Anisotropic Material Behavior Research Articles

Comprehensive measurement of three-dimensional thermal conductivity tensor using a beam-offset square-pulsed source (BO-SPS) approach

Accurately measuring the three-dimensional thermal conductivity tensor is essential for understanding and engineering the thermal behavior of anisotropic materials. Existing methods often struggle to isolate individual tensor elements, leading to large measurement uncertainties and time-consuming iterative fitting procedures. In this study, we introduce the Beam-Offset Square-Pulsed Source (BO-SPS) method for comprehensive measurements of three-dimensional anisotropic thermal conductivity tensors. This method uses square-pulsed heating and precise temperature rise measurements to achieve high signal-to-noise ratios, even with large beam offsets and low modulation frequencies, enabling the isolation of thermal conductivity tensor elements. We demonstrate and validate the BO-SPS method by measuring X-cut and AT-cut quartz samples. For X-cut quartz, with a known relationship between in-plane and cross-plane thermal conductivities, we can determine the full thermal conductivity tensor and heat capacity simultaneously. For AT-cut quartz, assuming a known heat capacity, we can determine the entire anisotropic thermal conductivity tensor, even with finite off-diagonal elements. Our results yield consistent principal thermal conductivity values for both quartz types, demonstrating the method's reliability and accuracy. This research highlights the BO-SPS method's potential to advance the understanding of thermal behavior in complex materials.

Anisotropic damage evolution in solid fractures: A novel phase field approach with multiple failure criteria and directional-dependent structural tensor

This study proposes a novel phase-field fracture model based on unified phase field theory, aiming to overcome current limitations in simulating material complex fracture behaviors. Through this model, analytical solutions for two-dimensional bars subjected to tensile or compressive stresses are provided, enabling the coupling of multiple failure criteria and further proficient simulation of mode-I, mode-II, and mixed mode-I/II fractures, effectively addressing challenges faced in modelling materials with different or complex failure modes under various loading conditions. Furthermore, to account for the strong anisotropic failure behavior of materials, a novel directional-dependent structural tensor is proposed. The tensor correlates fracture energy with crack surface orientation, facilitating precise characterization of material damage evolution with multiple potential crack orientations. This tensor ensures the consistency of phase-field fracture evolution with predefined fracture patterns. The effectiveness of the proposed model is validated through case studies, emphasizing its robustness and superior predictive capability in capturing fracture behavior under various conditions. This research provides a more accurate and universally applicable approach for simulating material failure, particularly for complex or multiple failure mode material failure simulations.

Analysis of the Anisotropic Cyclic Material Behavior of EN AW-1050A H24 Derived from Strain-Controlled Testing Using a Clip-On Extensometer and an Optical System

Due to its good conductive properties, unalloyed (pure) aluminum, such as EN AW-1050A H24, finds new fields of application in electromobility. To optimize components, the cyclic material behavior must be understood and described precisely as a foundation of a proper fatigue life estimation. Various cyclic tests were performed to not only derive the cyclic parameters to describe the material but also to find the most suitable procedure to deal with the challenges faced during the experiments. The main point of interest is the comparison between a surface-mounted clip-on extensometer and an optical system both used for strain control in cyclic tests. For the analysis of the anisotropic behavior of EN AW-1050A H24, un-notched flat specimens were extracted from sheet metal lengthways and crossways in respect to the rolling direction. While the cyclic material behavior for specimens of both directions of extraction is characterized by cyclic softening in general, the specimens extracted crossways show a strain-amplitude-dependent cyclic softening with strong strain localization especially at the contact points of the knives of the clip-on extensometer leading to an increased quantity of invalid experiments as well as sudden fractures. In the study, it was possible to show the benefits of a contactless optical strain control system when dealing with very soft metallic materials such as EN AW-1050A H24.

