Biaxial Stress Strain Research Articles

Estimation of the biaxial tensile behavior of ovine esophageal tissue using artificial neural networks

Diseases of the esophagus affect its function and often lead to replacement of long sections of the organ. Current healing methods involve the use of bioscaffolds processed from other animal models. Although the properties of these animal models are not exactly the same as those of the human esophagus, they nevertheless present a reasonable means of assessing the biomechanical properties of the esophageal tissue. Besides, sheep bear many similarities physiologically to humans and they also suffer from same diseases as humans. The morphology of their esophagus is also comparable to that of humans. Thus, in the study, an ovine esophagus was studied. Studies on the planar biaxial tests of the gross esophageal anatomy are limited. The composite nature of the gross anatomy of the esophagus makes the application of structure-based models such as Holzapfel-type models very difficult. In current studies the tissue is therefore often separated into specific layers with substantial collagen content. The effects of adipose tissue and other non-collagenous tissue often make the mechanical behavior of the esophagus widely diverse and unpredictable using deterministic structure-based models. Thus, it may be very difficult to predict its mechanical behavior. In the study, an NARX neural network was used to predict the stress–strain response of the gross anatomy of the ovine esophagus. The results show that the NARX model was able to achieve a correlation above 99.9% within a fitting error margin of 16%. Therefore, the use of artificial neural networks may provide a more accurate way of predicting the biaxial stress–strain response of the esophageal tissue, and lead to further improvements in the design and development of synthetic replacement materials for esophageal tissue.

Exploring Mechanical Properties Using the Hydraulic Bulge Test and Uniaxial Tensile Test with Micro-Samples for Metals

The hydraulic bulge test with micro-samples is expected to be useful in the damage assessment of long-service-period metals to understand the degeneration of their mechanical properties. Since the hydraulic bulge test has a different stress state from the classical uniaxial tensile test, we need to understand their correlation and differences. In this study, the hydraulic bulge test and the uniaxial tensile test are employed to analyze the mechanical properties of three typical metals used in pressure vessels: 316L, 16MnDR, and Q345R. By utilizing Kruglov’s vertex thickness and Panknin’s curvature radius equivalent, the pressure–displacement curves from the hydraulic bulge test are converted into biaxial stress–strain curves. Based on the equivalent plastic energy model, the biaxial stress–strain curves are converted into uniaxial stress–strain curves with an error less than 10% in the strain hardening stage, achieving the unified characterization of mechanical properties under different stress states. Moreover, the hydraulic bulge test provides a more extensive strain hardening stage, and the fracture strains are 9–16.5% larger than those of uniaxial tensile test. This paper provides a reference for using the hydraulic bulge test with micro-samples in studying the mechanical properties and presents the advantages of this novel test method.

A novel hydraulic bulge test in hot forming conditions

A novel hydraulic bulge test device was developed to evaluate high temperature biaxial stress–strain curves of quenchable boron steel sheets. The work mainly focuses on the resistance heating designed to assure a homogeneous temperature field in the dome area of the circular blank where the hydraulic pressure will be applied. The practical hot stamping conditions, including the heating and cooling steps, were reproduced to perform hydraulic bulge tests on the Usibor ®1500P steel for a temperature range between 700 to 900 °C, after an austenization step at 900 °C. Stress–strain curves were obtained from these expansion tests using the data extracted with a laser profilometer, due to the difficulties associated with the use of Digital Image Correlation at such high temperatures. Although the profilometer is a compromise solution, the comparisons between tensile and biaxial stress–strain results enable to verify the feasibility of the new device for the evaluation of the stress–strain curves at a high temperature in a biaxial state. The results point-out that, besides the difficulties with the acquisition of the strain fields and in the strain-rate control, there are also challenges in the interpretation of the metallurgical evolutions that can occur during the tests, which can affect the biaxial flow curves.

