Isotropic Linear Elastic Material Research Articles

Numerical study on honeycomb membrane-type acoustic metamaterial with added mass

This paper presents numerical investigations on the transmission loss (TL) of a honeycomb structure with embedded membrane to which small masses are attached. The structure is a lightweight honeycomb membrane-type acoustic metamaterial that presents excellent transmission loss especially at low frequencies. The added mass is a solid material that is attached to the membrane, which is modelled as a linear isotropic elastic material with fixed boundary conditions. The influences of the membrane material properties and of the added mass parameters on the transmission loss are presented. It is demonstrated that the resonant peak amplitude of the transmission loss and its frequency band can be controlled by the properties of the added mass. The various numerical simulation results of configurations with and without added masses as well as various membrane elastic properties are compared. The honeycomb structure used in this study constitutes generally the core layer in sandwich honeycomb panels. While the TL of the honeycomb structure alone is zero, due to the open cell distribution, the integration of a membrane within the honeycomb with added masses induces a significant improvement of the transmission loss. This lightweight metamaterial is shown to attenuate the low frequency noise.

Implementing PGD technique in solving the problem of identifying Young's modulus of linear elastic isotropic material from full-field measurements by FEMU method

Implementing PGD technique in solving the problem of identifying Young's modulus of linear elastic isotropic material from full-field measurements by FEMU method

Numerical investigation of solitary wave attenuation by a vertical plate-type flexible breakwater using an FVM–FEM coupled model. Part 1: Linear elastic isotropic material

The use of flexible breakwaters to protect offshore areas from wave impacts has increased in recent years, owing to their cost effectiveness, environmental friendliness, and simple installation. This study proposes a finite-volume-method–finite-element-method coupled model based on waves2Foam, preCICE, and CalculiX to investigate wave attenuation by a vertical plate-type flexible breakwater under the impact of a solitary wave. The numerical model was validated by comparing the current results with previous numerical and experimental results. The proposed coupled model appropriately predicted the intricate flow phenomena of solitary waves impacting the flexible breakwater. The study systematically discusses the wave attenuation performance and structural response of the flexible breakwater under the impact of a solitary wave by considering several prominent factors: the mass coefficient, stiffness coefficient, and Poisson's ratio. Implementing a flexible breakwater effectively reduced wave energy intensity through various mechanisms, such as wave overtopping, wave breaking, and the dynamic response of the flexible breakwater. The material density had a negligible impact on the efficiency of the flexible breakwater in terms of wave dissipation and structural response; by contrast, the flexibility and compressibility of the breakwater significantly influenced the efficiency of the flexible breakwater. Employing a flexible breakwater fabricated using a compressible material is recommended for protecting coastal regions from wave-induced damage.

Transverse domain wall dynamics in hybrid piezoelectric/ferromagnetic devices

This work investigates the static and dynamic features of transverse domain walls in a magnetostrictive, linear elastic isotropic ferromagnetic material under the action of magnetic field (axial and transverse) and electric current. The investigation is done in the framework of the extended Landau–Lifshitz–Gilbert equation by taking into account the effects of stresses induced by a piezoelectric actuator and Rashba spin‐orbit torque caused by structural inversion asymmetry. First, we obtain the expression of magnetization orientation into the two faraway domains, then characterize the static magnetization profile under the action of magnetoelastic and transverse magnetic fields. Next, we introduce a trial function (Schryer and Walker type). After that, by adopting the small angle approximation formalism, we derive the explicit expression of key quantities such as propagating transverse domain wall profile, excitation angle, transverse domain wall velocity, mobility, and displacement. Finally, we present the numerical illustrations of derived analytical results and find that they are in qualitatively good agreement with the recent numerical simulations and experimental observations.

