Anisotropic Material Model Research Articles

A simple integration algorithm for a non‐associated anisotropic plasticity model for sheet metal forming

SummaryIn this paper, an anisotropic material model based on a non‐associated flow rule and nonlinear mixed isotropic‐kinematic hardening is developed. The quadratic Hill48 yield criterion is considered in the non‐associated model for both yield function and plastic potential to account for anisotropic behavior. The developed model is integrated based on fully implicit backward Euler's method. The resulting problem is reduced to only two simple scalar equations. The consistent local tangent modulus is obtained by exact linearization of the algorithm. All numerical development was implemented into user‐defined material subroutine for the commercial finite element code ABAQUS/Standard. The performance of the present algorithm is demonstrated by numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

Numerical modeling of fluid-structure interaction in arteries with anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains.

The accurate prediction of transmural stresses in arterial walls requires on the one hand robust and efficient numerical schemes for the solution of boundary value problems including fluid-structure interactions and on the other hand the use of a material model for the vessel wall that is able to capture the relevant features of the material behavior. One of the main contributions of this paper is the application of a highly nonlinear, polyconvex anisotropic structural model for the solid in the context of fluid-structure interaction, together with a suitable discretization. Additionally, the influence of viscoelasticity is investigated. The fluid-structure interaction problem is solved using a monolithic approach; that is, the nonlinear system is solved (after time and space discretizations) as a whole without splitting among its components. The linearized block systems are solved iteratively using parallel domain decomposition preconditioners. A simple - but nonsymmetric - curved geometry is proposed that is demonstrated to be suitable as a benchmark testbed for fluid-structure interaction simulations in biomechanics where nonlinear structural models are used. Based on the curved benchmark geometry, the influence of different material models, spatial discretizations, and meshes of varying refinement is investigated. It turns out that often-used standard displacement elements with linear shape functions are not sufficient to provide good approximations of the arterial wall stresses, whereas for standard displacement elements or F-bar formulations with quadratic shape functions, suitable results are obtained. For the time discretization, a second-order backward differentiation formula scheme is used. It is shown that the curved geometry enables the analysis of non-rotationally symmetric distributions of the mechanical fields. For instance, the maximal shear stresses in the fluid-structure interface are found to be higher in the inner curve that corresponds to clinical observations indicating a high plaque nucleation probability at such locations. Copyright © 2015 John Wiley & Sons, Ltd.

Constitutive modelling of high strength titanium alloy Ti-6Al-4 V for sheet forming applications at room temperature

• A rigours set of experiments were performed to measure the initial yield surface of Ti-6Al-4V at room temperature under different-stress states. • A constitutive equation based anisotropic hardening model (HAH) model combined with the new determined yield function was proposed and implemented into the FEA- Abaqus implicit solver. • The proposed model showed ability to accurately predict the cyclic hardening response of Ti-6Al-4V, and therefore presents a promising approach for the prediction of deformation behaviour of Ti-6Al-4V alloy in sheet metal forming processes. To enable the design and optimisation of forming processes at room temperature the material behaviour of Ti-6Al-4 V needs to be accurately represented in numerical analysis and this requires an advanced material model. In particular, an accurate representation of the shape and size of the yield locus as well as its evolution during forming is important. In this study a rigorous set of experiments on the quasi-static deformation behaviour of a Ti-6Al-4 V alloy sheet sample at room temperature was conducted for various loading conditions and a constitutive material model developed. To quantify the anisotropy and asymmetry properties, tensile and compression tests were carried out for different specimen orientations. To examine the Bauschinger effect and the transient hardening behaviour in – plane tensile – compression and compression – tensile tests were performed. Balanced biaxial and plane strain tension tests were conducted to construct and validate the yield surface of the Ti-6Al-4 V alloy sheet sample at room temperature. A recently proposed anisotropic elastic-plastic constitutive material model, so-called HAH, was employed to describe the behaviour, in particular for load reversals. The HAH yield surface is composed of a stable component, which includes plastic anisotropy and is distorted by a fluctuating component. The key of the formulation is the use of a suitable yield function that reproduces the experimental observations well for the stable component. Meanwhile, the rapid evolution of the material structure must be captured at the macro - scale level by the fluctuating component embedded in the HAH model. Compared to conventional hardening equations, the proposed model leads to higher accuracy in predicting the Bauschinger effect and the transient hardening behaviour for the Ti-6Al-4 V sheet sample tested at room temperature.

