Isotropic Research Articles

The Thermoelastic Dynamic Response of a Rod Due to a Moving Heat Source under the Fractional-Order Thermoelasticity Theory

In this paper, the thermoelastic behavior of a rod made of an isotropic material under the action of a moving heat source was investigated using a new theory of thermoelasticity related to fractional-order time with two relaxation times. A mathematical model of the one-dimensional thermoelasticity problem was established based on the new thermoelasticity theory. We considered the symmetry of the material, and the fractional-order thermoelasticity control equation was given. Subsequently, the control equations were solved and analyzed using the Laplace transform and its inverse transform. This study examined the effects of fractional-order parameters, time, two thermal relaxation times, and the speed of movement of the heat source on the displacement, temperature, and stress distribution patterns in the rod.

Finite element graft stress for anteromedial portal, transtibial, and hybrid transtibial femoral drillings under anterior translation and medial rotation: an exploratory study

Stress concentration on the Anterior Cruciate Ligament Reconstruction (ACLr) for femoral drillings is crucial to understanding failures. Therefore, we described the graft stress for transtibial (TT), the anteromedial portal (AM), and hybrid transtibial (HTT) techniques during the anterior tibial translation and medial knee rotation in a finite element model. A healthy participant with a non-medical record of Anterior Cruciate Ligament rupture with regular sports practice underwent finite element analysis. We modeled TT, HTT, AM drillings, and the ACLr as hyperelastic isotropic material. The maximum Von Mises principal stresses and distributions were obtained from anterior tibial translation and medial rotation. During the anterior tibia translation, the HTT, TT, and AM drilling were 31.5 MPa, 34.6 Mpa, and 35.0 MPa, respectively. During the medial knee rotation, the AM, TT, and HTT drilling were 17.3 MPa, 20.3 Mpa, and 21.6 MPa, respectively. The stress was concentrated at the lateral aspect of ACLr,near the femoral tunnel for all techniques independent of the knee movement. Meanwhile, the AM tunnel concentrates the stress at the medial aspect of the ACLr body under medial rotation. The HTT better constrains the anterior tibia translation than AM and TT drillings, while AM does for medial knee rotation.

Negative reflection and total internal reflection at the internal surface of lithium niobate crystal

In this paper we analytically find out the expression for the wave vector and Poynting vector in the reflection domain for negative uniaxial material. We investigate the impact of the optical axis rotation and incident angle on the wave vector and Poynting vector reflected from the internal surface of lithium niobate crystal when the light is propagating from the denser anisotropic medium to the rarer isotropic medium. We derive the Brewster angle condition and discuss the walk-off between TE and TM polarized light. We explore where the wave vector and Poynting vector are parallel after reflection. In further analysis, we look into the phase differences between ordinary and extraordinary reflected light after total internal reflection from the internal surface of lithium niobate crystal. The necessary conditions for linear polarization and circular polarization have been established. The impact of optical axis orientation is also taken into consideration. The refractive index for the isotropic material for the desired polarization response has been found as 2.18, 2.1, and 2.03 at 632 nm, 1550 nm, and 3500 nm, respectively.

Anisotropic functionally graded nano-beam models and closed-form solutions in plane gradient elasticity

This study delves into the investigation of exact analytical solutions for the plane stress and displacement fields within linear homogeneous anisotropic nano-beam models of gradient elasticity. It focuses on solving the Helmholtz equation, which encompasses a second-order non-homogeneous linear partial differential equation in plane gradient elasticity theory, utilizing polynomial series-type solutions. The analysis centers on the utilization of gradient Airy stress functions to derive stress fields in the gradient theory. The research yields closed-form analytical solutions for Airy stress functions, stress, and strain fields in both classical and gradient theories. The study considers five distinct types of two-dimensional functionally graded cantilever beams with various boundary conditions: a cantilever anisotropic nano-beam subjected to a concentrated force at the free end, a cantilever anisotropic nano-beam under a uniform load, a simple anisotropic nano-beam under a uniform load, a propped cantilever anisotropic nano-beam under a uniform load, and a fixed end cantilever anisotropic nano-beam under a uniform load. General analytical solutions for the gradient stress and displacement fields of two-dimensional and one-dimensional anisotropic nano-beams under different boundary conditions are provided. The study showcases significant strain gradient size effects at the nano-scale through the derived analytical solutions for anisotropic beams. Additionally, it demonstrates that the strain gradient theory results for the limit case of the gradient coefficient c precisely align with results for isotropic and anisotropic materials in elasticity theory and classical theory. Furthermore, real-world applications are discussed, considering stress and displacement fields in real anisotropic materials such as TiSi2 single crystals and orthotropic materials, which are special cases of anisotropic materials like wood and epoxy as documented in the literature.