Optimal elastostatic cloaks

An elastic cloak hides a hole (or an inhomogeneity) from elastic fields. In this paper, a formulation of the optimal design of elastic cloaks based on the adjoint state method, in which the balance of linear momentum is enforced as a constraint, is presented. The design parameters are the elastic moduli of the cloak, and the objective function is a measure of the distance between the solutions in the physical and in the virtual bodies. Both the elastic medium and the cloak are assumed to be made of isotropic linear elastic materials. However, the proposed formulation can easily be extended to anisotropic solids. In order to guarantee smooth inhomogeneous elastic moduli within the cloak a penalization term is added to the objective function. Mixed finite elements are used for discretizing the weak formulation of the optimization problem. Several numerical examples of optimal elastic cloaks designed for both single and multiple loads are presented. We consider different geometries and loading types and observe that in some cases the optimal elastic cloaks for cloaking holes (cavities) are made of auxetic materials.

RESEARCH ON IMPACT LOADING OF A MOBILE TRACKED PLATFORM WITH AN AUTONOMOUS STABILIZATION SYSTEM

The work presents a developed 3D model of a mobile robotic platform with an autonomous stabilization system for reconnaissance operations. Mobile robotic platforms have been found to be widely used in intelligence because they can help gather information from dangerous and hard-to-reach places and reduce the risk to the lives of intelligence personnel. Unmanned aerial vehicles and mobile robotic platforms with tracks are mainly used in reconnaissance. An important distinguishing quality of tracked mobile robots is their maneuverability. Having an independent drive for each of the tracks separately, the mobile robot can easily change the direction of its own movement. A study on shock loads (external influences on the system that can cause deformation, damage or destruction) of a mobile tracked platform with an autonomous stabilization system was conducted and the obtained results were described. The SOLIDWORKS software environment was used to model the design of the mobile platform. For numerical studies on impact loads, it is advisable to use linear elastic isotropic materials and bilinear Mises plastic materials. The results of the simulation of the movement of the mobile platform of the developed structure and the stresses in the collision with different speeds of 1, 5, 10, 25 m/s and the platform material carbon steel and rubber are presented. It was established that when a mobile platform collides with speeds of up to 25 m/s, the maximum stresses do not exceed 1.85 MPa, which gives a sufficient margin of strength in the event of impact loads for the selected material of the mobile platform. The use of steel inserts allows you to reduce the value of the maximum contact stresses under impact load, but increases the cost of the mobile platform, increases the total weight and, accordingly, reduces the operating time from the installed power batteries.

MatNLI: An open-source MATLAB-based solver for the non-linear inversion in elastography

Elastography has emerged as one of the most promising non-invasive clinical tools. In elastography, a stiffness map or elastogram is generated by solving an inverse problem of elasticity utilizing the tissue motion data acquired using magnetic resonance imaging or ultrasound. Among various inverse algorithms devoted to elastography, non-linear inversion coupled with the finite element method has demonstrated excellent applicability in extracting complex physics of the tissue. The development and implementation of such an inverse algorithm are challenging and often unavailable to clinicians. In the present work, we offer an open-source parallel MATLAB implementation of an efficient non-linear inversion algorithm based on the finite element method for different isotropic material models, viz., linear elastic and viscoelastic materials in the regime of compressible and nearly incompressible materials. Additionally, the framework has been extended to account for anisotropy by assuming transversely isotropic material. For the optimization module, the gradient of the objective function to the model parameters has been computed using the Adjoint method. Different case studies involving smooth variations and piece-wise discontinuities in the material property distribution are explored, and the efficacy of the inversion algorithm in reconstructing the stiffness map is discussed. In addition, noise is added to the synthetic data to depict a realistic setup, i.e., to prevent inverse crimes, and enhance the numerical stability and robustness of the current implementation. The present framework with general-purpose computer implementation could be beneficial for academic and clinical uses and may aid researchers in strengthening their existing frameworks and developing new algorithmic ideas.