A multi-scale computational model for the passive mechanical behavior of right ventricular myocardium

We have previously demonstrated the importance of myofiber–collagen mechanical interactions in modeling the passive mechanical behavior of right ventricle free wall (RVFW) myocardium. To gain deeper insights into these coupling mechanisms, we developed a high-fidelity, micro-anatomically realistic 3D finite element model of right ventricle free wall (RVFW) myocardium by combining high-resolution imaging and supercomputer-based simulations. We first developed a representative tissue element (RTE) model at the sub-tissue scale by specializing the hyperelastic anisotropic structurally-based constitutive relations for myofibers and ECM collagen, and equi-biaxial and non-equibiaxial loading conditions were simulated using the open-source software FEniCS to compute the effective stress–strain response of the RTE. To estimate the model parameters of the RTE model, we first fitted a ’top-down’ biaxial stress–strain behavior with our previous structurally based (tissue-scale) model, informed by the measured myofiber and collagen fiber composition and orientation distributions. Next, we employed a multi-scale approach to determine the tissue-level (5 x 5 x 0.7 mm specimen size) RVFW biaxial behavior via ’bottom-up’ homogenization of the fitted RTE model, recapitulating the histologically measured myofiber and collagen orientation to the biaxial mechanical data. Our homogenization approach successfully reproduced the tissue-level mechanical behavior of our previous studies in all biaxial deformation modes, suggesting that the 3D micro-anatomical arrangement of myofibers and ECM collagen is indeed a primary mechanism driving myofiber–collagen interactions.

Seismic and failure behavior simulation for RC shear walls under cyclic loading based on vector form intrinsic finite element

Seismic performance and failure mode simulations for reinforced concrete (RC) structures are impeded by large deformations and material nonlinearity particularly when subjected to the combined action of compression, bending and shear. Structural deformation and failure analysis based on traditional finite element (FE) often fails for the small–deformation assumption and global equilibrium. Moreover, it remains difficult to obtain convergence results for the existing FE methods by applying general concrete constitutive models for the complicity of anisotropic materials. To simulate the hysteretic performance and the damage development process of the RC shear wall under cyclic loading, the vector form intrinsic finite element (VFIFE) method with independent particles was adopted and combined with the two-directional concrete constitutive model considering the loading and unloading rules to perform large deformation and damage estimations. Concrete planar triangular element and fiber element for steel bar equipped with the hysteretic constitutive models were used to model six RC shear walls with different design parameters. Owing to the merits of avoiding repeated accumulation of the global stiffness matrix for vector mechanics, the planar structural behaviors involving biaxial stress–strain and loading–unloading behavior were numerically demonstrated. The simulated results were in close agreement with the experimental tests, including the hysteretic loop, skeleton curve, bending–shear deformation, and damage mode. This research also provides successive evidence for damage process simulation by VFIFE for RC structures under seismic loading considering a comprehensive constitutive relation.

Ultimate tensile strength and biaxial stress–strain responses of aortic tissues—A clinical-engineering correlation

For over a decade, the team from the Aortic Institute at Yale University has worked closely with the bioengineering team of Dr. Wei Sun at Georgia Tech University. This paper presents the products of that collaboration.We provide clinical context by describing thoracic aortic dissection and its genesis as a prelude to the bioengineering findings. We discuss the genesis of aortic dissection, from the fundamental underlying genetic abnormality, through the degenerative aortic process, to the acute inciting factors and the dissection event itself. The inciting factor is usually an extreme hypertensive episode, occasioned by exertion or emotion.The bioengineering findings include the following: The aortic wall is stronger in the circumferential direction than in the longitudinal. Bicuspid aortic valve and bovine aortic arch morphology do not compromise aortic strength. Biaxial testing reveals a non-liner stress-strain response of aortic tissues. Dissected tissues become stronger over time, reflecting fibrotic connective tissue ingrowth in response to the dramatic tissue injury from the dissection event. Human aortic tissues stiffen at advanced age, in contradistinction to those of aged animals (porcine).Combining clinical and bioengineering perspectives yields a more complete and correlative understanding of the genesis of thoracic aortic dissection.

Experimental and Numerical Thickness Analysis of TRIP Steel under Various Degrees of Deformation in Bulge Test.

