Isotropic Research Articles

Ionic 2D Materials

2D materials are an exciting topic with a wide variety of applications in many research fields, from optoelectronics, photonics or qubit devices to catalysis. So far, these layered nanoscopic materials have been obtained by different procedures. In top-down approaches, from simple mechanical "Scotch tape" exfoliation to liquid exfoliation to break the weak non-covalent interactions between layers. In this project, the challenge was to obtain 2D flakes of a 3D ionic starting material with cubic rock salt structure (e.g. alkali halides NaCl, NaF, KCl, KF or CsF). They will have physical properties with substantial differences from those of known 2D materials. For example, there are few large bandgap 2D materials, almost exclusively BN layers. The BN bulk system has a band gap around 4 eV and its monolayer 6 eV, while the employed alkali halides in this project, the bulk vales are 10.0 eV (CsF), 10.9 eV (KF), 11.7 eV (NaF), KCl eV (8.5) and eV NaCl (8.6). This will open many applications that are now only restricted to BN layers. The crucial point is how it is possible to exfoliate an isotropic 3D material with ionic interactions in three spatial directions.(1,2) The intercalation of bromine molecules in CsF was corroborated, many years ago, by X-ray single-crystal diffraction.(1,3, see Figure) The intercalated structure is analogous to that of other conventional 2D materials; for example, graphene also with bromine molecules. This intercalation into the 3D structure of the alkali halide has two effects, one is to generate an anisotropic 2D structure with alternated monoatomic CsF layers and layers of Br2 molecules. The second important effect is that now for the exfoliation of the CsF-Br2 compound, only the non-ionic F···Br-Br interactions must be broken. Preliminary DFT calculations indicate that such contact energies are of the same order of magnitude as other non-covalent interactions of common 2D materials.The intercalation of such 2D materials has been performed by the intercalation of Br2 and IBr molecules combined with different exfoliation techniques (sonication-centrifugation, ball milling, microwaves..). The characterization of the 2D flakes has been performed using Atomic Force Microscopy. The final goal of this project is to make a profit from the large gap of such 2D systems for optoelectronic properties, such as single-photon emission.(1) Desmarteau, D. D.; Grelbig, T.; Hwang, S. H.; Seppelt, K., Angewandte Chemie-International Edition in English 1990, 29 (12), 1448-1449(2) Ruiz, E.; Alvarez, S., Journal of the American Chemical Society 1995, 117 (10), 2877-2883.(3) Drews, T.; Marx, R.; Seppelt, K., Chemistry-a European Journal 1996, 2 (10), 1303-1307. Figure 1

Study on unified strength theory and elastic–plastic stress update algorithm

The unified strength theory with the two-piecewise linear equations is more convenient and concise to calculate the strength of materials. It can fully explore the potential in the strength of materials and improve the economic benefits of engineering design. This study combines the semi-implicit return mapping algorithm and the Aitken accelerated iteration scheme and develops a plastic constitutive algorithm for isotropic softening materials based on the unified strength theory. The combining method can simplify the stress update and make the calculation of consistent tangent modulus easier. Furthermore, it can avoid solving the partial derivatives of the plastic flow rule and overcome the stress-deviating problem. The self-developed constitutive algorithm is used to simulate the elastic–plastic excavation process of a deep-lying circular tunnel. The numerical simulation results match well with the theoretical solution, verifying the correctness of the self-developed constitutive algorithm. Based on the self-developed constitutive algorithm, the stability of an underground mining stope is comprehensively analyzed, and its structural parameters are optimized. The research reveals the mechanism of stope instability, provides a reliable scientific basis for the mining design and decision-making, ensures the safe and efficient production of the stope, and achieves the expected goal.

A Dataset Generation Framework for Symmetry-Induced Mechanical Metamaterials

Abstract The surge in machine learning research and recent advancements in 3D printing technologies have significantly enriched materials science and engineering, particularly in the domain of mechanical metamaterials, which commonly consist of periodic truss materials. Despite the extensive exploration of their tailorable properties, truss-based metamaterial design has predominantly adhered to cubic and orthotropic unit-cells, a limitation arising from the conventional design method, where the type of symmetry related to the designed truss-based material is determined after the design process is done. To overcome this issue, this work introduces a groundbreaking 3D truss material designing framework that departs from this constraint by employing six distinctive material symmetries (cubic, hexagonal, tetragonal, orthotropic, trigonal, and monoclinic) within the design process. This innovative approach represents a versatile paradigm shift compared to previous design approaches. Furthermore, we are able to integrate anisotropy into the design framework, thus enhancing the property space exploration capability of the proposed design framework. Probing materials property space using our design framework demonstrates its capacity to achieve a diverse range of mechanical properties, surpassing even the most extensive datasets available in the literature. The proposed method facilitates the generation of a comprehensive truss dataset, which can be represented in a trainable continuous format suitable for machine learning and data-driven approaches. This advancement paves the way for the development of robust inverse design tools for truss materials, marking a significant contribution to the mechanical metamaterial community.