Dynamic buckling analysis of stiffened panels under in-plane uniaxial impact considering plate/web interaction

An analytical method is proposed by using the large-deflection theory to determine the axial dynamic buckling strength of stiffened panels with simply supported edges and isotropic linear-elastic materials. The buckling behavior of the attached plates and stiffener are separately expressed by various displacement functions. These displacement functions are expressed by trigonometric and hyperbolic series, which satisfy the boundary conditions and the motion governing equations for the stiffened panels. The method is validated by comparing its predictions with finite element results for a typical stiffened plate. Then, the influence of several critical parameters, including initial imperfection, impact load, and stiffener torsional rigidity, on the dynamic deflection and critical buckling load are studied. The results reveal that the local web behavior has a significant influence on the dynamic buckling behavior of stiffened panel.

Stress analysis of adhesive-bonded tubular-coupler joints with optimum-stiffness-composite adherend under axial tension, pressure, and thermal loading

With descriptions of fiber orientation variation, variable-stiffness composites (VSCs) have opened many new opportunities for structural designs because they offer tailorable material properties to increase the performance of composite structures. Using the concept of VSCs, this study aimed to determine the optimum adhesive-bonded tubular coupler joints subjected to tension, pressure, thermal load, and/or combinations thereof. The joint consists of three axisymmetric cylindrical adherends. The two inner adherends are made of a linear elastic isotropic material, whereas the outer adherend is composed of a symmetric balanced laminate. As the most complicated cases among others, owing to various stress components induced in the adherends and adhesive, the joints under these dominant in-plane normal force loadings are modeled to efficiently minimize stress concentrations in the thin adhesive layer. The unified theory of adhesive-bonded tubular joints was modified one step further to compute the optimum fiber angle variation using the constraint of linear distribution of the axial resultant forces in the adherends. From the methodological viewpoint, the results unveiled that the interfacial shear stress concentration in the adhesive layer was considerably diminished or even vanishes under all loading scenarios. The possibility of multiple optimum composite joints can be achieved, which otherwise are not straightforward to determine when using other analytical tubular joint models and optimization methods. Parametric studies of geometrical variables were also performed to provide a design guideline for optimum coupler joints with efficient mitigation of peak adhesive interfacial stresses.

Foreword to the special issue on new developments in structural stability.

Foreword to the special issue on new developments in structural stability.

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.

Elasticity imaging using physics-informed neural networks: Spatial discovery of elastic modulus and Poisson's ratio.

Elasticity imaging is a technique that discovers the spatial distribution of mechanical properties of tissue using deformation and force measurements under various loading conditions. Given the complexity of this discovery, most existing methods approximate only one material parameter while assuming homogeneous distributions for the others. We employ physics-informed neural networks (PINN) in linear elasticity problems to discover the space-dependent distribution of both elastic modulus (E) and Poisson's ratio (ν) simultaneously, using strain data, normal stress boundary conditions, and the governing physics. We validated our model on three examples. First, we experimentally loaded hydrogel samples with embedded stiff inclusions, representing tumorous tissue, and compared the approximations against ground truth determined through tensile tests. Next, using data from finite element simulation of a rectangular domain containing a stiff circular inclusion, the PINN model accurately localized the inclusion and estimated both E and ν. We observed that in a heterogeneous domain, assuming a homogeneous ν distribution increases estimation error for stiffness as well as the area of the stiff inclusion, which could have clinical importance when determining size and stiffness of tumorous tissue. Finally, our model accurately captured spatial distribution of mechanical properties and the tissue interfaces on data from another computational model, simulating uniaxial loading of a rectangular hydrogel sample containing a human brain slice with distinct gray matter and white matter regions and complex geometrical features. This elasticity imaging implementation has the potential to be used in clinical imaging scenarios to reliably discover the spatial distribution of mechanical parameters and identify material interfaces such as tumors. STATEMENT OF SIGNIFICANCE: Our work is the first implementation of physics-informed neural networks to reconstruct both material parameters - Young's modulus and Poisson's ratio - and stress distributions for isotropic linear elastic materials by having deformation and force measurements. We comprehensively validate our model using experimental measurements and synthetic data generated using finite element modeling. Our method can be implemented in clinical elasticity imaging scenarios to improve diagnosis of tumors and for mechanical characterization of biomaterials and biological tissues in a minimally invasive manner.

