Anisotropic Material Model Research Articles

Studies on gasketed flange joints under bending with anisotropic Hill plasticity model for gasket

The behavior of a gasketed flange joint under bending loads has been studied by three dimensional finite element analysis (FEA) and experiments. The in-plane and bending stiffness of spiral wound gaskets are considered using anisotropic Hill plasticity material model. The variation in bolt axial force of joints under bending load predicted by the finite element analysis compares well with the experimental results. The contact stress distribution obtained have significant variation in the pattern from the previous material models and consistent with the results of Bouzid [1] regarding flange rotation.

An anisotropic tertiary creep damage constitutive model for anisotropic materials

When an anisotropic material is subject to creep conditions and a complex state of stress, an anisotropic creep damage behavior is observed. Previous research has focused on the anisotropic creep damage behavior of isotropic materials but few constitutive models have been developed for anisotropic creeping solids. This paper describes the development of a new anisotropic tertiary creep damage constitutive model for anisotropic materials. An advanced tensorial damage formulation is implemented which includes both material orientation relative to loading and the degree of creep damage anisotropy in the model. A variation of the Norton-power law for secondary creep is implemented which includes the Hill’s anisotropic analogy. Experiments are conducted on the directionally-solidified bucket material DS GTD-111. The constitutive model is implemented in a user programmable feature (UPF) in ANSYS FEA software. The ability of the constitutive model to regress to the Kachanov-Rabotnov isotropic tertiary creep damage model is demonstrated through comparison with uniaxial experiments. A parametric study of both material orientation and stress rotation are conducted. Results indicate that creep deformation is modeled accurately; however an improved damage evolution law may be necessary.

Modelling Texturised Cast Structures in the Forging of Superalloys

The main objective of remelting processes commonly used in the production of super¬alloys is to obtain a columnar dendritic solidification structure throughout the whole ingot. Besides reduced microsegregation, this cast structure features a preferred orientation, which is depending on the primary dendrites’ growth direction and therefore closely related to the ingot’s pool shape. As a result, non-isotropic material behaviour can be observed during initial forging operations. Since the correct prediction of material flow is a prerequisite for the further analysis of forging processes by means of numerical simulation, the solidification texture’s influence on plastic flow was accounted for by the application of an anisotropic material model. The model according to Barlat was used to scale the flow stress with respect to the crystal orientations observed in the examination of vacuum arc remelted alloy 718, thereby considering the flow stress’ dependency on strain, strain rate and temperature. The parameters defining the material's anisotropy could be determined by the upsetting of cylindrical specimen from a remelted ingot.

Numerical Modeling of Post-Processing of Composite Materials

This paper focuses on learning about post-processing of composite materials in the current context of Manufacturing Engineering education in Spain. The use of composites has been significantly increased in different sectors in industry during the last decades. The students,taking manufacturing courses in engineering study plans, need basic formation concerning post-processing of composites. Due to the complexity of the process, powerful numerical tools are needed to develop practical models focused on damage prediction. Learning skills include modeling of anisotropic materials and specific concepts of composite such as machining induced damage.

Investigation of 3D anisotropic electrical conductivity in TIG welded 5A06 Al alloy using eddy currents

Electrical conductivity undergoes changes in the weld zones of the material. In this study, its anisotropic components along longitudinal, transverse and through-thickness directions have been investigated nondestructively using circular eddy current probe with Hall Effect sensor. The electromagnetic forward model has been solved with material resistivity input profiles corresponding to tensile and compressive residual stresses in a typical welded joint. For reconstruction of 3D anisotropic electrical conductivity, constrained linear least square optimization has been used. Compared with measurements based on calibration with homogeneous specimen or calculated assuming isotropic material properties in forward model, the results indicate that change in conductivity is significantly larger. A quantitative comparison is made between results based on isotropic and anisotropic material models. The conductivity mapping is required for residual stress measurement in components and structures.