Critical Velocities of Single-layer and Two-layer Composite Tubes of Transversely Isotropic Materials Based on a Potential Function Method in 3-D Elasticity

Abstract Critical velocities of a single-layer tube of a transversely isotropic material and a two-layer composite tube consisting of two perfectly-bonded cylindrical layers of dissimilar transversely isotropic materials are analytically determined using the potential function method of Elliott in three-dimensional (3-D) elasticity. The displacement and stress components in each transversely isotropic layer of the tube subjected to a uniform internal pressure moving at a constant velocity are derived in integral forms by applying the Fourier transform method. The solution includes those for a tube composed of two dissimilar cubic or isotropic materials as special cases. In addition, it is shown that the model for the two-layer composite tube can be reduced to that for the single-layer tube. Closed-form expressions for four critical velocities are derived for the single-layer tube. The lowest critical velocity is obtained from plotting the velocity curve and finding the inflection point for both the single-layer and two-layer composite tubes. To illustrate the newly developed models, two cases are studied as examples – one for a single-layer isotropic steel tube and the other for a two-layer composite tube consisting of an isotropic steel inner layer and a transversely isotropic glass-epoxy outer layer. The numerical values of the lowest critical velocity predicted by the new 3-D elasticity-based models are obtained and compared with those given by existing models based on thin- and thick-shell theories.

A Methodology for Post-Necking Analysis in Isotropic Metals

Metallic materials are commonly characterized through tensile tests. For ductile metals, a consistent part of the test occurs after the necking onset. A first estimate of the post-necking behavior could be obtained by extrapolating the mathematical model that fits the pre-necking law. However, as well known, the accuracy of the predictions would not be guaranteed. Therefore, over the past decades many efforts have been devoted to dealing with the necking phenomenon. The most popular correction formula proposed by Bridgman is an analytical method based on the neck geometry. Despite being widely used, it may not be accurate at large strains due to the assumption of uniform distribution of the equivalent stress and equivalent strain in the specimen minimum cross-section. Starting from Bridgman’s idea and in order to overcome its limitations, the present paper develops an efficient method to calibrate the hardening law of isotropic metallic materials at large strains. The proposed method requires to record the outer contour of the necking zone during the test and to build a dataset of necking deformed shapes. Experimental quasi-static tensile tests were analyzed with the proposed approach, which appears promising when critically compared with other methods.

Topological optimization in 3D-magnetostatics: development of adjoint methods using the equations of magnetic moments

Purpose The purpose of this paper is mainly to develop the adjoint method within the method of magnetic moment (MMM) and thus, to provide an efficient new way to solve topology optimization problems in magnetostatic to design 3D-magnetic circuits. Design/methodology/approach First, the MMM is recalled and the optimization design problem is reformulated as a partial derivative equation-constrained optimization problem where the constraint is the Maxwell equation in magnetostatic. From the Karush–Khun–Tucker optimality conditions, a new problem is derived which depends on a Lagrangian parameter. This problem is called the adjoint problem and the Lagrangian parameter is called the adjoint parameter. Thus, solving the direct and the adjoint problems, the values of the objective function as well as its gradient can be efficiently obtained. To obtain a topology optimization code, a semi isotropic material with penalization (SIMP) relaxed-penalization approach associated with an optimization based on gradient descent steps has been developed and used. Findings In this paper, the authors provide theoretical results which make it possible to compute the gradient via the continuous adjoint of the MMMs. A code was developed and it was validated by comparing it with a finite difference method. Thus, a topology optimization code associating this adjoint based gradient computations and SIMP penalization technique was developed and its efficiency was shown by solving a 3D design problem in magnetostatic. Research limitations/implications This research is limited to the design of systems in magnetostatic using the linearity of the materials. The simple examples, the authors provided, are just done to validate our theoretical results and some extensions of our topology optimization code have to be done to solve more interesting design cases. Originality/value The problem of design is a 3D magnetic circuit. The 2D optimization problems are well known and several methods of resolution have been introduced, but rare are the problems using the adjoint method in 3D. Moreover, the association with the MMMs has never been treated yet. The authors show in this paper that this association could provide gains in CPU time.

Precise Crystal Orientation Identification and Twist-Induced Giant Modulation of Optical Anisotropy in 1T'-ReS2.