Application of the finite element method to the endochronic theory of thermoplasticity for isotropic materials in a plane stress state

Abstract To describe the nonlinear deformation of isotropic materials under non-isothermal loading, it is proposed to use the endochronic theory of thermoplasticity. In this study, the governing equations of this theory are obtained for the general case of loading and for the case of a plane stress state. The calculated dependences of the finite element method in relation to endochronic theory are given, and computational methods of solution are also presented. In the last part of the study, an example of calculating a thin plate under complex loading is considered.

A large deformation viscoelasticity theory for elastomeric materials and its numerical implementation in the open-source finite element program FEniCSx

Elastomeric solid materials typically exhibit a pronounced viscoelastic response. In this paper we consider a large deformation viscoelasticity theory for isotropic elastomeric materials which uses a multi-branch multiplicative decomposition of the deformation gradient. We then describe the numerical implementation of the theory in the open-source finite element program FEniCSx. Several example simulations which demonstrate the capability of the theory and its numerical implementation to model stress-relaxation, creep, stretch-rate sensitivity, hysteresis, damped inertial oscillations, and dynamic column buckling are shown. The source codes for these simulations are provided. The theory and the codes presented in this paper lay the foundation for future extensions of the theory and its numerical implementation to include the effects of coupling with thermal, electrical, and magnetic fields — extensions which are of central importance in modeling the response of soft-active materials.

Reconfigurable Three-Dimensional Thermal Dome

Thermal metamaterial represents a groundbreaking approach to control heat conduction, and, as a crucial component, thermal invisibility is of utmost importance for heat management. Despite the flourishing development of thermal invisibility schemes, they still face two limitations in practical applications. First, objects are typically completely enclosed in traditional cloaks, making them difficult to use and unsuitable for objects with heat sources. Second, although some theoretical proposals have been put forth to change the thermal conductivity of materials to achieve dynamic invisibility, their designs are complex and rigid, making them unsuitable for large-scale use in real three-dimensional (3D) spaces. Here, we propose a concept of a thermal dome to achieve 3D invisibility. Our scheme includes an open functional area, greatly enhancing its usability and applicability. It features a reconfigurable structure, constructed with simple isotropic natural materials, making it suitable for dynamic requirements. The performance of our reconfigurable thermal dome has been confirmed through simulations and experiments, consistent with the theory. The introduction of this concept can greatly advance the development of thermal invisibility technology from theory to engineering and provide inspiration for other physical domains, such as direct current electric fields and magnetic fields.

Adaptive topology optimization for enhancing resistance to brittle fracture using the phase field model

Computational cost is one of the challenges in the field of fracture resistance topology optimization. An efficient topology optimization approach is proposed for enhancing resistance to structural fracture based on the adaptive isogeometric–meshfree method. The mesh can be adaptively refined in the computational and design domains simultaneously to capture the fracture and structural boundary delicately, which significantly reduces the degree of freedom and improves the efficiency of the topology optimization problems related to crack propagation. The proposed approach naturally inherits the advantages of both the computer-aided design and continuity of the higher-order basis functions, where the geometry and the analysis models in the process of topology optimization are integrated. The problem is formulated to maximize the absorbed energy throughout the crack process using the solid isotropic material with penalization method under volume constraints. The phase field method is used for modeling crack propagation, thereby eliminating the need of an explicit representation of the crack surface and complex tracking procedures, while a delicate mesh is still required. With this approach, the external work required during the fracture process is maximized, and the crack growth is delayed remarkably. Several representative examples are demonstrated to verify the effectiveness of the present approach in fracture-resistance-enhanced topology optimization, and the computational cost shows remarkable improvement.