A representative-sandwich model for simultaneously coupled mechanical-electrical-thermal simulation of a lithium-ion cell under quasi-static indentation tests

The safety behavior of lithium-ion batteries under external mechanical crush is a critical concern, especially during large-scale deployment. We previously presented a sequentially coupled mechanical-electrical-thermal modeling approach for studying mechanical-abuse-induced short circuit. In this work, we study different mechanical test conditions and examine the interaction between mechanical failure and electrical-thermal responses, by developing a simultaneously coupled mechanical-electrical-thermal model. The present work utilizes a single representative-sandwich (RS) to model the full pouch cell with explicit representations for each individual component such as the active material, current collector, separator, etc. Anisotropic constitutive material models are presented to describe the mechanical properties of active materials and separator. The model predicts accurately the force-strain response and fracture of battery structure, simulates the local failure of separator layer, and captures the onset of short circuit for lithium-ion battery cells under sphere indentation tests with three different diameters. Electrical-thermal responses to the three different indentation tests are elaborated and discussed. Numerical studies are presented to show the potential impact of test conditions on the electrical-thermal behavior of the cell after the occurrence of short circuit.

Effect of reinforcement volume fraction and orientation on a hybrid tissue engineered aortic heart valve with a tubular leaflet design

Transcatheter aortic valve implantation of fibrin-based tissue engineered heart valves with a tubular leaflet construct have been developed as an alternative to invasive traditional surgical heart valve implantation. In general, they are well suited for the pulmonary position, but display insufficient mechanical properties for the aortic position. To enable the application of tissue-engineered valves in the systemic circulation, the tissue is reinforced with a textile scaffold. The current study seeks to compare the effect of varying the fiber volume fraction and orientation of bidirectional textile reinforcement on the closed-valve configuration. An anisotropic large deformation material model based on structural tensors was chosen and the materials were characterized. A finite element model was constructed of the heart valve, and the pinching and suturing of the corners along with application of pressure was simulated. Virtual experiments were conducted with fiber volume fractions of 0.1, 0.01, 0.001, and 0.0001 for ±45° fiber orientations. Furthermore, volume fraction was held at 0.01 and fiber orientations of 0°, ±15°, ±30°, ±45°, ±60°, ±75° and 90° from the tube’s axial direction were simulated and compared. It was shown that increasing the fiber volume fraction decreased the maximum principle strain in the valve, but lead to less closure. Additionally, the effect of fiber orientation affected the strains differently at different locations, depending on the local deformed geometry. This indicates that a non-uniform fiber distribution using tailored fiber placement could be used to optimize reinforcement design.

Constitutive behaviour of quasi-brittle materials with anisotropic friction

This paper presents an approach to a constitutive model for anisotropic quasi-brittle materials, developed in the framework of rate independent softening plasticity, involving a yield criterion in which an anisotropic friction tensor is involved. It turns out to be useful for materials characterized by ultimate behaviour which varies according to the direction, such as composite materials, anisotropic rocks, textiles, masonry. A geometrical representation of the limit domain in the case of plane stress, together with the results of laboratory tests is presented and discussed.

Finite element modelling of off-road tyres for radial tyre model parameterization

This paper investigates the possibility of using a coarse finite element model with bulk material properties, to model the vertical force–displacement characteristics of a tyre, for the purpose of tyre model parameterization. The paper proves the approach on an off-road tyre of a light truck. The practical application is intended, however, for very large tyres where physical testing is not feasible. The paper indicates that it is feasible to obtain bulk material properties from tensile tests on specimens cut from different positions on a tyre and to use these test results to parameterize suitable non-linear anisotropic material models. The non-linear elements defined in the neo-Hookean model and the Ogden model, as well as the elements with different linear orthogonal stiffnesses, are combined with each other to simulate the global material properties of the tread and the sidewall of the tyre. The global behaviour of the finite element model is analysed by comparing experimental results and simulation data on a flat surface as well as various lateral and longitudinal cleats. The results confirm that the finite element model can predict with acceptable accuracy the vertical force–displacement characteristics, as well as the sidewall deformation of the tyre under static loading conditions on a flat surface and also on various different cleats, by using equivalent (global) material properties. The approach is sufficiently accurate to be used in the parameterization of various tyre models.

On the Use of Biaxial Properties in Modeling Annulus as a Holzapfel-Gasser-Ogden Material.