The ability to precisely identify crystal orientation as well as to nondestructively modulate optical anisotropy in atomically thin rhenium dichalcogenides is critical for the future development of polarization programmable optoelectronic devices, which remains challenging. Here, we report a modified polarized optical imaging (POI) method capable of simultaneously identifying in-plane (Re chain) and out-of-plane (c-axis) crystal orientations of the monolayer to few-layer ReS2, meanwhile, propose a nondestructive approach to modulate the optical anisotropy in ReS2 via twist stacking. The results show that parallel and near-cross POI are effective to independently identify the in-plane and out-of-plane crystal orientations, respectively, while regulating the twist angle allows for giant modulation of in-plane optical anisotropy from highly intrinsic anisotropy to complete optical isotropy in the stacked ReS2 bilayer (with either the same or opposite c-axes), as well modeled by linear electromagnetic theory. Overall, this study not only develops a simple optical method for precise crystal orientation identification but also offers an efficient light polarization control strategy, which is a big step toward the practical application of anisotropic van der Waals materials in the design of nanophotonic and optoelectronic devices.

Optimal design of elastic plates

This paper is concerned with optimal design problems in the setting of the KirchhoffLove model for pure bending of a thin solid symmetric plate under a transverse load. For two isotropic elastic materials with a prescribed amount, the goal is to find their rearrangement within the domain that forms a least compliant structure. The homogenization method is used as a relaxation tool to overcome the lack of a classical solution of optimal design problem. Neccessary conditions of optimality were derived and an optimality criteria method for the single state compliance minimization problems is developed and tested on several examples.

Lightweight Potential of Anisotropic Plate Lattice Metamaterials

Additive manufacturing enables the production of lattice structures, which have been proven to be a superior class of lightweight mechanical metamaterials whose specific stiffness can reach the theoretical limit of the upper Hashin–Shtrikman bound for isotropic cellular materials. To achieve isotropy, complex structures are required, which can be challenging in powder bed additive manufacturing, especially with regard to subsequent powder removal. The present study focuses on the Finite Element Method simulation of 2,5D anisotropic plate lattice metamaterials and the investigation of their lightweight potential. The intentional use of anisotropic structures allows the production of a cell architecture that is easily manufacturable via Laser Powder Bed Fusion (LPBF) while also enabling straightforward optimization for specific load cases. The work demonstrates that the considered anisotropic plate lattices exhibit high weight-specific stiffnesses, superior to those of honeycomb structures, and, simultaneously, a good de-powdering capability. A significant increase in stiffness and the associated surpassing of the upper Hashin–Shtrikman bound due to anisotropy is achievable by optimizing wall thicknesses depending on specific load cases. A stability analysis reveals that, in all lattice structures, plastic deformation is initiated before linear buckling occurs. An analysis of stress concentrations indicates that the introduction of radii at the plate intersections reduces stress peaks and simultaneously increases the weight-specific stiffnesses and thus the lightweight potential. Exemplary samples illustrate the feasibility of manufacturing the analyzed metamaterials within the LPBF process.

Bound states in the continuum for antisymmetric lamb modes in composite plates made of isotropic materials

In this study, we report a numerical design and observation of bound states in the continuum (BICs) for Lamb waves. BICs for elastic-wave systems, especially in non-periodic configurations, are difficult to obtain due to their intricate polarization states. However, the study in this matter has become very important, especially in the field of opto-mechanics or other multi-field couplings at micro or nanoscales. To illustrate the design concept, we simulate the introduction of a piece of silica (SiO2) into a thin infinite Si plate and show that, for specific aspect ratios, BICs for elastic waves can be predicted. We present numerical results for both two-dimensional (2D) rectangular plates and three-dimensional (3D) disk structures. Moreover, we also investigate the modal contributions of both the background and inclusion media during the occurrence of BICs, further verifying the physical background of our design strategy. Although we have focused our work on asymmetric Lamb modes, the current method can also be applied to construct other types of elastic-wave BICs, providing a powerful tool for metamaterial device prototyping based on the control or guiding of elastic waves.

Study on Fracture Characteristics of Layered Sandstone under Asymmetric Loading.