FlexScale: Modeling and Characterization of Flexible Scaled Sheets

We present a computational approach for modeling the mechanical behavior of flexible scaled sheet materials---3D-printed hard scales embedded in a soft substrate. Balancing strength and flexibility, these structured materials find applications in protective gear, soft robotics, and 3D-printed fashion. To unlock their full potential, however, we must unravel the complex relation between scale pattern and mechanical properties. To address this problem, we propose a contact-aware homogenization approach that distills native-level simulation data into a novel macromechanical model. This macro-model combines piecewise-quadratic uniaxial fits with polar interpolation using circular harmonics, allowing for efficient simulation of large-scale patterns. We apply our approach to explore the space of isohedral scale patterns, revealing a diverse range of anisotropic and nonlinear material behaviors. Through an extensive set of experiments, we show that our models reproduce various scale-level effects while offering good qualitative agreement with physical prototypes on the macro-level.

A 2-D fabric anisotropic hyperelastic constitutive model based on micromechanics analysis

The analysis of the large deformation process of two-dimensional (2-D) fabrics helps to obtain the new distribution of yarns’ orientation and fiber in-plane density, which exert a considerable influence on the mechanical properties of the 2-D fabric composite component. By examining the underlying micromechanics involved in the shearing process, we developed a shear constitutive law within an anisotropic hyperelastic constitutive model framework, which is capable of capturing the large deformation of 2-D fabrics precisely. The constitutive law introduces parameters with specific physical meanings, facilitating their acquisition and modification. The proposed model was implemented in ABAQUS using a dedicated subroutine, UANISOHYPER_INV, for defining anisotropic hyperelastic material behavior through invariant formulation. The shear properties of 2/2 twill fabric were examined, and the parameters of the shear constitutive model were determined via bias-extension tests and corresponding finite element computations. The accuracy and reliability of the proposed model were validated through a hemispherical stamping test on the 2-D fabric and frame shear experiments performed by other researchers. This work contributes to the field by providing a robust method for characterizing and predicting the shear behavior of textile composites, thus enhancing the design and optimization of advanced fabric materials.

Experiments on the material and stability performance of slender WAAM plated structures

An experimental study has been carried out to investigate the material and stability performance of WAAM 316L stainless steel plates supported along both edges. The experiments were facilitated by testing a series of square hollow section (SHS) stub columns and tensile coupons extracted from the plates manufactured along with the stub columns. The tensile test results provided the material properties to be used for later analysis of the stub column tests, and indicated anisotropic material behaviour while displaying satisfactory material ductility. The SHS stub column dimensions fall in the range of ‘slender’ cross-sections as defined by Eurocode 3. Their geometric profiles were 3D laser scanned and analysed prior to the compression tests. The failure modes and load carrying capacities of the WAAM SHS stub columns were analysed and compared to the specimens in previous similar studies. The use of the Effective Width Equation in Eurocode 3 and the Continuous Strength Method for the design of slender WAAM stainless steel plates are evaluated.

Design and validation of a new ring hoop plane strain test for characterizing the anisotropic plastic behavior of tubular materials

The accurate characterization of the plastic behavior of tubular materials is challenging due to the difficulties in acquiring proper specimens for mechanical testing. In this study, we propose a novel testing technique, namely the ring hoop plane strain Test (RHPST), as a supplementary test for characterizing materials experiencing distinct strain paths compared to standard uniaxial tensile tests. To design a suitable ring specimen’s geometry that satisfies the necessary plane strain conditions, we developed a meta-modelling approach merging response surface method (RSM) and the finite element method (FEM). Experimental tests are conducted on RHPST specimens, and 3D digital image correlation (DIC) technique is used to monitor the strain fields within the specimen's gauge section. However, observations indicate the presence of edge effects on the gauge specimen. These edge effects significantly influence and limit the homogeneity of the plane strain field. To tackle this limitation, a correction procedure is developed for separating the authentic plane strain area, constituting approximately 78% of the RHPST specimen's width. Furthermore, we successfully fabricated a novel grooved ring specimen (GRHPST), which exhibits a wider region of the plane strain state encompassing up to 90% of the gauge width, while minimizing the impact of edge effects. The true stress-true strain curve obtained from the GRHPST specimen exhibits exceptional agreement with the curve predicted using the Hill48 yield criterion. Notably, no additional corrections are required for the measured true stress-true strain curve, thereby affirming the efficacy of the GRHPST specimen as an adept test for characterizing the anisotropic plastic behavior of AA6063 tubes.