Computation of two dimensional mixed-mode stress intensity factor rates using a complex-variable interaction integral

The well-known interaction integral, also known as the M-integral or I-integral, is a method to compute the mixed-mode stress intensity factors (SIFs) for fracture mechanics problems. The capabilities of the M-integral are extended here to compute derivatives of the SIFs with respect to the crack extensions for an isotropic linear elastic material under static loading. These derivatives were calculated using the complex Taylor series expansion (CTSE) numerical differentiation method. The derivatives of the auxiliary fields are calculated by applying CTSE directly to the M-integral formulation. The derivatives of the actual displacement fields are computed using a hypercomplex-variable finite element method (ZFEM) that also employs CTSE. SIF rates with respect to all crack tips are computed in a single analysis. The method is general and can be easily extended to other two-dimensional loading scenarios and different material models in a straightforward manner through the use of the appropriate auxiliary fields. The complex-variable M-integral was implemented within the commercial finite element software Abaqus through a user-defined element subroutine (UEL). Numerical examples demonstrate the high accuracy of the method.

Providing a virtual material for simple estimation of fracture in U-notched highly orthotropic specimens with nonlinear behavior under mixed mode I/II loading

This research investigates the fracture toughness of U-notched Russian pine specimens with highly orthotropic nonlinear behavior under mixed mode I/II loading conditions theoretically and experimentally. The notch strength of orthotropic specimens is successfully predicted by introducing a novel two-step model of material simplification. Adopting this model, the nonlinear orthotropic material is equated with a virtual linear elastic isotropic material by coupling the Virtual Isotropic Material Concept and the Equivalent Material Concept. Therefore, the linear elastic notch fracture mechanics criteria, such as the mean stress and point stress models, can be basically employed to predict the notch fracture toughness of U-notched specimens made of nonlinear orthotropic material. Accordingly, the experimentally obtained notch strength of nonlinear orthotropic samples is predicted in the form of fracture limit curves and the curves of fracture initiation angle. It is shown that the two-step model proposed can be successfully applied for mixed mode I/II fracture estimation of notched orthotropic specimens with nonlinear behavior.

Isogeometric topology optimization of strain gradient materials

In this paper optimal topologies of isotropic linear elastic strain gradient materials are investigated by means of isogeometric topology optimization. The employment of strain gradient theory allows not only to capture the microstructural effects of materials but also to regularize stress/strain concentration phenomena and to address the so-called wedge forces. Isogeometric analysis is used in order to meet the requirements of higher-order continuity of strain gradient elasticity theory. For the purpose of determining the constitutive parameters of strain gradient materials, a novel experiment is conceived by using the Digital Image Correlation (DIC) technique. The so-called SIMP (Solid Isotropic Material with Penalization) method is applied to interpolate the material stiffness tensors (including the fourth-order and the sixth-order stiffness tensor) by power law with penalty. Benchmark numerical experiments are conducted to illustrate the computational effectiveness and numerical robustness of the proposed method.

Stress intensity factors, T-stresses and higher order coefficients of the Williams series expansion and their evaluation through molecular dynamics simulations