In engineering practice, layered rock masses often display obvious anisotropy while deforming and failing, and the failure mode directly impacts the engineering construction stability. In this study, the fracture failure load, fracture toughness, crack deflection angle, and failure mode of a layered rock mass under different fracture modes were analyzed by utilizing improved asymmetric semi-circular disc specimens. According to the constitutive model of transversely isotropic materials, the maximum tensile stress (MTS), maximum energy release rate (MERR), and maximum strain energy density (MSED) calculation formulas were modified, and the calculation formulas of the three prediction criteria under anisotropic materials were derived. The calculation results were compared with the experimental results. The results show that the fracture toughness and crack deflection angle were significantly affected by the weak bedding plane. As a result of applying the MTS criterion, the results are closer to the experimental results, providing a solid foundation for engineering deformation, failure, and fracture analyses.

Real‐time topology optimization via learnable mappings

AbstractIn traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering contexts. This work proposes a multi‐stage machine learning strategy that aims to predict an optimal topology and the related stress fields of interest, either in 2D or 3D, without resorting to any iterative analysis and design process. The overall topology optimization is treated as regression task in a low‐dimensional latent space, that encodes the variability of the target designs. First, a fully‐connected model is employed to surrogate the functional link between the parametric input space characterizing the design problem and the latent space representation of the corresponding optimal topology. The decoder branch of an autoencoder is then exploited to reconstruct the desired optimal topology from its latent representation. The deep learning models are trained on a dataset generated through a standard method of topology optimization implementing the solid isotropic material with penalization, for varying boundary and loading conditions. The underlying hypothesis behind the proposed strategy is that optimal topologies share enough common patterns to be compressed into small latent space representations without significant information loss. Results relevant to a 2D Messerschmitt‐Bölkow‐Blohm beam and a 3D bridge case demonstrate the capabilities of the proposed framework to provide accurate optimal topology predictions in a fraction of a second.

BASES OF THE METHOD OF PHYSICAL MODELING OF THE PROCESS OF CRUSHING OF MUNICIPAL SOLID WASTE

A large number of studies are aimed at increasing the energy efficiency of grinding processes of various solid materials, while maintaining the values ​​of other important indicators, such as material consumption, productivity, etc. Based on this trend, a new method for physically modeling the process of grinding municipal solid waste (MSW) was proposed for the first time. Existing physical modeling techniques are designed for homogeneous and isotropic materials (for example, soil, crushed stone, snow, coal, etc.). The strength properties of solid waste vary widely due to the significant heterogeneity of their components. Consequently, when crushing solid waste, traditional crusher designs have low efficiency in terms of energy intensity, material intensity and product quality. The purpose of this work is to develop a new technique for physical modeling of the grinding process, based on the main principles of similarity theory and modeling, considering the properties of waste heterogeneity. As a result of the research, a block diagram of the physical modeling methodology for the interaction of the working bodies of impact crushing machines with solid waste was developed. A list of tasks for the modeling process and similarity criteria have been determined based on the development of rheological models of the “working body - municipal solid waste” system and the laws of mechanics that characterize the waste grinding process. Based on the developed similarity criteria, scale equations for the grinding process are substantiated and formulas are derived for determining the expected parameters of the original based on the parameters measured on the model. The developed methodology makes it possible to create a crusher design with improved energy efficiency indicators with the least material and labor costs.

Orthotropic failure criteria based on machine learning and micro-mechanical matrix adapting coefficient

Several studies have examined the use of fibrous and non-fibrous anisotropic materials in various industries and proposed failure criteria for consideration. These criteria can be categorized into theories that address specific failure modes and those that do not. However, these theories often fail to address both the representation of inherent material properties and the combination of different loading modes. To address this, a micromechanical approach called micromechanical modeling of laminates (“MACML”) has been developed, which gradually transitions from anisotropic to isotropic materials by incorporating reinforcement and adapting coefficients. MACML combines machine learning (ML) techniques and introduces a new method to identify safe and failure-prone regions in composites. This approach allows for independence from the influence of fibers by representing them as an active stress proportion of the isotropic matrix. Additionally, standard experimental procedures can be applied based on the isotropic matrix, and experimental results have been conducted to validate the established failure criteria in the MACML method.

Anisotropic materials with abnormal Poisson's ratios and acoustic velocities.

Isotropic materials are required to adhere to various mechanical principles due to their limited thermal stability. For instance, it is essential for Poisson's ratio to be within the range of -1 to 0.5, and the longitudinal wave velocity must exceed the transverse wave velocity. Nevertheless, perfect crystals, as anisotropic materials, have the ability to defy conventional rules. Through the integration of high-throughput processes and first-principles calculations, a comprehensive exploration of known materials was conducted, resulting in the establishment of a database featuring an extreme anisotropic mechanism. This included the identification of abnormal Poisson's ratios (with the directional Poisson's ratio ranging from -3.00 to 3.67), the discovery of extreme negative linear compressibility, the determination of the upper and lower limits of the sound velocity, and other associated properties. Several materials with abnormal Poisson's ratios (<-1 or >0.5) were listed, and their peculiar mechanical behavior, wherein the volume decreased counterintuitively with uniaxial tension, was discussed. Finally, this study focused on the velocities of longitudinal and transverse waves, with specific emphasis on materials exhibiting transverse wave velocities that exceeded the longitudinal wave velocities.

