Anisotropic Material Behavior Research Articles

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.

Quantification of the influence of anisotropic plastic yielding on cold rolling force

Anisotropic mechanical properties in sheet material are of high importance, in particular for material to be used in stamping or deep drawing applications. The cold rolling process has a marked influence on the degree of anisotropy in the final product. However, the influence of material anisotropy on the cold rolling process itself has so far not been rigorously investigated. In this work, the degree of normal anisotropy is determined for two low-carbon steel grades after various degree of cold rolling reduction, both by X-ray diffraction as well as by tensile testing. The experimental work shows that material with high cold rolling reduction has non-negligible anisotropic properties; as a consequence the rolling force is seriously overestimated by cold rolling models with an isotropic yield criterion. It is therefore proposed to use the Hill48 yield criterion (instead of the von Mises criterion) in cold rolling models, this criterion takes anisotropic material behaviour into account. A comparison of cold rolling experiments with model predictions confirms that including the Hill48 yield criterion significantly improves the accuracy of a cold rolling model.

Large strain correction for tunnel analyses considering hydromechanical coupling and ground anisotropy

The deformations resulting from tunnel analyses for heavily squeezing ground may be very large, necessitating numerical formulations that consider geometric nonlinearity. Alternatively, for a certain class of problems, routine small strain analyses can be performed, and their results can be corrected to account for large strains by means of a simple hyperbolic expression proposed a few years ago. The present paper shows that this correction equation is sufficiently accurate for practical purposes even in the case of anisotropic material behaviour and for hydromechanically coupled, steady state or transient analyses of tunnels. The accuracy of the equation prediction varies amongst these cases but is satisfactory overall for the purpose of preliminary calculations, thus broadening its value and usefulness as a preliminary design tool.

A machine-learning interatomic potential to understand the anisotropic fracture behavior of BaZrO3 material

The complex operating environment severely tests the mechanical stability of the electrolyte material BaZrO3 (BZO), which affects the performance of solid oxide fuel cells(SOFCs). Molecular dynamics (MD) simulation provides an efficient method to research the mechanical behavior of nanocrystalline materials. In the interest of researching the mechanical behavior of BZO materials utilizing a machine learning (ML) MD approach, this article has established the most effective ML potential with DFT reliability. By contrasting the lattice constants and elastic constants with the DFT data, the precision of the potential was confirmed. By simulating the uniaxial tensile mechanical behavior of the BZO models without crack and with a central crack in the crystal orientation of [100] and [110], we found that the BZO material has a significant anisotropic property. In the crack-free model, the BZO crack propagation mode in the [100] crystal orientation is a shear fracture. The central microcrack tilts downward and expands symmetrically in the [110] crystal-oriented BZO model. When the initial structure with a central crack, the fracture mode changes significantly, and in both crystal orientations, the crack fracture along the BaO plane, the crack expands horizontally in the BZO model in the [100] crystal orientation and the crack expands zigzag in the BZO model in the [110] crystal orientation. The calculations of fracture strength, critical energy release rate, and fracture toughness show that the [110] crystal-oriented BZO has a stronger resistance to fracture than the [100] crystal-oriented BZO model.

Rotating bending fatigue behaviour and quasi‐static tensile properties of Wire Arc Additively Manufactured 308L stainless steel

AbstractWire Arc Additive Manufacturing (WAAM) is a direct energy deposition method used to manufacture steel components by using an electric arc as a heat source to melt a metal wire and deposit it layer by layer. In this study, monotonic tensile tests, standardized Charpy impact tests, and rotating bending fatigue tests are executed to characterize the mechanical properties of WAAM 308L stainless steel using specimens extracted from additively manufactured plates. In particular, monotonic tensile properties are investigated in three directions: that is 0, 90, and 45 degrees with respect to the plane of deposition, whereas the fatigue strength is quantified for one direction only, i.e. 90 degrees since this is deemed to be the weakest.The mechanical characterization highlights that WAAM 308L SS shows an anisotropic behaviour, an enhanced strain‐rate sensitivity, and an overall reduced yield strength as compared to the base material 308L. The anisotropic material behaviour is explained by the microstructure morphology since the austenite grains form anisotropic columnar zones due to an uneven heat profile during production. During the fatigue tests, the relatively high strain rate sensitivity causes susceptibility to self‐heating at relatively low loading frequencies, i.e. below 100Hz.