Simulating Elastoplastic and Anisotropic Behavior in Thermoplastic Additively Manufactured Components: An Application-Oriented Modeling Approach.

This paper presents a comprehensive approach aimed at developing a coupled process-structure simulation that integrates anisotropic and elastoplastic material behavior for plastic components manufactured through Fused Filament Fabrication (FFF) 3D printing. The simulation incorporates material orientation considerations, linking the process simulation with structural simulation. Subsequently, stress and strain values from the simulations are compared with the test results. Moreover, the fracture behavior of components manufactured in this way is also taken into account in relation to material orientation. The executed simulations have yielded successful outcomes, affirming the efficacy of the anisotropic and elastoplastic simulation across all strand orientations. Special attention is paid to the application of the method. Here, the simulation method introduced in this contribution with the approaches for describing the material behavior under mechanical load can be used in the future in the dimensioning of FFF manufactured plastic components to predict the deformation behavior and failure, especially under consideration of a well economic and efficient virtual product development.

Study of Anisotropic Behavior in Sheet Metal Forming.

Since sheet metal exhibits significant anisotropy in processing and forming, which has a significant impact on its performance during processing, forming, and use, we explore the anisotropic behavior of materials in the forming process of sheet metal. The ability of the Yld2000-2d criterion to describe anisotropic behavior is analyzed, and its accuracy for characterization of the anisotropic behavior of metal plates is improved, based on which anisotropic behavior is predicted in three-dimensional space. Theoretical and experimental results on the anisotropy of sheet metal are compared, and two materials, 5754O aluminum alloy and DP980 steel plate, are tested and analyzed, and the anisotropic behaviors, such as three-point bending and cylindrical deep-drawing, are well predicted.

High-cycle shakedown, ratcheting and liquefaction behavior of anisotropic granular material with fabric evolution: Experiments and constitutive modelling

Although the mechanical response of granular materials strongly depends on the interplay between their anisotropic internal structure (fabric) and loading direction, such coupling is not explicitly considered in existing high-cycle experimental datasets and models. High-cycle experiments on granular specimens specifically prepared with various fabric orientations are presented. It is found that the high-cycle strain accumulation behavior can change remarkably, from shakedown to ratcheting, when the fabric orientation deviates more from the loading direction. Inspired by the experimental observations, a fabric-dependent anisotropic high-cycle model is proposed, by proper recasting of an existing model formulated within Critical State Theory, into the framework of Anisotropic Critical State Theory. The model explicitly accounts for the fabric evolution, which is linked to plastic modulus, dilatancy and kinematic hardening rules. The model can quantitatively reproduce the high-cycle strain accumulation (i.e., shakedown and ratcheting) under drained conditions, as well as pre-liquefaction and post-liquefaction responses granular materials having widely ranged fabric anisotropy, densities and cyclic loading types using a unified set of constants. It exhibits a unique feature of simulating the distinct high-cycle strain accumulation and liquefaction of granular material with various fabric anisotropy, while the existing high-cycle models treat them equally. The successful reproduction of the anisotropic sand element response under high-cycle drained and undrained conditions makes it possible to perform whole life analysis of various foundations on granular soil subjected to high-cycle loading events.