An improved peridynamics topology optimization formulation for compliance minimization

This work proposes an improved peridynamics density-based topology optimization framework for compliance minimization. One of the main advantages of using a peridynamics discretization relies in the fact that it provides a consistent regularization of classical continuum mechanics into a nonlocal continuum, thus containing an inherent length scale called the horizon. Furthermore, this reformulation allows for discontinuities and is highly suitable for treating fracture and crack propagation. Partial differential equations are rewritten as integrodifferential equations and its numerical implementation can be straightforwardly done using meshfree collocation, inheriting its advantages. In the optimization formulation, Solid Isotropic Material with Penalization (SIMP) is used as interpolation for the design variables. To improve the peridynamic formulation and to evaluate the objective function in a energetically consistent manner, surface correction is implemented. Moreover, a detailed sensitivity analysis reveals an analytical expression for the objective function derivatives, different from an expression commonly used in the literature, providing an important basis for gradient-based topology optimization with peridynamics. The proposed implementation is studied with two examples illustrating different characteristics of this framework. The analytical expression for the sensitivities is validated against a reference solution, providing an improvement over the referred expression in the literature. Also, the effect of using the surface correction is evidenced. An extensive analysis of the horizon size and sensitivity filter radius indicates that the current method is mesh-independent, i.e. a sensitivity filter is redundant since peridynamics intrinsically filters length scales with the horizon. Different optimization methods are also tested for uncracked and cracked structures, demonstrating the capabilities and robustness of the proposed framework.

An intelligent design system for tailored metamaterial properties

Metamaterials are widely studied for their ability to carry human designs and realize exotic, specific physical properties. However, the existing metamaterial design methods are highly dependent on the experience and expertise of the designers. Unlocking the potential of metamaterials requires efficient design methods accessible beyond expert users. This work presents a novel intelligent design system (IDS) for fabricating metamaterials with designated mechanical properties without extensive expertise. The IDS leverages a combined approach of particle swarm and moving morphable components topology optimization, capitalizing on swarm intelligence for efficient material structure generation. The proposed IDS successfully generates tailored metamaterial matrices exhibiting desired elastic properties like Poisson's ratio and elastic modulus for orthotropic and isotropic materials. Innovative development of fuzzy models is achieved to optimize convergence mapping of isotropic mechanical metamaterials for user guidance. Notably, it achieves this even without requiring an initial design, completing the process within minutes and offering seamless integration with MATLAB for portability. From the pre-determination of convergence before design to the export of fabrication models after design, IDS provides a new path to designing metamaterials without needing research experience. This comprehensive, user-friendly system holds immense potential for expansion into 3D design and various metamaterial classes, acting as a valuable bridge for non-experts to achieve metamaterial design.

Evaluation of a decomposition-based interpolation method for fourth-order fiber-orientation tensors: An eigensystem approach

We propose and assess a new decomposition-based interpolation method on fourth-order fiber-orientation tensors. This method can be used to change the resolution of discretized fields of fiber-orientation tensors, e.g., obtained from flow simulations or computer tomography, which are common in the context of short- and long-fiber–reinforced composites. The proposed interpolation method separates information on structure and orientation using a parametrization which is based on tensor components and a unique eigensystem. To identify this unique eigensystem of a given fourth-order fiber-orientation tensor in the absence of material symmetry, we propose a sign convention on tensor coefficients. We explicitly discuss challenges associated with material symmetries, e.g., non-distinct eigenvalues of the second-order fiber-orientation tensor and propose algorithms to obtain a unique set of parameters combined with a minimal number of eigensystems of a given fourth-order fiber-orientation tensor. As a side product, we specify for the first time, parametrizations and admissible parameter ranges of cubic, tetragonal, and trigonal fiber-orientation tensors. Visualizations in terms of truncated Fourier series, quartic plots, and tensor glyphs are compared.

Pattern formation in odd viscoelastic fluids

Nonreciprocal interactions fueled by local energy consumption can be found in biological and synthetic active matter at scales where viscoelastic forces are important. Such systems can be described by “odd” viscoelasticity, which assumes fewer material symmetries than traditional theories. Here we study odd viscoelasticity analytically and using lattice Boltzmann simulations. We identify a pattern-forming instability which produces an oscillating array of fluid vortices, and we elucidate which features govern the growth rate, wavelength, and saturation of the vortices. Our observation of pattern formation through odd mechanical response can inform models of biological patterning and guide engineering of odd dynamics in soft active matter systems. Published by the American Physical Society 2024