A new texture descriptor for data-driven constitutive modeling of anisotropic plasticity

Constitutive modeling of anisotropic plastic material behavior traditionally follows a deductive scheme, relying on empirical observations that are cast into analytic equations, the so-called phenomenological yield functions. Recently, data-driven constitutive modeling has emerged as an alternative to phenomenological models as it offers a more general way to describe the material behavior with no or fewer assumptions. In data-driven constitutive modeling, methods of statistical learning are applied to infer the yield function directly from a data set generated by experiments or numerical simulations. Currently these data sets solely consist of stresses and strains, considering the microstructure only implicitly. Similar to the phenomenological approach, this limits the generality of the inferred material model, as it is only valid for the specific material employed in the virtual or physical experiments. In this work, we present a new generic descriptor for crystallographic texture that allows an explicit consideration of the microstructure in data-driven constitutive modeling. This descriptor compromises between generality and complexity and is based on an approximately equidistant discretization of the orientation space. We prove its ability to capture the structure–property relationships between a variety of cubic–orthorhombic textures and their anisotropic plastic behavior expressed by the yield function Yld2004-18p. Three different machine learning models trained with the descriptor can predict yield loci as well as r-values of unseen microstructures with sufficient accuracy. The descriptor allows an explicit consideration of crystallographic texture, providing a pathway to microstructure-sensitive data-driven constitutive modeling.

A general model for anisotropic pseudo-elasticity and viscoelasticity at finite strains

Given the growing demand for simulating anisotropic material behavior at finite strains, constitutive modeling is in a challenging position to combine descriptive capabilities for several inelastic phenomena with the numerical feasibility for real-world applications. In this article, we develop a material model capable of reproducing anisotropy, viscoelasticity, stress softening, and permanent set by merging several pre-existing frameworks. Each constitutive effect is discussed separately in terms of its thermodynamics and mechanical interpretation and successively built on top of each other. Here, the pseudo-elastic approach to permanent set occupies a special place, with a novel discussion of its applicability to generic deformations. We show that the formulation does not lead to physical behavior in general, but can be constrained in such a way to produce appropriate stress predictions in an average sense. Examples of the stress response in several different deformation modes are visualized throughout. The capabilities and possible shortcomings of the formulation are highlighted and at the end a simple numerical algorithm for stress computation is presented.

On implementation of fibrous connective tissues’ damage in Abaqus software

Connective fibrous tissues, such as tendons and ligaments, in humans and animals exhibit hyperelastic behaviour. The constitution of the material of these tissues is anisotropic due to the presence of the collagen fibres, where one family of fibres is the typical case. Traumatic events and/or aging may sometimes lead to the damage of the tissue. The study of motion of affected joints or limbs is usually not permitted in vivo. This is where finite element method (FEM) becomes useful as a premise for general analysis, surgical planning or designing of implants and medical treatment. One of the most often used FEM commercial programs is the field of the biomechanics is Abaqus. The present study discusses the potential of user subroutine UANISOHYPER_INV in this code to analyse response of transversely isotropic tissue with damage in quasi-static range. This subroutine requires providing the material energy function and its derivatives only. The stress tensor and constitutive matrix are computed by the software automatically. To the best of the Authors’ knowledge this procedure provides the easiest way to simulate the anisotropic hyperelastic material behaviour in Abaqus. In this study its usage is extended onto the damage response simulation. The verification of the approach and its validation against experimental data indicates its efficiency.

