Isotropic Research Articles

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.

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.

A novel multiscale prediction strategy for simulating the progressive damage behavior of plain-woven bamboo fabrics reinforced epoxy resin composites

This study proposed a novel multiscale prediction strategy, including mesoscale and macroscale damage evolution modeling, to investigate the effective properties and progressive damage failure behavior of plain-woven reinforced composites (PWRCs) under various external loads (tension, compression). A high-precision mesoscale representative volume element (RVE) that could accurately describe the local mechanical behavior of PWRCs was developed by combining experimental characterization (scanning electron microscope and X-ray computed tomography) and numerical simulation. To solve the problem of inaccurate prediction results caused by multiscale characteristics and complex stress changes in the damaged area of PWRCs, the strain-based 3D Hashin failure criterion and the multiscale damage models were used to predict the damage initiation and evolution of mesoscale reinforcement (bamboo fiber yarn bundle) and macroscale composites, respectively. Considering the damage evolution law of isotropic materials, a damage model based on the Von Mises criterion was used to characterize the damage initiation and evolution of mesoscale matrix epoxy resin (EP) under external loading. The effective properties and mechanical behavior of the PWRCs were transferred from mesoscale to macroscale through the progressive homogenization method. The bilinear constitutive relationship of the mixed-mode cohesive element was used to characterize the interlaminar failure of the PWRCs. Finally, the corresponding mechanical characterization (tension, compression) of the PWRCs was carried out. Moreover, the experimental results were highly consistent with the simulation results, verifying the reliability of the novel multiscale prediction strategy in investigating the mechanical response of the PWRCs at multiple scales and revealing the damage mechanism of the PWRCs.

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.

Analytical prediction and numerical verification of stress concentration profile around an in-situ tow break in resin-impregnated filament-wound composites

A new empirical analytical approach is developed for predicting the stress concentration profile around an in-situ tow break in filament-wound composites. A shear-lag analysis is firstly performed to solve for the perturbational axial displacement of the broken tow and resultant debonding lengths. Solution of stress field caused by tangential load on the surface of an elastic half space is then utilized in combination with superposition principle to obtain the overload magnitudes in the neighboring tows. Subsequently, high-fidelity finite element analysis on a representative uni-directional laminate model under different stress states is performed, and excellent overall agreement is observed between analytical and numerical predictions. The proposed method takes into account essential aspects such as transversely isotropic material properties, in-situ stress states and their effect on the interfacial frictional forces in the debonded interfaces, and thus provides a convenient way to evaluate the stress concentration factors in damaged filament-wound composites. In addition, this approach can be applied to yield auxiliary failure evaluation criteria for statistical strength prediction or finite element modeling of filament-wound composites or similar 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.

Topology optimization based on improved DoubleU-Net using four boundary condition datasets

Topology optimization is extensively employed in engineering design. However, applying deep learning to solve topology optimization problems faces challenges owing to limited training data and model adaptability to various boundary conditions. To address these challenges, this research has employed a solid isotropic material with a penalization method to produce a dataset of 400,000 2D samples covering four boundary conditions. Each boundary condition includes two resolution datasets. Moreover, an improved DoubleU-Net model is proposed for real-time topology optimization, ensuring high-accuracy predictions. On the test dataset, the average Intersection over Union (IoU) accuracies of the proposed model for the four boundary conditions above are 93.26%, 96.71%, 96.35% and 97.38%. This research also investigated the impact of different structural datasets on the model's generalization capability. The experimental results indicate that the model trained on random structures exhibits excellent testing performance and demonstrates robust generalization capability.

Effective mechanical behaviors of transverse isotropic materials containing compressible liquid inclusions with surface effects

Porous media with fluid-saturated microchannels, prevalent in biomaterials, tissue engineering materials and flexible electronic devices, can be modelled as transverse isotropic materials. Surface effects can influence significantly the macro-mechanical responses of such materials, particularly for soft materials with micro- or nano-scale channels. In this study, we first develop constitutive laws for fluid saturated porous materials with microchannels by integrating the top-down (homogenization) approach with the bottom-up (micromechanics) approach. We then explicitly establish a connection between surface effects and macro-mechanical responses. Employing the generalized self-consistent model (GSCM), we estimate the effective parameters (i.e., coefficients in constitutive equations governing macro-mechanical responses), with fluid compressibility and surface effects accounted for. Our findings reveal that, as surface energy increases, the effective transverse shear modulus is enlarged, the effective plane strain bulk modulus, the unit uniaxial straining modulus and the cross modulus are all reduced, but the axial shear modulus remains nearly unchanged. As an application, we characterize the mechanical behaviors of the transverse isotropic fluid-saturated porous material with surface effects by connecting the classic Mandel solution with the estimated effective parameters. The pore pressure exhibits the Mandel-Cryer effect. The insights gained from this study are valuable for comprehending and exploring the intricate ways in which surface effects influence the mechanical responses of transversely isotropic fluid-saturated porous materials featuring sufficiently small channels.

Optimal design of elastic plates

This paper is concerned with optimal design problems in the setting of the Kirchhoff–Love 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.

Influence of the sensitivity of plastic deformation to the third invariant on the stress state achievable during stretch forming of isotropic materials

Influence of the sensitivity of plastic deformation to the third invariant on the stress state achievable during stretch forming of isotropic materials

Multiscale design based on non-penalization smooth-edged material distribution for optimizing topology (SEMDOT)

This paper presents a concurrent topology optimization method for macro and micro phases based on non-penalization smooth-edged material distribution for optimization topology (SEMDOT) method. Although there is existing research on the multiscale design method, grayscale elements are always emerged especially for penalization method for example the solid isotropic material penalization (SIMP) method, also high computational cost are required when large scale of elements are utilized for obtaining high resolution structures. The methodology proposed here aims to apply a new tech called non-penalization SEMDOT method to find the optimum layout on both scales of elements, it is assumed that the macro structure is composed of periodic materials and both element scales are optimized through their linearly interpolated grid points. The effective macroscopic properties are evaluated by the homogenization method. The approach could provide smooth and clear boundaries for multiscale system without grayscale elements or high computational cost. A series of numerical examples are presented to demonstrate the effectiveness and the efficiency of the proposed method.