Anisotropic model to describe chemo-mechanical response of Ni-rich cathode materials

In the context of lithium-ion battery technology, LiNixMnyCozO2 (x ≥ 0.8) (Ni-rich NMC) is considered a promising cathode material for next-generation batteries due to its high energy density. However, rapid capacity fade caused by mechanical failure hinders commercialization in the battery market. Anisotropic deformation in the basal and normal directions is the main source of mechanical damage to Ni-rich NMC. In this study, we developed a fully coupled chemo-mechanical model that rigorously accounts for the anisotropic features of anisotropic diffusivity, anisotropic stress-induced diffusion and anisotropic mechanical deformation. Using the model, we investigate the effects of anisotropic and concentration-dependent lattice strains on the chemo-mechanical behavior of a single-crystalline Ni-rich NMC particle through a comparative study with the cases of a fully isotropic model, constant properties and an isotropic diffusion approximation. Numerical simulations reveal that due to the anisotropic features, Ni-rich NMC materials generate larger concentration gradients and associated higher stresses than isotropic materials, thereby enhancing the possibility of mechanical fractures. The comparative study reveals that the anisotropy in diffusivity plays an important role in high stress generation of anisotropic electrode materials. On the other hand, the anisotropy in stress-induced diffusion has small effect on the stress level of anisotropic materials; thus, isotropic approximation of the stress-induced diffusion term is reasonably allowed in the anisotropic chemo-mechanical models. The simulation results indicate that although anisotropic electrode materials are used in a single crystal structure, they are not advantageous compared to isotropic materials in terms of mechanical stability. This study provides fundamental insight into the role of the anisotropic chemo-mechanical behavior of Ni-rich cathode materials, which will help in the better design of robust, high-capacity batteries.

A framework for neural network based constitutive modelling of inelastic materials

Given the significant recent advances in added layer manufacturing and materials engineering, new types of materials or new material micro-structures are becoming available at a fast rate. The finite element analysis of structures or structural components requires a constitutive model that describes the behaviour of the new materials. The formulation of accurate constitutive equations is generally complex and time consuming. Hence, suitable machine learning strategies may be used to render this process obsolete and bridge the gap between experimental data and finite element analysis. In this work, a generic stress update procedure is presented that is suitable for the modelling of rate-independent, elastic or inelastic, isotropic or anisotropic material behaviour. The proposed strategy is based on a recurrent neural network architecture and must be trained on stress and strain data sequences that represent physical or numerical experiments. A training strategy based on gradient-free optimisation is presented. It is shown that piecewise linear behaviour, such as uniaxial elasto-plasticity, can be represented exactly. Further numerical examples include uniaxial damage mechanics and elasto-plasticity under plane strain conditions. An efficient criterion for the verification of thermodynamic consistency is proposed and applied to the trained stress update models. The strategy is compared to GRU or LSTM based architectures and shown to offer advantages.

Pavement Analysis with the Consideration of Unbound Granular Material Nonlinearity

Accurate pavement design and evaluation requires the execution of response analysis. Pavement materials’ behavior does not necessarily conform to the assumptions of the multi-linear elastic theory usually adopted during pavement analysis. In particular, the unbound granular materials located in the base and sub-base layers behave in a nonlinear elastic manner, which can be captured through advanced constitutive modeling of their resilient modulus. The finite element method enables us to code constitutive models and quantify potential variations in pavement responses because of different mechanistic assumptions. In this study, variations in response are investigated for a typical structure of a flexible pavement considering the nonlinear anisotropic behavior of the unbound materials together with their initial stress–strain state. To demonstrate the impact of their behavior on the outcome of pavement analysis, variable asphalt concrete layer thicknesses and moduli are assumed, such that they cover a large spectrum of roadways. It was found that pavement responses can be calculated up to 3.5 times higher than those retrieved from the conventional linear analysis. This comparison means that the alterative mechanistic modeling of the unbound granular materials can be proved to be more conservative (i.e., leading to higher strains) in terms of pavement design and analysis. From a practical perspective, this study alerts pavement scientists and engineers engaged in pavement design to a more reliable performance prediction, which is needed to bridge the gap between advanced modeling and routine analysis.