On the initiation of hydraulic fractures in anisotropic rocks

This paper addresses hydraulic fracture initiation from an initially notch-free wellbore situated in an anisotropic host rock, where the rock mass is subjected to an in-situ stress state that is also anisotropic in nature. In such conditions, hydraulic fracture initiation is fully characterized by three parameters, namely initiation pressure, initiation orientation, and initiation length. While a strength-based criterion captures only two of these parameters, break-down pressure and orientation, the evaluation of initiation length requires a mixed criterion approach in which both stress and energy conditions are met. We extend the existing mixed criterion formulation for isotropic rocks to also include anisotropic material behavior. We then investigate how material anisotropy interacts with stress anisotropy to determine the break-down pressure as well as the size and orientation of the starter crack. The results show that material anisotropy can overshadow the stress anisotropy, in the sense that it can drive the crack towards the weakest plane. It is demonstrated from a fracture energy perspective that the initiation length cannot extend as large as the fracture process zone length even when the wellbore size is unrealistically large. The difference between initiation pressures predicted by the mixed criterion and strength-based theory rises as the wellbore size decreases. Based on these observations, applying the mixed criterion is essential especially in relatively small wellbores.

Improved Mean Value‐Amplitude Method for Determination of Orientation‐Dependent Modulus of Short Fiber‐Reinforced Thermoplastics

Short fiber‐reinforced thermoplastics such as 30% by weight glass fiber‐reinforced polyamide 46 (PA46GF30) are considered as substitute material for lightweight metallic parts. Despite the short fiber length, a distinct fiber orientation caused by local shear flow conditions during injection molding is obtained. This results in anisotropic material properties, which should be considered in the design phase of a component. Material properties are obtained by mechanical testing, e.g., tensile tests of specimens. These specimens have their own inherent microstructure consisting of different layers with different fiber orientations. The recently proposed mean value‐amplitude method enables the correlation of the Young's modulus to the eigenvalues of the fiber orientation tensor. The study presented herein applies a physically based improvement of the mean value‐amplitude method by consideration of the real fiber length. The results are very accurate for the description of the anisotropic material behavior and can be implemented in simulation tools for component design very easily.

Characterisation of out-of-plane shear behaviour of anisotropic sheet materials based on indentation plastometry

This paper presents a new methodology for characterising the out-of-plane plastic anisotropy behaviour of sheet metal, based on indentation testing. Conventionally, advanced yield criteria are used to describe plastic anisotropy, requiring multiple in-plane mechanical tests (such as uniaxial and biaxial tests) to calibrate a model. However, in certain forming applications (e.g. blanking, ironing and incremental forming), the influence of mechanical behaviour through thickness cannot be ignored, necessitating the characterisation of out-of-plane material behaviour. To do this, a 3D plastic anisotropy model must be used and calibrated for the out-of-plane shear parameters, which can be difficult to determine. Researchers often assume an isotropic case or equal shear parameters for in-plane and out-of-plane behaviour. More advanced calibrations involve the crystal plasticity model. In this work, we propose a two-stage calibration procedure. In the first stage, we calibrate the in-plane parameters of the YLD2004–18p yield function conventionally. In the second stage, after fixing the in-plane parameters, we determine the remaining out-of-plane shear parameters based on the results of the ball indentation test. We show for the first time that out-of-plane shear parameters can be determined from a macro-mechanical test for a 2.42 mm thick cold-rolled AA5754-H22 series aluminium sheet.