Besides the biology, stresses and strains within the tissue greatly influence the location of damage initiation and mode of failure in an intervertebral disk. Finite element models of a functional spinal unit (FSU) that incorporate reasonably accurate geometry and appropriate material properties are suitable to investigate such issues. Different material models and techniques have been used to model the anisotropic annulus fibrosus, but the abilities of these models to predict damage initiation in the annulus and to explain clinically observed phenomena are unclear. In this study, a hyperelastic anisotropic material model for the annulus with two different sets of material constants, experimentally determined using uniaxial and biaxial loading conditions, were incorporated in a 3D finite element model of a ligamentous FSU. The purpose of the study was to highlight the biomechanical differences (e.g., intradiscal pressure, motion, forces, stresses, strains, etc.) due to the dissimilarity between the two sets of material properties (uniaxial and biaxial). Based on the analyses, the biaxial constants simulations resulted in better agreements with the in vitro and in vivo data, and thus are more suitable for future damage analysis and failure prediction of the annulus under complex multiaxial loading conditions.

Isogeometric Kirchhoff-Love shell formulations for biological membranes.

Computational modeling of thin biological membranes can aid the design of better medical devices. Remarkable biological membranes include skin, alveoli, blood vessels, and heart valves. Isogeometric analysis is ideally suited for biological membranes since it inherently satisfies the C1-requirement for Kirchhoff-Love kinematics. Yet, current isogeometric shell formulations are mainly focused on linear isotropic materials, while biological tissues are characterized by a nonlinear anisotropic stress-strain response. Here we present a thin shell formulation for thin biological membranes. We derive the equilibrium equations using curvilinear convective coordinates on NURBS tensor product surface patches. We linearize the weak form of the generic linear momentum balance without a particular choice of a constitutive law. We then incorporate the constitutive equations that have been designed specifically for collagenous tissues. We explore three common anisotropic material models: Mooney-Rivlin, May Newmann-Yin, and Gasser-Ogden-Holzapfel. Our work will allow scientists in biomechanics and mechanobiology to adopt the constitutive equations that have been developed for solid three-dimensional soft tissues within the framework of isogeometric thin shell analysis.

Fluid-structure interaction in abdominal aortic aneurysms: Structural and geometrical considerations

Rupture of the abdominal aortic aneurysm (AAA) is the result of the relatively complex interaction of blood hemodynamics and material behavior of arterial walls. In the present study, the cumulative effects of physiological parameters such as the directional growth, arterial wall properties (isotropy and anisotropy), iliac bifurcation and arterial wall thickness on prediction of wall stress in fully coupled fluid-structure interaction (FSI) analysis of five idealized AAA models have been investigated. In particular, the numerical model considers the heterogeneity of arterial wall and the iliac bifurcation, which allows the study of the geometric asymmetry due to the growth of the aneurysm into different directions. Results demonstrate that the blood pulsatile nature is responsible for emerging a time-dependent recirculation zone inside the aneurysm, which directly affects the stress distribution in aneurismal wall. Therefore, aneurysm deviation from the arterial axis, especially, in the lateral direction increases the wall stress in a relatively nonlinear fashion. Among the models analyzed in this investigation, the anisotropic material model that considers the wall thickness variations, greatly affects the wall stress values, while the stress distributions are less affected as compared to the uniform wall thickness models. In this regard, it is confirmed that wall stress predictions are more influenced by the appropriate structural model than the geometrical considerations such as the level of asymmetry and its curvature, growth direction and its extent.

Transversely isotropic material characterization of the human anterior longitudinal ligament

The present work represents the first study to report transversely isotropic material parameters for the human anterior longitudinal ligament (ALL) in the thoraco-lumbar spine. Force-deformation data from multi-axial testing was collected from 30 cadaveric spine test specimens using an anisotropic quarter punch test technique. The experimental data was fit to a commonly used anisotropic soft tissue material model using an FEA system identification technique. The material model correlated well with the experimental response (R2≥0.98). The constitutive parameter values, as well as the nonlinear anisotropic stress–strain response of the ALL specimens are reported to facilitate application to biomechanical models (including finite element models) of the spine.

Influence of isotropic and anisotropic material models on the mechanical response in arterial walls as a result of supra-physiological loadings

As accepted in the literature, arterial tissues have in principle anisotropic material properties. Although some very special situations in arteries exist where isotropic constitutive models may approximate the real material behavior with sufficient accuracy, the larger part of analyses requires an anisotropic model. In particular for overstretched arteries, as e.g. a result of a balloon angioplasty, an accurate representation of the complex softening phenomena is important and then the consideration of anisotropy may be necessary. However, a variety of publications found in the literature, where such supra-physiological loading situations are analyzed to optimize e.g. stent designs, consider isotropic models. Therefore, in this contribution, the response of an isotropic and an anisotropic material model is compared in numerical calculations where arteries are subjected to supra-physiological loading. The constitutive formulations include the typical nonlinear stiffening of the fiber response as well as softening due to microscopic damage. In detail, the isotropic and the anisotropic model are adjusted to the same experimental stress–stretch curves of different arterial layers and then both models are applied to finite element simulations of overstretched arterial walls. As it turns out a significant difference is obtained for both calculations showing the importance of anisotropic models for these loading situations.