A local constitutive model with anisotropy for ratcheting under 2D axial-symmetric isobaric deformation

A local constitutive model for anisotropic granular materials is introduced and applied to isobaric (homogeneous) axial-symmetric deformation. The simplified model (in the coordinate system of the bi-axial box) involves only scalar values for hydrostatic and shear stresses, for the volumetric and shear strains as well as for the new ingredient, the anisotropy modulus. The non-linear constitutive evolution equations that relate stress and anisotropy to strain are inspired by observations from discrete element method (DEM) simulations. For the sake of simplicity, parameters like the bulk and shear modulus are set to constants, while the shear stress ratio and the anisotropy evolve with different rates to their critical state limit values when shear deformations become large. When applied to isobaric deformation in the bi-axial geometry, the model shows ratcheting under cyclic loading. Fast and slow evolution of the anisotropy modulus with strain. Lead to dilatancy and contractancy, respectively. Furthermore, anisotropy acts such that it works “against” the strain/stress, e.g., a compressive strain builds up anisotropy that creates additional stress acting against further compression.

Modelling and Analysis of the Bottom Frames of Multi-Story Masonry Buildings Exposed to Fire

The multi-story masonry buildings with reinforced concrete frames on ground floors collapse more easily than pure frames when bottom frames exposed to fire, for reasons that fire load of its ground floors is relatively large, and the ratio of dead load to the total loads is also large, deformations of joists caused by fire produce adverse effect on arch mechanism of masonry. For the purpose of loading temperature on steel bars and concrete for fire resistance analysis of reinforced concrete structures in ABAQUS, separated loading method is proposed firstly in this article. The Hill yield criterion for compression and the Rankine yield criterion for tension are adopted to establish anisotropic elasto-plastic material model for masonry. The process simulation from temperature rises to buildings collapse is realized. A parametric study is conducted to investigate the effects on fire resistance of the bottom frames when the bottom floors exposed to fire due to the change in effective load ratio, section size and reinforcement ratio. The study shows that the failure mode of the bottom frames exposed to fire is mainly due to columns collapse. Bottom fames designed with seismic class I and II have relatively more safety storage than non-seismic designed bottom frames to resist the fire load effect, and they can satisfy time limits of fire resistance.

Spatial contact problems for a prestressed incompressible elastic layer

Two problems are considered on frictionless indentation of a stamp into the upper face of a layer with a homogeneous field of initial stresses present in the layer. The model of an isotropic incompressible nonlinearly-elastic material determined by the Mooney potential is used. The following two cases are studied: the lower face of the prestressed layer is rigidly fixed, and the lower face of a prestressed layer is supported by a rigid foundation without friction. It is assumed that the additional stresses due to the action of the stamp on the layer are small as compared with the initial stresses. This assumption makes it possible to linearize the problems of determining the additional stresses. In what follows, the problems are reduced to solving two-dimensional integral equations (IE) of the first kind with symmetric irregular kernels with respect to the pressure in the contact region. As an example, the case of an elliptic (in plan) stamp acting on a layer is considered. The spatial contact problem for a prestressed elastic half-space was first considered in [1].

Modeling failure of soft anisotropic materials with application to arteries

The arterial wall is a composite where the preferred orientation of collagen fibers induces anisotropy. Though the hyperelastic theories of fiber-reinforced composites reached a high level of sophistication and showed a reasonable correspondence with the available experimental data they are short of the failure description. Following the tradition of strength of materials the failure criteria are usually separated from stress analysis. In the present work we incorporate a failure description in the hyperelastic models of soft anisotropic materials by introducing energy limiters in the strain energy functions. The limiters provide the saturation value for the strain energy which indicates the maximum energy that can be stored and dissipated by an infinitesimal material volume. By using some popular constitutive models enhanced with the energy limiters we analyze rupture of a sheet of arterial material under the plane stress state varying from the uniaxial to equal biaxial tension. We calculate the local failure criteria including the maximum principal stress, the maximum principal stretch, the von Mises stress, and the strain energy at the moment of the sheet rupture. We find that the local failure criterion in the form of the critical strain energy is the most robust among the considered ones. We also find that the tensile strength–the maximum principal stress–that is usually obtained in uniaxial tension tests might not be appropriate as a failure indicator in the cases of the developed biaxiality of the stress–strain state.

