

This paper reviews a procedure that allows for extracting primary photoelectron or Auger electron emissions from homogeneous isotropic samples. It is based on a quantitative dielectric description of the energy losses of swift electrons travelling nearby surfaces in presence of stationary positive charges. The theory behind the modeling of the electron energy losses, implemented in a freely available QUEELS-XPS software package, takes into account intrinsic and extrinsic effects affecting the electron transport. The procedure allows for interpretation of shake-up and multiplet structures on a quantitative basis. We outline the basic theory behind it and illustrate its capabilities with several case examples. Thus, we report on the angular dependence of the intrinsic and extrinsic Al 2s photoelectron emission from aluminum, the shake-up structure of the Ag 3d, Cu 2p, and Ce 3d photoelectron emission from silver, CuO and CeO2, respectively, and the quantification of the two-hole final states contributing to the L3M45M45 Auger electron emission of copper. These examples illustrate the procedure, that can be applied to any homogeneous isotropic material.

Двопараметрична модель зони передруйнування у квазіпружному матеріалі біля вершини міжфазної тріщини

A model of the pre-fracture zone, which under plane strain conditions extends from the tip of the interface crack at an angle to the plane interface of two different homogeneous isotropic materials, has been developed. The pre-fracture zone is represented by the displacement discontinuity line, on which the strength condition of the Mises-Hill type is satisfied. The parameters of the model are the tensile resistance and shear resistance of the material in which the zone develops. The model takes into account brittle and ductile fracture mechanisms and can be used to describe the quasi-brittle fracture of a piece-homogeneous body with an interface crack. The possibility of a transition between brittle and ductile fracture mechanisms is shown when the ratio of tensile and shear resistance of the material changes.

Local discontinuous Galerkin schemes for an ultrasonic propagation equation with fractional attenuation

The goal of this article is to develop local discontinuous Galerkin (LDG) schemes for solving a time fractional equation describing the ultrasonic wave in a homogeneous isotropic porous material. Two novel semi-discrete LDG schemes are designed for the considered model. The semi-discrete LDG schemes are constructed by splitting the original model into a coupled system. The first semi-discrete scheme follows the traditional LDG method by splitting second-order space derivative. The second one splits the original model for both time and space derivatives. The discontinuous Galerkin is used for the spatial discretization. Two kinds of fully discrete LDG schemes are presented by using the Grünwald-Letnikov and L1 approximation formulas for the time fractional derivatives. The $ L^2 $ norm stability and convergence analysis are carried out for both semi-discrete and fully discrete LDG schemes. The stability analysis reveals that the numerical schemes are unconditionally stable in $ L^2 $ norm and convergence with optimal convergence rate. Finally, numerical examples are presented to test the effectiveness of the proposed schemes and the correctness of the theoretical analysis.

On Transformation Form-Invariance in Thermal Convection.

Over the past two decades, effective control of physical fields, such as light fields or acoustics fields, has greatly benefited from transforming media. One of these rapidly growing research areas is transformation thermotics, especially embodied in the thermal conductive and radiative modes. On the other hand, transformation media in thermal convection has seldom been studied due to the complicated governing equations involving both fluid motion and heat transfer terms. The difficulty lies in the robustness of form invariance in the Navier-Stokes equations or their simplified forms under coordinate transformations, which determines whether the transformation operations can be executed on thermal convection to simultaneously regulate the flow and thermal fields. In this work, we show that thermal convection in two-dimensional Hele-Shaw cells keeps form-invariance, while its counterpart in general creeping flows or general laminar flows does not. This conclusion is numerically verified by checking the performances of invisible devices made of transformation media in convective environments. We further exploit multilayered structures constituted of isotropic homogeneous natural materials to realize the anisotropic inhomogeneous properties required for transformation media. Our results clarify the long-term confusion about the validation of the transformation method in thermal convection and provide a rigorous foundation and classical paradigm on inspiring various fascinating metadevices in both thermal and flow fields.