Molecular dynamics method and finite element analysis are applied for the analysis of the stress field in the neighborhood of the crack tip in a copper plate with a single edge notch. The molecular dynamics simulations implemented in a classical molecular dynamics code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) are aimed at evaluating classical continuum linear elastic fracture mechanics parameters such as stress intensity factors, T-stresses and higher order coefficients of the Williams power series expansion of the near crack stress field for Mode I, Mode II and Mixed Mode (Mode I + Mode II) loadings of the cracked specimen in isotropic linear elastic materials. The key objective of the study is the comparison of continuum and atomistic approaches for the estimation of the near crack tip fields using the example of one of the most common cracked configurations. Stress intensity factors, T-stresses and higher order coefficients of the Williams series expansion for a copper plate with the single edge notch under Mode I and Mixed Mode loadings are evaluated by atomistic modeling and by finite element method. The wide class of the computations in LAMMPS is performed. The atomistic values of stress intensity factors and higher order terms of the Williams series expansion are compared with the values obtained from the numerical solutions given by finite element method. It is shown that the continuum fracture theory successfully describes fracture and the near crack tip fields even at extremely confined singular stress field of only several nanometers. The angular distributions of the stress components from atomistic modeling are retrieved and compared with the angular distributions of the stresses from continuum linear elastic fracture mechanics. The comparison shows good agreement between two approaches.

Self-powering vibration sensor based on a cantilever system with a single-electrode mode triboelectric nanogenerator

Here, we report a vibration sensor based on a single-electrode mode triboelectric nanogenerator (TENG). The main objective of this study is to develop a vibration sensor (architecture) that can be employed in any application with minor design changes to meet individual objectives. Hence, a cantilever-based vibration system is selected, which offers optimum design control in fine-tuning the sensor to operate in the desired frequency spectrum. The cantilever’s proof mass is suspended by isotropic linear elastic material constituting a scalable and tunable cantilever–mass system. The oscillations create contact separation between the triboelectric-active layers (i.e. fluorinated ethylene–propylene copolymer and screen-printed zinc oxide), which develop triboelectric waveforms. This voltage waveform is used for both sensing and powering mechanisms. At resonance, the device produces peak-to-peak voltage, short-circuit current, and power density of 25 V, 10 µA, and 1.38 W m−2, respectively. To measure the influence of change in cantilever properties, we varied the number of cantilevers and evaluated the sensor performance. The sensor is reliable with >99% accuracy in a broad frequency range of 0–400 Hz. The sensor exhibits a maximum sensitivity of 14 V g−1 and can charge a 1 µF capacitor to 2.75 V in <150 s. The sensor is further tested on a lab-scale vacuum pump with known (induced) faults to estimate the sensor’s competence in detecting the machinery faults. Considering the market acceptability, the sensor is developed with established manufacturing techniques such as screen-printing, and laser cutting. This study hopes to bridge the lab-to-market gap for TENG-based (vibration) sensors.

Coefficients of the williams power expansion of the near crack tip stress field in continuum linear elastic fracture mechanics at the nanoscale

The paper presents the analysis of the stress field in the neighborhood of the crack tip by molecular dynamics method implemented in a classical molecular dynamics code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The molecular dynamics simulations are aimed at computing continuum linear elastic fracture mechanics parameters such as stress intensity factors, T-stresses and higher order coefficients of the Williams power series of the stress field in an isotropic linear elastic material. The overwhelming objective of the study is the comparison of continuum and atomistic approaches for the estimation of the near crack tip fields. Stress intensity factors, T-stresses and higher order coefficients of the Williams series expansion for a copper plate with a central crack under Mode I and Mixed Mode loadings are evaluated by atomistic modelling. The wide class of the computational experiments in LAMMPS is realized. The atomistic values of stress intensity factors and higher order terms of the Williams series expansion are compared with the values obtained from the classical solutions of continuum linear elastic fracture mechanics. It is shown that the continuum fracture theory successfully describes fracture and the near crack tip fields even at extremely confined singular stress field of only several nanometers. The circumferential distributions of the stress tensor components from atomistic modeling are retrieved and compared with the angular distributions of the stresses from linear elastic fracture mechanics. The comparison shows good agreement between two approaches.