Effects of intima stiffness and plaque morphology on peak cap stress

BackgroundRupture of the cap of a vulnerable plaque present in a coronary vessel may cause myocardial infarction and death. Cap rupture occurs when the peak cap stress exceeds the cap strength. The mechanical stress within a cap depends on the plaque morphology and the material characteristics of the plaque components. A parametric study was conducted to assess the effect of intima stiffness and plaque morphology on peak cap stress.MethodsModels with idealized geometries based on histology images of human coronary arteries were generated by varying geometric plaque features. The constructed multi-layer models contained adventitia, media, intima, and necrotic core sections. For adventitia and media layers, anisotropic hyperelastic material models were used. For necrotic core and intima sections, isotropic hyperelastic material models were employed. Three different intima stiffness values were used to cover the wide range reported in literature. According to the intima stiffness, the models were classified as stiff, intermediate and soft intima models. Finite element method was used to compute peak cap stress.ResultsThe intima stiffness was an essential determinant of cap stresses. The computed peak cap stresses for the soft intima models were much lower than for stiff and intermediate intima models. Intima stiffness also affected the influence of morphological parameters on cap stresses. For the stiff and intermediate intima models, the cap thickness and necrotic core thickness were the most important determinants of cap stresses. The peak cap stress increased three-fold when the cap thickness was reduced from 0.25 mm to 0.05 mm for both stiff and intermediate intima models. Doubling the thickness of the necrotic core elevated the peak cap stress by 60% for the stiff intima models and by 90% for the intermediate intima models. Two-fold increase in the intima thickness behind the necrotic core reduced the peak cap stress by approximately 25% for both intima models. For the soft intima models, cap thickness was less critical and changed the peak cap stress by 55%. However, the necrotic core thickness was more influential and changed the peak cap stress by 100%. The necrotic core angle emerged as a critical determinant of cap stresses where a larger angle lowered the cap stresses. Contrary to the stiff and intermediate intima models, a thicker intima behind the necrotic core increased the peak cap stress by approximately 25% for the soft intima models. Adventitia thickness and local media regression had limited effects for all three intima models.ConclusionsFor the stiff and intermediate intima models, the cap thickness was the most important morphological risk factor. However for soft intima models, the necrotic core thickness and necrotic core angle had a bigger impact on the peak cap stress. We therefore need to enhance our knowledge of intima material properties if we want to derive critical morphological plaque features for risk evaluation.

Creep fatigue of a directionally solidified Ni-base superalloy - smooth and cylindrically notched specimens

Turbine blade life modelling is complicated by the presence of notches, dwells, high temperatures, thermal cycles and temperature gradients. Furthermore, directionally so- lidified (DS) Ni-base superalloys are highly anisotropic. This work seeks to characterize the response of the DS Ni-base superalloy CM247LC subjected to isothermal low cycle fatigue at either 750 or 950 °C. This study considers the effects of strain rate, dwells at the maximum temperature, and stress concentrations. Experiments were conducted under uniaxial loading on smooth and cylindrically notched round-bar specimens in both longitudinal and transverse orientations. The location of the creep-fatigue crack is at the maximum Hill's effective stress in the notched specimens. In addition, the notch behaviour is discussed in light of finite element analysis using an anisotropic elastic-crystal viscoplastic material model.