To design a reliable forming process it is necessary to determine the mechanical and formability properties of the processed material, which are used as input parameters for forming simulations. High-strength steel is irreplaceable as a material for producing the deformation zones of current automobiles. This type of steel can be processed by conventional or unconventional forming methods. In the sheet forming process, the material is usually under uniaxial and biaxial stress. The bulge test is utilized for determination of biaxial stress–strain curves, which are often used as input material data for forming simulations. In this work, numerical simulations of bulge tests using TRIP RAK 40/70 steel were performed to study the impact of yield criteria and hardening laws on the accuracy of thickness prediction of the deformed steel sheet. Additionally, the impact of different solvers and integration schemes on the thickness prediction was tested. Furthermore, the impact of various degrees of deformation (various dome heights) on thickness prediction accuracy was evaluated. Numerical results showed a good correlation with experimental data. When the Hill90 yield criterion was used, the software with implicit solver was more accurate in predicting thickness compared to software with explicit integration scheme, in most cases. In addition, the thickness prediction of parts with lower deformation was more accurate compared to parts with greater deformation (higher dome height).

A mechanical relation model for biaxial tension of nanofibrous membrane

It is important to evaluate the mechanical biocompatibility of nanofibrous membranes used in tissue engineering. This investigation proposed a modeling analysis to predict the biaxial behavior of randomly oriented nanofibrous membranes. An electrospinning process prepared poly(ε-caprolactone) nanofibers. The uniaxial stress–strain curve of a single nanofiber and the biaxial stress–strain curves of the membranes were experimentally obtained. The applicability of the analytical model was verified by the comparison between modeling prediction and experimental data. Experimental stress was lower than the predicted stress until large plastic deformation occurred because of structural imperfections, prestress, and the stretch-induced orientation in the membranes.

Determination of biaxial stress–strain curves for superplastic materials by means of bulge forming tests at constant stress

As the characterization of superplastic materials requires elevated temperatures and strain rate control, standard bulge testing procedure with optical measuring systems is not feasible for the determination of biaxial stress–strain curves. Standard superplastic bulge forming tests performed at constant pressure can be used for the identification of material constants or formability evaluation, but they are not applicable for accurate characterization of deformation behavior providing stress–strain curves at constant strain rates. The present paper is aimed to provide a technique for the direct characterization of stress–strain behavior of superplastic materials in conditions of biaxial tension. This technique is based on bulge forming testing with a closed-loop pressure control procedure allowing one to maintain the value of the effective stress at the dome pole at the predefined constant level. Thus, the variation of strain rate is reduced compared to the constant pressure testing. The results are evaluated using a double-step numerical procedure which provides the way to calculate the stress–strain curves, corresponding to constant referenced strain rates. The developed technique was used to characterize superplastic aluminum alloy Alnovi-U in conditions of biaxial tension at 500°C.

Cruciform Specimen Machining Using EDM and a New Design Verification for Biaxial Testing

Cruciform flat specimen is mostly used to investigate experimentally the in-plane biaxial mechanical behavior of sheet metals. In this study, a modified cruciform specimen design is proposed and validated against the performance of current standard design. The existing standard cruciform specimen prepared through laser cutting for sheet metal can accurately provide biaxial stress–strain curve through biaxial tensile test by ensuring superior homogeneous stress and strain field in gauge section. However, preparation of such specimen using laser cut is cumbersome, expensive and prone to errors. The current standard cruciform specimen design features slotted arm of fixed length and width with specific gauge. Few other designs also feature reduced gauge section to localize failure. Both need high precision of laser cutting and machining to prepare specimens which can achieve biaxial stress–strain curve for more than 4% equivalent plastic strain level. The proposed specimen design features running slits in all four arms of specimen with uniform gauge section machined using electrical discharge machining (EDM) owing to higher accuracy and minimum heat-affected zone (HAZ). This technique also avoids machining effects with an understanding that proposed specimen design is to determine the yield behavior of material only. Also, specimen fabricated from as received sheets and without any thickness reduction in gauge area allows the user to keep full thickness in biaxial condition. The modified design qualifies the commonly accepted performance criteria for cruciform specimen, i.e., stress and strain distribution in the gauge section is found to be homogeneous and the biaxial stress–strain curve can be generated until 4% of equivalent plastic strain. The proposed specimen design is evaluated experimentally by conducting biaxial test at various stress ratios, and it is compared with alike experiments using standard specimen design. One automotive grade material, interstitial-Free high-strength (IFHS) steel sheet of thickness 0.70 mm is tested in this study to validate the specimen design.