Nondestructive measurements of elastic constants of thin rods based on guided waves

Thin rods have been widely used in mechanical systems. The elastic constants, such as Young’s modulus and Poisson’s ratio, are of great interest for evaluating the quality of thin rods. This paper proposes a nondestructive method, utilizing longitudinal guided waves at low frequency and flexural guided waves at high frequency, to approximate bar waves and transverse bulk waves, respectively. According to the approximate velocities of bar waves and transverse bulk waves, the elastic constants can be determined inversely. Both simulation and experiment are conducted on thin aluminum rods with known elastic constants. The measurement errors are less than 2.03%, demonstrating the correctness of proposed method. Then, the proposed method is applied on 20 thin basalt rods and 30 basalt fibers. The incident frequency ranges from 0.3 to 1.8 MHz, and the diameter of thin rods ranges from 0.58 to 1.51 mm. The determined Young’s modulus is 4.30% higher than the value from the destructive tensile tests, and the determined Young’s moduli increase linearly with the chemical content (Al2O3, MgO, TFe2O3, and TiO2). The proposed method and associated experimental and simulation techniques can be used in the quality control and nondestructive testing of rod-like structures made by homogenous isotropic linear elastic materials.

Effect of Displacement Degree of Distal Chevron Osteotomy on Metatarsal Stress: A Finite Element Method.

Simple SummaryIn this study, the finite element method was used to explore the effect of distal chevron osteotomy displacement on metatarsal stress. For the subjects used in this study, the metatarsal stress was minimized by moving 4 mm. For the displacement of chevron osteotomy, both postoperative stability and stress distribution of metatarsal should be considered. The most appropriate distance is suggested to be obtained by combining HVA, IMA, age, body weight, and metatarsal width. The finite element method can be used for preoperative estimation of chevron osteotomy and guide the operation.Background: The stress of foot bone can effectively evaluate the functional damage caused by foot deformity and the results of operation. In this study, the finite element method was used to investigate the degree of displacement of distal chevron osteotomy on metatarsal stress and metatarsophalangeal joint load; Methods: Four finite element models of displacement were established by using the CT images of a patient with moderate hallux valgus (hallux valgus angle and intermetatarsal angle were 26.74° and 14.09°, respectively), and the validity of the model was verified. Each finite element model consisted of bones and various cartilage structures, ligaments, and plantar fascia, as well as encapsulated soft tissue. Except for soft tissue, the material properties of other parts were isotropic linear elastic material, and the encapsulated soft tissue was set as nonlinear hyperelastic material. The mesh was tetrahedral mesh. Link elements were used in ligament and plantar fascia. A ground reaction force with a half-body weight was applied at the bottom of the floor to simulate the ground reaction when standing. The upper surfaces of the encapsulated soft tissue, distal tibia, and distal fibula were fixed. The stress distribution of metatarsals and the stress of cartilage of the first metatarsophalangeal joint were compared and analyzed; Results: Compared with the hallux valgus without osteotomy, the stress of the first metatarsals and second metatarsals of 2–4 mm decreased, and the stress of the interarticular cartilage of the first metatarsophalangeal joint with 4 mm was reduced. In the case of 6 mm, the stress value between the first metatarsal and the first metatarsophalangeal joint increased, and 4 mm was the most suitable distance; Conclusions: Compared with the hallux valgus without osteotomy, the stress of the first metatarsals and second metatarsals of 2–4 mm decreased, and the stress of the interarticular cartilage of the first metatarsophalangeal joint with 4 mm was reduced. In the case of 6 mm, the stress value between the first metatarsal and the first metatarsophalangeal joint increased, and 4 mm was the most suitable distance. For the degree of displacement of the distal chevron osteotomy, the postoperative stability and the stress distribution of metatarsal bone should be considered. Factors such as hallux valgus angle, intermetatarsal angle, patient’s age, body weight, and metatarsal width should be considered comprehensively. The factors affecting osteotomy need to be further explored. The degree of displacement of osteotomy can be evaluated by FE method before the operation, and the most suitable distance can be obtained.