The effect of angulation in abdominal aortic aneurysms: fluid–structure interaction simulations of idealized geometries

Abdominal aortic aneurysm (AAA) represents a degenerative disease process of the abdominal aorta that results in dilation and permanent remodeling of the arterial wall. A fluid structure interaction (FSI) parametric study was conducted to evaluate the progression of aneurysmal disease and its possible implications on risk of rupture. Two parametric studies were conducted using (i) the iliac bifurcation angle and (ii) the AAA neck angulation. Idealized streamlined AAA geometries were employed. The simulations were carried out using both isotropic and anisotropic wall material models. The parameters were based on CT scans measurements obtained from a population of patients. The results indicate that the peak wall stresses increased with increasing iliac and neck inlet angles. Wall shear stress (WSS) and fluid pressure were analyzed and correlated with the wall stresses for both sets of studies. An adaptation response of a temporary reduction of the peak wall stresses seem to correlate to a certain extent with increasing iliac angles. For the neck angulation studies it appears that a breakdown from symmetric vortices at the AAA inlet into a single larger vortex significantly increases the wall stress. Our parametric FSI study demonstrates the adaptation response during aneurysmal disease progression and its possible effects on the AAA risk of rupture. This dependence on geometric parameters of the AAA can be used as an additional diagnostic tool to help clinicians reach informed decisions in establishing whether a risky surgical intervention is warranted.

Micromechanics of diffuse axonal injury: influence of axonal orientation and anisotropy

Multiple length scales are involved in the development of traumatic brain injury, where the global mechanics of the head level are responsible for local physiological impairment of brain cells. In this study, a relation between the mechanical state at the tissue level and the cellular level is established. A model has been developed that is based on pathological observations of local axonal injury. The model contains axons surrounding an obstacle (e.g., a blood vessel or a brain soma). The axons, which are described by an anisotropic fiber-reinforced material model, have several physically different orientations. The results of the simulations reveal axonal strains being higher than the applied maximum principal tissue strain. For anisotropic brain tissue with a relatively stiff inclusion, the relative logarithmic strain increase is above 60%. Furthermore, it is concluded that individual axons oriented away from the main axonal direction at a specific site can be subjected to even higher axonal strains in a stress-driven process, e.g., invoked by inertial forces in the brain. These axons can have a logarithmic strain of about 2.5 times the maximum logarithmic strain of the axons in the main axonal direction over the complete range of loading directions. The results indicate that cellular level heterogeneities have an important influence on the axonal strain, leading to an orientation and location-dependent sensitivity of the tissue to mechanical loads. Therefore, these effects should be accounted for in injury assessments relying on finite element head models.

Anisotropic material model and wave propagation simulations for shocked pentaerythritol tetranitrate single crystals

An anisotropic continuum material model was developed to describe the thermomechanical response of unreacted pentaerythritol tetranitrate (PETN) single crystals to shock wave loading. Using this model, which incorporates nonlinear elasticity and crystal plasticity in a thermodynamically consistent tensor formulation, wave propagation simulations were performed to compare to experimental wave profiles [J. J. Dick and J. P. Ritchie, J. Appl. Phys. 76, 2726 (1994)] for PETN crystals under plate impact loading to 1.2 GPa. Our simulations show that for shock propagation along the [100] orientation where deformation across shear planes is sterically unhindered, a dislocation-based model provides a good match to the wave profile data. For shock propagation along the [110] direction, where deformation across shear planes is sterically hindered, a dislocation-based model cannot account for the observed strain-softening behavior. Instead, a shear cracking model was developed, providing good agreement with the data for [110] and [001] shock orientations. These results show that inelastic deformation due to hindered and unhindered shear in PETN occurs through mechanisms that are physically different. In addition, results for shock propagation normal to the (101) crystal plane suggest that the primary slip system identified from quasistatic indentation tests is not activated under shock wave loading. Overall, results from our continuum simulations are consistent with a previously proposed molecular mechanism for shock-induced chemical reaction in PETN in which the formation of polar conformers, due to hindered shear, facilitates the development of ionic reaction pathways.