Extension of a shell‐like RVE model to represent transverse shear effects in textile reinforced composites

AbstractTextile reinforcements have long been used in shell‐like components like tires, belts, hoses and, in particular, air spring bellows. These bellows consist of a certain number of cords embedded in soft rubber, resulting in high membrane stiffness to absorb tensile forces and low resistance to changes in curvature. The embedded cords are produced by twisting multifilament yarns. Modelling and simulation of bellows is a challenging task. Thereby, the complex internal geometry, large deformations as well as the strongly anisotropic and nonlinear material behavior have to be taken into account in a computationally efficient manner. One approach is the application of multiscale analyses in conjunction with representative volume elements (RVE). Within this study, a through‐thickness RVE based on in‐plane periodic microstructures is applied. The local behavior of the cords is represented by an anisotropic constitutive model that regards directions and mechanical properties of filaments, which result from previous cord twisting simulations. In this contribution, an extension of the classical periodic boundary conditions (PBC) is presented, which considers curvature, pressure load, and, in particular, transverse shear. The RVE is used to simulate the stresses and strains in cord‐rubber composites under realistic load conditions. Moreover, it is employed for homogenizing the mechanical behavior and, thus, for developing a suitable constitutive model for shells.

Modeling the anisotropic squeeze flow during hot press consolidation of thermoplastic unidirectional fiber-reinforced tapes

The anisotropic material behavior of continuous-fiber-reinforced composites that is evident in their mechanical properties should also be considered in their processing. An important step in the processing of thermoplastic unidirectional (UD) fiber-reinforced tapes is consolidation, where a layup consisting of locally welded UD tape layers is firmly bonded. Compression of the molten thermoplastic matrix material during consolidation leads to a squeeze flow, the direction of which is determined by the fibers. This work presents a model that describes the influence of fiber direction on compression and flow behavior, implemented in the computational fluid dynamics (CFD) software tool OpenFOAM®. To validate the simulation results, we performed experiments in a laboratory consolidation unit, capturing the squeeze flow with cameras and then quantifying it by gray-scale analysis. The specimens used were UD polycarbonate tapes (44% carbon fibers by volume) of various sizes and with various fiber directions. The simulation allows prediction of the changes in specimen geometry during consolidation and is a first step towards optimizing the process by avoiding extensive squeeze flow.

A New Regression Model for the Prediction of the Stress-Strain Relations of Different Materials.

Experimental flow stress-strain data under different stress states are often used to calibrate the plastic constitutive model of anisotropic metal materials or identify the appropriate model that is able to reproduce their plastic deformation behavior. Since the experimental stress-strain data are discrete, they need to be mathematically returned to a continuous function to be used to describe an equivalent hardening increment. However, the regression results obtained using existing regression models are not always accurate, especially for stress-strain curves under biaxial stress loading conditions. Therefore, a new regression model is proposed in this paper. The highest-order term in the recommended form of the new model is quadratic, so the functional relationships between stress-strain components can be organized into explicit expressions. All the experimental data of the uniform deformation stage can be substituted into the new model to reasonably reproduce the biaxial experimental stress-strain data. The regression results of experimental data show that the regression accuracy of the new model is greatly improved, and the residual square sum SSE of the regression curves of the new model reduced to less than 50% of the existing three models. The regression results of stress-strain curves show significant differences in describing the yield and plastic flow characteristics of anisotropic metal materials, indicating that accurate regression results are crucial for accurately describing the anisotropic yielding and plastic flow behaviors of anisotropic metal materials.

Anisotropic compressive properties and behavior of a bio-based composite material

In this work, the composite materials made of straw fibers from the cereal crop as bio-aggregates and lime as a binder have been developed. The compressive properties and behavior of composite specimens have been examined for various test speeds and directions. The highest density and compressive strengths are 391 kg/m3 and 0.170 MPa, respectively, in which the compressive strength is obtained in the parallel direction tested composite specimen. The highest Young’s modulus in global values is found to be 2.25 MPa for specimen test at parallel direction and 10 mm/min of speed rate of loading test. In the speed rates of 100 mm/min, stress values are faster and bigger than the specimens conducted at 10 mm/min of speed rates at the same strain level. The different behavior of specimens is obviously seen in the parallel and pouring testing specimens. The composites had been debonding on fibers-binders, buckling in fibers, and then they had been in densification. However, the debonding and buckling process are not clearly visible in the pouring directions specimen tested. Before densification, it had regularly compacting process.