Characterization and Modeling of Anisotropic Fracture of Advanced High-Strength Steel Sheets

<div class="section abstract"><div class="htmlview paragraph">As an engineering approach of balanced complexity and accuracy, the Generalized Incremental Stress-State dependent damage Model (GISSMO) in LS-DYNA<sup>®</sup> has now been widely adopted by the automotive industry to predict metallic materials’ fracture occurrences in both forming and crashworthiness simulations. Calibration of the nominal GISSMO is typically based on material characterization data along a certain representative material orientation. Nevertheless, many rolled or extruded metallic materials, such as advanced high-strength steel (AHSS) sheets, exhibit accentuated anisotropic fracture behavior, even though, notably, some of these materials show comparatively weak anisotropic plasticity in the meantime. Accordingly, in this work, the deformation and fracture behavior of a selected AHSS grade, Q&P980 steel, was first characterized based on a series of mechanical experiments under simple shear, uniaxial tension, plane strain, and equi-biaxial tension conditions. Then, material models were calibrated based on the plasticity and fracture data. Two fracture models, either stress- or strain-based, were applied to fit the fracture loci of the target material, which then could be directly implemented into the material cards in LS-DYNA<sup>®</sup>. Particularly, to simulate the anisotropic fracture behavior of the target material, an extended GISSMO material card (eGISSMO) was introduced and highlighted in this work. Unlike the nominal GISSMO, the eGISSMO integrated the different anisotropic fracture loci and damage accumulation along three material orientations (longitudinal, diagonal, and transverse) into a single material card. In the subsequent validation based on a customized three-point-bending (3PB) testing setup on hat-section samples, only the finite element (FE) model using the calibrated eGISSMO successfully simulated the anisotropic fracture bifurcation observed in the actual experiments.</div></div>

Predicting anisotropic behavior of textured PBF-LB materials via microstructural modeling

It is well established that large temperature gradients cause strong textures in as-built metal parts manufactured via laser beam powder bed fusion. Columnar grains with a preferred crystallographic orientation dominate the microstructure of such materials resulting in a pronounced anisotropic mechanical behavior. Such materials are often studied with the help of tensile tests and corresponding numerical simulations in different loading directions. For the purpose of simulations, the microstructure is usually modeled with a statistically representative volume element (RVE). In the present study, two RVE modeling techniques, based on different texture sampling algorithms, have been compared for their property prediction capabilities. It was found that the model, based on an equally weighted crystallographic orientations set, sufficiently predicted macroscopic mechanical properties and also reduced the computational cost. Furthermore, an efficient method to rotate the boundary conditions for tensile test simulations under different loading directions was developed, thereby reducing the required number of RVE models to just one. The method was compared with an alternate method, where, an RVE model with rotated microstructure was subjected to unchanged boundary conditions. For this study, tensile test simulation results were compared with data from destructive material tests for predominantly single-phase austenitic stainless steel (EN 1.4404/AISI 316L).

A nonlocal microplane approach to model textile reinforced concrete at finite deformations

The contribution at hand focuses on the introduction of a new constitutive approach at finite deformations to represent an initially anisotropic material behavior accounting for fibers within a microplane model. To capture the specific behavior of concrete structures, a formulation is chosen, which is characterized by damage and plasticity phenomena. To achieve a consistent formulation for finite strain plasticity, a description relative to the plastic intermediate configuration is adopted. Therefore, a simulation of fiber reinforced concrete is enabled at large strains, which overcomes downsides of previous formulations. To overcome numerical instabilities, which can occur in softening phenomena, an implicit gradient enhancement is utilized. The novel formulations, within the microplane framework, enable a sufficiently close approximation of fiber reinforced concrete structures. In the numerical examples, it is demonstrated, that the newly introduced fiber formulation leads to physically meaningful results. Furthermore, a validation of the proposed model is carried out for concrete undergoing more than 30 % strain. Additionally, the fiber formulation is compared to tension tests carried out on textile reinforced concrete. It can be demonstrated, that the proposed formulations can be applied for different volume percentages of fiber reinforcement in concrete structures. As a consequence, it is now possible to simulate fiber reinforced concrete structures consistently for arbitrarily large strains.