A method for thein situmeasurement of evolving elliptical cross-sections in initially cylindrical Taylor impact specimens

This paper presents a novel approach to the classic Taylor impact experiment using an ultra-high-speed camera and mirror arrangement to measure the elliptical cross-section of a specimen in situ as a function of time. This optical measurement technique is used to quantify the key aspects of material behaviour, such as the area strain perpendicular to the impact direction and the lengths of the semimajor and semiminor axes of the elliptical sample cross-section, which were caused by anisotropic plastic deformation, as functions of time and the axial position. The application of this technique gives access to previously unattainable data on the anisotropic plastic deformation of Taylor impact specimens and therefore has the potential to provide a more rigorous method of validation for anisotropic constitutive material models. To demonstrate the feasibility of the new method, experiments were carried out on cylindrical Taylor impact specimens machined from strongly textured high-purity zirconium plate. The surface geometry of a recovered specimen was measured using a coordinate measurement machine and compared with the optically measured surface geometry reconstructed from post-impact images. Excellent agreement between the two methods was found.

Self-assembled quantum dots in a liquid-crystal-tunable microdisk resonator

GaAs-based semiconductor microdisks with high quality whispering gallery modes ( Q > 4000 ) have been fabricated. A layer of self-organized InAs quantum dots (QDs) served as a light source to feed the optical modes at room temperature. In order to achieve frequency tuning of the optical modes, the microdisk devices have been immersed in 4-cyano-4 ′ -pentylbiphenyl (5CB), a liquid crystal (LC) with a nematic phase below the clearing temperature of T C ≈ 34 ∘ C . We have studied the device performance in the temperature range of T = 20 – 50 ∘ C , in order to investigate the influence of the nematic–isotropic phase transition on the optical modes. Moreover, we have applied an AC electric field to the device, which leads in the nematic phase to a reorientation of the anisotropic dielectric tensor of the liquid crystal. This electrical anisotropy can be used to achieve electrical tunability of the optical modes. Using the finite-difference time domain (FDTD) technique with an anisotropic material model, we are able to describe the influence of the liquid crystal qualitatively.

Mechano-regulation of mesenchymal stem cell differentiation and collagen organisation during skeletal tissue repair

A number of mechano-regulation theories have been proposed that relate the differentiation pathway of mesenchymal stem cells (MSCs) to their local biomechanical environment. During spontaneous repair processes in skeletal tissues, the organisation of the extracellular matrix is a key determinant of its mechanical fitness. In this paper, we extend the mechano-regulation theory proposed by Prendergast et al. (J Biomech 30(6):539-548, 1997) to include the role of the mechanical environment on the collagen architecture in regenerating soft tissues. A large strain anisotropic poroelastic material model is used in a simulation of tissue differentiation in a fracture subject to cyclic bending (Cullinane et al. in J Orthop Res 20(3):579-586, 2002). The model predicts non-union with cartilage and fibrous tissue formation in the defect. Predicted collagen fibre angles, as determined by the principal decomposition of strain- and stress-type tensors, are similar to the architecture seen in native articular cartilage and neoarthroses induced by bending of mid-femoral defects in rats. Both stress and strain-based remodelling stimuli successfully predicted the general patterns of collagen fibre organisation observed in vivo. This provides further evidence that collagen organisation during tissue differentiation is determined by the mechanical environment. It is envisioned that such predictive models can play a key role in optimising MSC-based skeletal repair therapies where recapitulation of the normal tissue architecture is critical to successful repair.