Uniaxial stress effect on the electronic structure of quantum materials

Uniaxial stress has proven to be a powerful experimental tuning parameter for effectively controlling lattice, charge, orbital, and spin degrees of freedom in quantum materials. In addition, its ability to manipulate the symmetry of materials has garnered significant attention. Recent technical progress to combine uniaxial stress cells with quantum oscillation and angle-resolved photoemission techniques allowed to study the electronic structure as function of uniaxial stress. This review provides an overview on experimental advancements in methods and examines studies on diverse quantum materials, encompassing the semimetal WTe2, the unconventional superconductor Sr2RuO4, Fe-based superconductors, and topological materials.

An efficient multi-field dynamic model for 3D wave propagation in saturated anisotropic porous media

An efficient multi–field coupled dynamic model for saturated anisotropic porous materials is proposed here. The mathematical formulation of the dynamic deformation–diffusion problem is developed starting from the mixture theory and the definition of the effective stress for anisotropic poro–elasticity, taking into account also the fluid phase compressibility and anisotropic permeability. The effective stress principle is properly extended through the Biot tensor to predict the coupling between the shear stress of the solid skeleton and the pore fluid pressure. Numerical solution of the coupled problem is obtained by inf-sup stable Finite Element spaces. A fundamental issue for the computational efficiency of the coupled model is the numerical solution of the resulting large–size and non–symmetric discrete problem. In this work, we develop a fully implicit monolithic solver based on the Bi–Conjugate Gradient Stabilized (Bi-CGStab) algorithm accelerated via an ad–hoc Multi–Physics Reduction (MPR) preconditioning technique. The proposed advances are implemented in the 3D GeoMatFem research code and several numerical analyses are performed to test the potential and computational efficiency of the proposed tool. In particular, we focus on 3D wave propagation applications in fully saturated single and multi-layered anisotropic media. Numerical results show that our implementation is able to identify the shear wave splitting phenomenon due to the different degree of material symmetry between the solid phase and the whole porous material.

The stacking sequence optimisation of a filament wound composite bicycle frame using the data-driven evolutionary algorithm EvoDN2

ABSTRACT This work focusses on identifying the optimal stacking sequence for composite tubes in mountain bike frames using a data-driven model combined with evolutionary algorithms. The objective is to find a frame that is sufficiently stiff while meeting the requirements of weight, strength, and minimum tube wall thickness. The decision variables are the ply winding angles and the ply thicknesses of each tube. The study performs designs for two load cases – Starting and Uphill – and explores two types of winding: the gradual winding of individual layers (1ply) and the winding of layers between predefined inner and outer layers with variable thicknesses (TW). Additionally, the design process is applied to frames made of isotropic materials, such as steel, aluminium, and titanium, using the same methodology to allow for comparison of results. The article demonstrates the successful application of this methodology to common sports equipment, suggesting its potential for beneficial use in other common composite frame structures.

Experimental and numerical study on mechanical behavior of 3D printed adhesive joints with polycarbonate substrates

AbstractAdhesive joints play a crucial role in enhancing the structural integrity and performance of 3D printed parts. The purpose of this study is to investigate the failure load and behavior of polycarbonate (PC) single lap joints (SLJs) produced by fused deposition modeling (FDM) using experimental and finite element analysis (FEA) methods. The FEA of joints presents a new approach by integrating PC substrates with Hill yield criterion, transversely isotropic material and adhesive layer with cohesive zone modeling (CZM). The study focused on the effect of printing angles (0°, 45°, and 90°) and overlap lengths (12.5 and 25 mm) on the performance of SLJs. The influence of 3D printing parameters on the mechanical behavior of PC joints was investigated by tensile testing of SLJs. The experimental failure load was 1586 N for a 12.5 mm joint at 90° and 4115 N for a 25.4 mm joint at 0°. Comparison of the experimental and FEA failure loads of the joints showed maximum and minimum differences of 11.98% and 1.34%, respectively. This result showed that the proposed model is applicable for determining the joint strength as a function of the printing angle and monitoring the joint damage behavior.