Density-Based Isogeometric Topology Optimization of Shell Structures

Shell structures with high stiffness-to-weight ratios are desirable in various engineering applications. Topology optimization serves as a popular and effective tool for generating optimal shell structures. The solid isotropic material with penalization (SIMP) method is often chosen because of its simplicity and convenience. However, SIMP method is typically integrated with conventional Finite Element Analysis (FEA) which has limitations in computational accuracy. Achieving high accuracy with FEA necessitates a substantial number of elements, leading to computational burdens. In addition, the discrete representation of the material distribution function may result in rough boundaries. Owing to these limitations, this paper proposes an Isogeometric Analysis (IGA) based SIMP method for optimizing the topology of shell structures based on Reissner–Mindlin theory. This method uses Non-Uniform Rational B-Splines (NURBS) to represent both the shell structure and the material distribution function with the same basis functions, allowing for higher accuracy and smoother boundaries. The optimization model takes compliance as the objective function with a volume fraction constraint and the coefficients of the density function as design variables, resulting in an optimized shell structure defined by the material distribution function. To obtain fairing boundaries of the holes in the optimized shell structure, further process is conducted by fitting the boundaries with fair B-spline curves automatically. Furthermore, the proposed IGA-SIMP framework is applied to generate porous shell structures by imposing different local volume fraction constraints. Numerical examples are provided to demonstrate the feasibility and efficiency of the IGA-SIMP method, showing that it outperforms the FEA-SIMP method and produces smoother boundaries.

Stress–diffusion coupling. Application to interstitial diffusion

A numerical study of the stress–diffusion coupling theory based on the Cahn–Larché method is presented in the case of interstitial diffusion. Indeed, the interaction between diffusion and stress fields has been widely studied in the past. Most of the studies focused on the effect of chemical stress due to mass transport on diffusion. The majority of the studies have been focusing on the coupling between external mechanical and chemical stresses with diffusion. In this study, the effect of stress/strain on mobility and stress gradient mobility and driving forces are presented, based on the model of Voorhees and Larché. The analytical solutions are detailed, from general equations (interstitial diffusion, elastic material) to a macroscopic model (interstitial diffusion, isotropic elastic material, infinite dilute solution, 2D axisymmetric). Numerical simulations for different samples thickness and β parameter helped to better understand and then experimentally identify the prevailing effect of stress on mobility or diffusion driving forces. These studies demonstrated the impact of constant compressive and tensile stress on diffusion kinetics through the mobility term of the equation, as well as the effects of negative and positive stress gradients via the Nernstian term. The results show that constant compressive stress and negative stress gradient hinder the diffusion. On the contrary, tensile stress and positive stress gradient promote the diffusion. This work also demonstrates the importance of coupling between mobility and Nernstian effect on the diffusion promotion.

Geometrically nonlinear topology and fiber orientation optimization of composite structures using membrane-embedded model

The membrane-embedded model can be efficiently used in the finite element analysis of composite structures considering geometrical nonlinearity because of its practicability. This paper extends this model to the topology and fiber orientation optimization considering geometrical nonlinearity. The discrete design variables of topology and fiber orientation are continuous by the solid isotropic material with penalization method and bi-value coding parameterization method. An optimized interpolation scheme for the membrane-embedded model is constructed for geometrical nonlinearity. The filtering function is added to improve the convergence of the fiber orientation. To reduce the computational complexity, topology and fiber orientation are independently updated at each iteration during the optimization process. Numerical examples demonstrate the effectiveness of the proposed method for membrane-embedded composite considering geometrical nonlinearity.

Free-form metamaterials design with isotropic materials.

Free-form metamaterials design with isotropic materials.

Parameter Equivalence and Impedance Characteristics of NiTi Wires Embedded in Nitrile Butadiene Rubber Based on Secondary Bridging Model

This article presents a metal matrix composite material consisting of NiTi wires embedded in nitrile butadiene rubber (NBR) that preserves NBR’s inherent acoustic characteristics while enabling acoustic modification through the NiTi phase transition induced by stress and temperature. The macroscopic mechanical parameters of transversely isotropic NiTi-NBR composite materials are derived by means of a secondary bridging model that takes into account interfacial phases. On this basis, the acoustic impedance properties and absorption coefficient of composite materials were examined as a function of NiTi volume fraction using the transfer matrix method. The accuracy and effectiveness of the theoretical method were verified by comparing the calculated results with finite element simulation. The research results indicated that regulating the volume fraction of NiTi can lead to the anticipated value of the input impedance of composite materials, improving impedance matching with media like water and rubber, which offers novel insights and a theoretical foundation for the development of underwater sound-absorbing materials.