Anisotropic Materials Behavior Modeling Under Shock Loading

In this paper, the thermodynamically and mathematically consistent modeling of anisotropic materials under shock loading is considered. The equation of state used represents the mathematical and physical generalizations of the classical Mie–Grüneisen equation of state for isotropic material and reduces to the Mie–Grüneisen equation of state in the limit of isotropy. Based on the full decomposition of the stress tensor into the generalized deviatoric part and the generalized spherical part of the stress tensor (Lukyanov, A. A., 2006, “Thermodynamically Consistent Anisotropic Plasticity Model,” Proceedings of IPC 2006, ASME, New York; 2008, “Constitutive Behaviour of Anisotropic Materials Under Shock Loading,” Int. J. Plast., 24, pp. 140–167), a nonassociated incompressible anisotropic plasticity model based on a generalized “pressure” sensitive yield function and depending on generalized deviatoric stress tensor is proposed for the anisotropic materials behavior modeling under shock loading. The significance of the proposed model includes also the distortion of the yield function shape in tension, compression, and in different principal directions of anisotropy (e.g., 0 deg and 90 deg), which can be used to describe the anisotropic strength differential effect. The proposed anisotropic elastoplastic model is validated against experimental research, which has been published by Spitzig and Richmond (“The Effect of Pressure on the Flow Stress of Metals,” Acta Metall., 32, pp. 457–463), Lademo et al. (“An Evaluation of Yield Criteria and Flow Rules for Aluminium Alloys,” Int. J. Plast., 15(2), pp. 191–208), and Stoughton and Yoon (“A Pressure-Sensitive Yield Criterion Under a Non-Associated Flow Rule for Sheet Metal Forming,” Int. J. Plast., 20(4–5), pp. 705–731). The behavior of aluminum alloy AA7010 T6 under shock loading conditions is also considered. A comparison of numerical simulations with existing experimental data shows good agreement with the general pulse shape, Hugoniot elastic limits, and Hugoniot stress levels, and suggests that the constitutive equations perform satisfactorily. The results are presented and discussed, and future studies are outlined.

A non-associated constitutive model with mixed iso-kinematic hardening for finite element simulation of sheet metal forming

In this paper an anisotropic material model based on non-associated flow rule and mixed isotropic–kinematic hardening was developed and implemented into a user-defined material (UMAT) subroutine for the commercial finite element code ABAQUS. Both yield function and plastic potential were defined in the form of Hill’s [Hill, R., 1948. A theory of the yielding and plastic flow of anisotropic metals. Proc. R. Soc. Lond. A 193, 281–297] quadratic anisotropic function, where the coefficients for the yield function were determined from the yield stresses in different material orientations, and those of the plastic potential were determined from the r-values in different directions. Isotropic hardening follows a nonlinear behavior, generally in the power law form for most grades of steel and the exponential law form for aluminum alloys. Also, a kinematic hardening law was implemented to account for cyclic loading effects. The evolution of the backstress tensor was modeled based on the nonlinear kinematic hardening theory (Armstrong–Frederick formulation). Computational plasticity equations were then formulated by using a return-mapping algorithm to integrate the stress over each time increment. Either explicit or implicit time integration schemes can be used for this model. Finally, the implemented material model was utilized to simulate two sheet metal forming processes: the cup drawing of AA2090-T3, and the springback of the channel drawing of two sheet materials (DP600 and AA6022-T43). Experimental cyclic shear tests were carried out in order to determine the cyclic stress–strain behavior and the Bauschinger ratio. The in-plane anisotropy ( r-value and yield stress directionalities) of these sheet materials was also compared with the results of numerical simulations using the non-associated model. These results showed that this non-associated, mixed hardening model significantly improves the prediction of earing in the cup drawing process and the prediction of springback in the sidewall of drawn channel sections, even when a simple quadratic constitutive model is used.

The equivalent plastic strain-dependent Yld2000-2d yield function and the experimental verification

Abstract An equivalent plastic strain-dependent anisotropic material model was developed for 5754O aluminum alloy sheet. In the developed model, the anisotropy coefficients for Barlat’s Yld2000-2d anisotropic yield function were established as a function of the equivalent plastic strain. The developed anisotropic material model was implemented into the commercial FEM code ABAQUS as a user material subroutine (UMAT) for simulations. In order to evaluate the accuracy of the developed material model, biaxial tensile tests were carried out using cruciform specimens and a biaxial loading testing machine. The results show that the developed material model predicts the experimental results better than the other three material models (Yld2000-2d, Mises and Hill48 yield functions). It is also found that the developed material model describes the uniaxial tensile test curves better than Yld2000-2d yield function. The deep drawing test for 5754O aluminum alloy sheet was carried out and was simulated with different material models. The comparison between the experimental and simulation results indicates that the developed material model predicts the earing profile better than other material models. It is concluded that the equivalent plastic strain-dependence of the material coefficients should be considered for the accurate prediction of the anisotropic deformation behavior of materials.