Tests of Wooden Specimens from Scots Pine (Pinus sylvestris) with the Help of Anisotropic Plasticity Material Model

Tests of Wooden Specimens from Scots Pine (Pinus sylvestris) with the Help of Anisotropic Plasticity Material Model

Progression of abdominal aortic aneurysm towards rupture: refining clinical risk assessment using a fully coupled fluid-structure interaction method.

Rupture of abdominal aortic aneurysm (AAA) is associated with high mortality rates. Risk of rupture is multi-factorial involving AAA geometric configuration, vessel tortuosity, and the presence of intraluminal pathology. Fluid structure interaction (FSI) simulations were conducted in patient based computed tomography scans reconstructed geometries in order to monitor aneurysmal disease progression from normal aortas to non-ruptured and contained ruptured AAA (rAAA), and the AAA risk of rupture was assessed. Three groups of 8 subjects each were studied: 8 normal and 16 pathological (8 non-ruptured and 8 rAAA). The AAA anatomical structures segmented included the blood lumen, intraluminal thrombus (ILT), vessel wall, and embedded calcifications. The vessel wall was described with anisotropic material model that was matched to experimental measurements of AAA tissue specimens. A statistical model for estimating the local wall strength distribution was employed to generate a map of a rupture potential index (RPI), representing the ratio between the local stress and local strength distribution. The FSI simulations followed a clear trend of increasing wall stresses from normal to pathological cases. The maximal stresses were observed in the areas where the ILT was not present, indicating a potential protective effect of the ILT. Statistically significant differences were observed between the peak systolic stress and the peak stress at the mean arterial pressure between the three groups. For the ruptured aneurysms, where the geometry of intact aneurysm was reconstructed, results of the FSI simulations clearly depicted maximum wall stress at the a priori known location of rupture. The RPI mapping indicated several distinct regions of high RPI coinciding with the actual location of rupture. The FSI methodology demonstrates that the aneurysmal disease can be described by numerical simulations, as indicated by a clear trend of increasing aortic wall stresses in the studied groups, (normal aortas, AAAs and rAAAs). Ultimately, the results demonstrate that FSI wall stress mapping and RPI can be used as a tool for predicting the potential rupture of an AAA by predicting the actual rupture location, complementing current clinical practice by offering a predictive diagnostic tool for deciding whether to intervene surgically or spare the patient from an unnecessary risky operation.

Computer-Aided Study of Materials’ Microstructure Influence on Cracks' Propagation Pattern in Brittle Anisotropic Bodies

The purpose of the presented study is a solution of a boundary-value problem, a visualization and a study of crack propagation pattern of a plane specimen of an anisotropic brittle material by computer modeling method. As main software for the research, MSC Nastran finite-element analysis package is used. As a result of the presented study, a methodology for a creation of finite-element models of various structural constituents and specimens with consideration of material’s microstructure is developed. Developed methodology is tested during the creation of finite-element model of the specimen assigned for a fracture with stress concentrators of varying forms and with a consideration of hypothetical structure, consisting of three types of crystallite with different mechanical properties. The methodology is proposed for an evaluation of kinetics and visualization of the crack growth in models of isotropic and anisotropic brittle materials. As the result of step-by-step visualization of the crack growth, animation files in AVI-format are created, which allow us to analyze the process of the material fracture. A theoretical equation is proposed for determination of the crack growth trajectory, which defines a relationship between a work needed for the crack growth and stresses in the specimen and its geometric parameters. An influence of the material on the trajectory of the crack growth is determined. Results of the presented study can serve as a tool for development of new materials with a high crack resistance due to their optimal microstructure. Developed methodologies allow you to determine desired location, size, shape of grains and their mechanical properties in microstructure of created material, without fabrication of many expensive full-size specimens.