Model-Based Assessment of Elastic Material Parameters in Rheumatic Heart Disease Patients and Healthy Subjects

Non-invasive measurements are important for the development of new treatments for heart failure, which is one of the leading causes of death worldwide. This study aimed to develop realistic subject-specific computational models of human biventricles using clinical data. Three-dimensional finite element models of the human ventricles were created using cardiovascular magnetic resonance images of rheumatic heart disease (RHD) patients and healthy subjects. The material parameter optimization uses inverse modeling based on the finite element method combined with the Levenberg–Marquardt method (LVM) by targeting subject-specific hemodynamics. The study of elastic myocardial parameters between healthy subjects and RHD patients showed an elevated stiffness in diseased hearts. In particular, the anisotropic material behavior of the healthy and diseased cardiac tissue significantly differed from one another. Furthermore, as the LVEF decreased, the stiffness and its orientation-dependent parameters increased. The simulation-derived LV myocardial circumferential and longitudinal stresses were negatively associated with the LVEF. The sensitivity analysis result demonstrated that the observed significant difference between the elastic material parameters of diseased and healthy myocardium was not exclusively attributable to an increased LVEDP in the diseased heart. These results could be applied to future computational studies for developing heart failure treatment.

Exploring structural, thermodynamic, elastic, electro-optic, and thermoelectric characteristics of double perovskites Rb2XInBr6 (X = Na, K) for photovoltaic applications: A DFT approach

The structural, thermodynamic, elastic, electro-optic, and thermoelectric properties of the emerging double perovskites Rb2XInBr6 (X = Na, K) were investigated. The cubic phase of Rb2KInBr6 and Rb2NaInBr6 wasverified by tolerance factor (τ) values of 0.89 and 0.83, respectively. The negative formation energies and Gibbs free energies of both perovskites demonstrated their thermodynamic stability. The elastic parameters suggested the mechanical stability, brittle character, and anisotropic behavior of both materials. The electronic band gap and density of states calculations confirmed the presence of a direct band gap (Eg) for Rb2KInBr6 and Rb2NaInBr6, having an Eg of 3.2 eV and2.6 eV, respectively. The present research focuses on the investigation of light energy absorption, polarization, refractive index, and optical loss throughout the energyspectrum ranging from zero to 10 eV. The optical parameters were appropriate for photovoltaic systems since the absorption occurs in the ultraviolet range. The thermoelectric characteristics, as measured by the use of the BoltzTraP code, revealed that the maximum ZT values were determined to be 0.73and 0.72, respectively, for both materials. Despite the presence of moderate optical absorption and a ZT value in these materials, it is necessary to investigate efficient techniques for adjusting the electronic band gapto enhance the material's optical and thermoelectric response, therefore making it more suitable for practical applications in energy generation.

Single-test evaluation of directional elastic properties of anisotropic structured materials

When the elastic properties of structured materials become direction-dependent, the number of their descriptors increases. For example, in two-dimensions, the anisotropic behavior of materials is described by up to 6 independent elastic stiffness parameters, as opposed to only 2 needed for isotropic materials. Such high number of parameters expands the design space of structured materials and leads to unusual phenomena, such as materials that can shear under uniaxial compression. However, an increased number of properties descriptors and the coupling between shear and normal deformations render the experimental evaluation of material properties more challenging. In this paper, we propose a methodology based on the virtual fields method to identify six separate stiffness tensor parameters of two-dimensional anisotropic structured materials using just one tension test, thus eliminating the need for multiple experiments, as it is typical in traditional methods. The approach requires no stress data and uses full-field displacement data and global force data. We show the accuracy of our method using synthetic data generated from finite element simulations as well as experimental data from additively manufactured specimens.