The Effect of Chopped Carbon Fibers on the Mechanical Properties and Fracture Toughness of 3D-Printed PLA Parts: An Experimental and Simulation Study

The incorporation of fiber reinforcements into polymer matrices has emerged as an effective strategy to enhance the mechanical properties of composites. This study investigated the tensile and fracture behavior of 3D-printed polylactic acid (PLA) composites reinforced with chopped carbon fibers (CCFs) through experimental characterization and finite element analysis (FEA). Composite samples with varying CCF orientations (0°, 0°/90°, +45°/−45°, and 0°/+45°/−45°/90°) were fabricated via fused filament fabrication (FFF) and subjected to tensile and single-edge notched bend (SENB) tests. The experimental results revealed a significant improvement in tensile strength, elastic modulus, and fracture toughness compared to unreinforced PLA. The 0°/+45°/90° orientation exhibited a 3.6% increase in tensile strength, while the +45°/−45° orientation displayed a 29.9% enhancement in elastic modulus and a 29.9% improvement in fracture toughness (259.12 MPa) relative to neat PLA (199.34 MPa√m). An inverse correlation between tensile strength and fracture toughness was observed, attributed to mechanisms such as crack deflection, fiber bridging, and fiber pull-out facilitated by multi-directional fiber orientations. FEA simulations incorporating a transversely isotropic material model and the J-integral approach were conducted using Abaqus, accurately predicting fracture toughness trends with a maximum discrepancy of 8% compared to experimental data. Fractographic analysis elucidated the strengthening mechanisms, highlighting the potential of tailoring CCF orientation to optimize mechanical performance for structural applications.

Tensile fracture of blunt V-notches in rectangular plates additively manufactured from Acrylonitrile Butadiene Styrene with different raster angles

In this research, the tensile fracture behavior of rectangular specimens made of Acrylonitrile Butadiene Styrene (ABS) containing double-edge blunt V-notches is evaluated. The specimens are printed using the fused deposition modeling (FDM) technique with five different raster angles and three different notch tip radii. To simplify the complex calculations related to the anisotropic behavior of these specimens, the Virtual Isotropic Material Concept (VIMC) is used in conjunction with three well-known linear elastic notch fracture mechanics (LENFM) criteria, i.e., the mean stress (MS), point stress (PS), and averaged strain energy density (ASED) criteria as well as the extended finite element method (XFEM). It is shown that all these fracture models can predict the load-bearing capacity of the 3D-printed notched specimens by acceptable accuracies, where the best predictions belong to the MS criterion with the critical distance obtained directly from the finite element method, and the least accurate predictions belong to the XFEM method.

Tuning the high reflectance Goos-Hänchen shift based on quasi-bound states in the continuum through vanadium dioxide material asymmetric metasurface

To dynamically tune the high-reflectance Goos and Hänchen (GH) shift, a vanadium dioxide metasurface is proposed in this paper, whose material asymmetry parameter can be tuned by the ambient temperature. The material symmetry and geometric symmetry of the metasurface are broken by controlling the material asymmetry parameter γ and incident angle θ, and three symmetry-protected quasi-bound states in the continuum (QBICs) resonances with high-quality factors are excited. Based on the electric/magnetic field vector and multipole decomposition, the three QBIC resonances are excited due to the magnetic quadrupole. The QBIC resonances are applied to dynamically tune the high-reflectance GH shift, and the influence laws of γ and θ on the high-reflectance GH shift are analyzed.

Numerical simulation of wave propagation by using a hybrid method with an arbitrary order accuracy in both spatial and temporal approximations

This paper introduces an innovative numerical methodology designed to achieve high precision solution of acoustic wave propagation problem in isotropic material. During the temporal discretization process, the Krylov deferred correction (KDC) technique is employed, wherein a new variable is introduced to handle the second-order time derivative in the governing equations. An improved strategy is adopted for precisely implementing boundary conditions. Following this, the arbitrary-order generalized finite difference method (GFDM) is employed to simulate the transformed boundary value problem at each time step, enabling our framework to select the Taylor series expansion order arbitrarily. Ultimately, a hybrid numerical approach for wave problems is developed to achieve arbitrary-order accuracy in both spatial and temporal approximations. The developed scheme undergoes validation through four different numerical experiments in two- or three-dimension, wherein the numerical solutions obtained are compared with either analytical solutions or results from COMSOL software.