Experimental investigation of the mechanical properties of neoprene coated nylon woven reinforced composites

In this study, the mechanical behaviour of neoprene coated nylon woven fabric composites was assessed using biaxial loading based on hydraulic bulge test method and uniaxial tensile method at varied environmental testing conditions. Results indicating failure modes, ultimate strengths and strains from the uniaxial testing of the composites were compared and recommendations for application of the composite material in structural design are reported. A through thickness approximate homogeneous modulus from the weft and warp uniaxial tests results of the membrane for a simple linear elastic anisotropic material model was used in ABAQUS finite element software to simulate the bulge test experiments. Results from the numerical analysis were found to replicate the bulge experiments to a first approximation. This approach offers useful application for the FE modelling and design of offshore inflatable structures made of coated woven fabrics which are typified by large size and complex geometries, as it reduces computational cost and potentially eliminates the need for a complex material description involving detailed theoretical derivations and advanced programming to implement.

Computational analysis of the radial mechanical performance of PLLA coronary artery stents

Stents have been an effective tool to restore and maintain the patency of narrowed blood vessels, but they must have sufficient radial strength. Biodegradable stent materials have substantially lower mechanical properties than permanent stents. The stent geometry and material properties must be considered simultaneously when assessing stent performance. Material tests were performed to determine the mechanical characteristics of high-molecular-weight poly-l-lactic acid (PLLA). The results were used to calibrate an anisotropic elastic-plastic material model. Three distinct geometries were analysed with a range of material stiffness values in a finite element analysis to investigate their comparative effect on the radial strength, recoil, and radial stiffness. The performance of the different geometries varies substantially, with one particular geometry, with the highest material stiffness of 9GPa, exceeding the desired radial strength of 300mmHg.

Finite element analysis of abdominal aortic aneurysms: geometrical and structural reconstruction with application of an anisotropic material model

Finite element analysis of abdominal aortic aneurysms: geometrical and structural reconstruction with application of an anisotropic material model

Shock wave compression of hexagonal-close-packed metal single crystals: Time-dependent, anisotropic elastic-plastic response of beryllium

Understanding and modeling the response of hcp metals to high stress impulsive loading is challenging because the lower crystal symmetry, compared to cubic metals, results in a significantly more complex material response. To gain insight into the inelastic deformation of hcp metals subjected to high dynamic stresses, shock wave compression of single crystals provides a useful approach because different inelastic deformation mechanisms can be examined selectively by shock compression along different crystal orientations. As a representative example, we report, here, on wave propagation simulations for beryllium (Be) single crystals shocked along the c-axis, a-axis, and several low-symmetry directions to peak stresses reaching 7 GPa. The simulations utilized a time-dependent, anisotropic material model that incorporated dislocation dynamics, deformation twinning, and shear cracking based descriptions of inelastic deformation. The simulation results showed good overall agreement with measured wave profiles for all the different crystal orientations examined [Pope and Johnson, J. Appl. Phys. 46, 720 (1975)], including features arising from wave mode coupling due to the highly anisotropic inelastic response of Be. This good agreement demonstrates that the measured profiles can be understood in terms of dislocation slip along basal, prismatic, and pyramidal planes, together with deformation twinning along {101¯2} planes. Our results show that the response of shocked Be single crystals involves the simultaneous operation of multiple, distinct inelastic deformation mechanisms for all orientations except the c-axis. For shocked c-axis Be, the measured wave profiles do not provide good discrimination between pyramidal slip and other inelastic deformation mechanisms, such as shear cracking. The findings presented here provide insight into the complex inelastic deformation response of shocked Be single crystals and are expected to be useful for other hcp crystals. More broadly, the present work demonstrates the potential of shock wave propagation along low-symmetry directions to examine, and discriminate between, different inelastic deformation mechanisms in crystalline solids.

Mechanical Characterization of Foils with Compression in Their Planes

An experimental-computational procedure is proposed and numerically validated for combined compression and bending tests and for identification of parameters in anisotropic elastic-plastic material models of the mechanical behavior of foils, specifically of paperboards and laminates for liquid containers. From the experimental standpoint, the proposed technique generalizes the instrumentation and “modus operandi” of traditional uni-axial testing with the following novel provisions: the foil specimen is stabilized by two elastic “blocks” of a well known polymeric material (therefore, such system is called “sandwich” herein); “full-field” displacement measurements by a digital image correlation (DIC) technique are envisaged, and examined by sensitivity analyses with respect to the sought parameters; the experimental data provided by DIC might be enriched by the digitalized relationship between external loading and imposed displacements in the test; test simulations (“direct analyses”) are performed by finite element modeling and the sought parameters governing the specimen behavior are assessed by minimization of a discrepancy function (inverse analysis); the minimization by mathematical programming is made fast and economical by radial basis functions (RBF) interpolations based on preliminary proper orthogonal decomposition (POD).