Plasticity and ductility of an anisotropic recrystallized AA2198 Al-Cu-Li alloy in T3 and T8 conditions during proportional and non-proportional loading paths: simulations and experiments

The anisotropic material behaviour of a recrystallized AA2198 Al-Cu-Li alloy in T3 and T8 conditions was assessed by proportional loading of uniaxial-tension specimens in rolling (L), transverse (T) and diagonal (D) orientations. The width and longitudinal strains were measured to quantify plastic anisotropy. Notched-tension samples were tested in L and T directions. The material showed weak anisotropy in terms of stress strain curves and a moderate plastic anisotropy, consistent with its texture obtained by EBSD. An anisotropic Bron-Besson type material model was identified using this data base and a micro shear-only (SO) test. The model succeeded in predicting the behaviour of micro specimens for proportional tension-only (TO) loading and non-proportional load path changes including 'shear to tension' (ST) as well as 'tension to shear' (TS) tests. The non-proportional loading was achieved using a newly designed cross shaped sample. It was loaded in one direction, unloaded and subsequently loaded in the orthogonal direction till fracture. The average stretch to fracture of both alloys measured by a four point frame optical extensometer decreased by 29 % and 16 % for T3 and T8 respectively for the 'shear to tension' experiment compared to the proportional TO experiment. The average stretch to fracture of 'tension to shear' tests was reduced by 10 % for 2198T3 and hardly reduced for 2198T8 compared to the stretch to fracture of the SO tests, but subject to strong scatter. FE simulations showed local accumulated strain to fracture values that were similar for all loading histories for the T8 condition (0.73 − 0.84). Lower strain to fracture values were found in T3 condition (0.45 − 0.73), despite the enhanced macroscopic ductility in tension. This was attributed to larger less localized plastic zones, especially for the ST test. The ductility scatter was attributed to necking and damage development in tension that can affect strain localization, associated fracture path and ductility, as observed by DIC and fractography.

Non-linear elastic tension–compression asymmetric anisotropic model for fibre-reinforced composite materials

We present a novel constitutive model capable of describing non-linear anisotropic fibre-reinforced materials with different responses in tension and compression under a general stress state. The model is based on the original one-dimensional Ramberg–Osgood model, which is generalized to a multiaxial stress state and anisotropic material behaviour under thermodynamic requirements. To account for tension–compression asymmetry under a multiaxial stress state, the model is extended by the use of the stress triaxiality invariant as an indicator of stress state type, e.g. shear, uniaxial or biaxial tension, compression, etc. The model is implemented in ABAQUS/Explicit via the VUMAT subroutine and verified on two material datasets, which are an S2-glass/E773-epoxy and a reinforced polyester composite material. In comparison with other models, the proposed model provides an elegant formulation for the description of all the aforementioned phenomena, resulting in a simple calibration procedure based on uniaxial tensile and compressive tests.

Vibroacoustic metamaterials as add-on solution for noise reduction in existing housing structures

Vibroacoustic metamaterials (VAMM) have the potential to reduce unwanted noise components in a very targeted and narrow-band frequency range. Many VAMM concepts are based on mechanical resonators that act as vibration absorbers in their natural frequency and thus absorb energy that would otherwise be radiated in the form of airborne sound and perceived as noise. Often, during the design phase, it is not yet possible to adequately assess which surfaces will be acoustically problematic and in which frequency ranges disturbing noise components are going to be. In addition, many VAMM concepts can only be manufactured using additive manufacturing (AM) processes, due to their complex geometry. However, AM parts often have strongly anisotropic material behavior, depending on the manufacturing process, which makes a prediction of the vibroacoustic behavior even more difficult. Direct integration into casing structures during the design phase is therefore not practical and economically feasible in most cases. This paper therefore investigates the extent to which retrofitted resonators can be effectively used in existing casing structures. For this purpose, FDM-printed bending resonators made of ABS and PLA are used, which have already been measured with regard to their natural frequencies in a previous publication. Different variants are attached to a demonstrator housing and the surface vibration velocity is measured using a 3D laser scanning vibrometer, and compared with the basic variant without resonators. The radiated airborne sound is also measured. Furthermore, a comparison is made with a dynamic FEM simulation in order to be able to evaluate its prediction quality, in particular with regard to the additively manufactured resonators.