Cellular automata modeling of the kinetics of static recrystallization during the post-hydroforming annealing of steel tube

A modeling setup based on the cellular automata (CA) method was developed to model the kinetics of static recrystallization (SRX) in hydroformed steel tubes undergoing the annealing process. In addition, the impact of multiaxial deformations on the kinetics of SRX within the hydroformed steel tube was investigated. First, hoop and axial strains developing at the pole of the steel tube during hydroforming were obtained from the digital image correlation measurements. Then, an exact analytical solution was employed to calculate the corresponding hoop and axial stresses at the pole of the bulged tube. Using these biaxial stress–strain curves, the stored energy was calculated for the hydroformed tube specimen. Second, the actual grain topology and crystallographic orientation of grains in the deformed specimen were obtained with the electron backscatter diffraction. Third, the calculated stored energy as well as the microstructural and crystallographic data was incorporated into the CA model as initial conditions to predict the kinetics of SRX in the specimen during annealing. Finally, to assess the accuracy of the CA model, experimental and predicted results were compared in terms of grain topology data including the grain size and aspect ratio distributions, as well as the rate of recrystallization during annealing. A reasonable agreement between the experimental and CA predictions in partial and fully recrystallized specimens was achieved inferring the validity of the developed algorithm and the modeling setup to predict the SRX kinetics during the post-tube hydroforming annealing process.

A hyper-elastic thermal aging constitutive model for rubber-like materials

Different phenomenological, empirical, and micromechanical constitutive models have been proposed to describe the behavior of incompressible isotropic hyper-elastic materials. Among these models, very few have accounted for the thermal aging effect on the model constants and parameters. This article introduces a new empirical constitutive hyper-elastic model for thermally aged hyper-elastic materials. The model named “the weight function based (WFB) model” considers the effect of aging temperature and time on its parameters. The WFB model formulation can facilitate fatigue analysis and lifetime prediction of rubber-like materials under aging conditions. The WFB model in this article defines all rubber-like material properties, such as fracture stretch, strength, and stiffness, by predicting the full stress–strain curve at any aging time and temperature. The WFB model was tested on natural rubber for uniaxial and biaxial loading conditions. More than 100 specimens were aged and tested uniaxially under various temperatures and aging times to extract the stress–strain behavior. The temperatures used in the test ranged from 76.7°C to 115.5°C, and the aging time ranged from 0 to 600 hours (hrs). A classical bulge test experiment was generated to extract the biaxial natural rubber material behavior. An ABAQUS finite element analysis model was created to simulate and verify the generated biaxial stress–strain curve. The proposed model represents the aging effect on the tested natural rubber under uniaxial and biaxial loading conditions with an acceptable error margin of less than 10% compared to experimental data.

Experimental evaluation of PMMA simulated tunnel stability under dynamic disturbance using digital image correlation

The dynamic disturbance is a non-ignorable external factor inducing rock mass instability around underground caverns. In this paper, the failure characteristics of the polymethylmethacrylate (PMMA) simulated tunnel under coupled biaxial static stress and high strain rate dynamic disturbance are experimentally investigated. The effects of lateral pressure coefficient, overbreak and underbreak, fault, and dynamic disturbance direction on the PMMA simulated tunnel failure are considered. During the tests, the two-dimensional digital image correlation (DIC) technique is used to monitor the failure process. The results indicate that the contribution of the dynamic disturbance on the failure of the PMMA simulated tunnel is closely related to the static in-situ stress. Sufficient static stress is essential for PMMA simulated tunnel failure under dynamic disturbance. The effect of the lateral pressure coefficient is not monotonic but depends on the relationship between horizontal and vertical in-situ stresses. For specimens with prefabricated defects, the cracks always initiate from the protruding defects with rough boundary. Thus, in areas where the tunnel is seriously under-excavated or over-excavated with rough boundary, attention should be taken to prevent and mitigate the severe damage caused by dynamic disturbances. The effect of the fault on the PMMA simulated tunnel stability depends on both the distance between the fault and the tunnel, and the dip of the fault. Most devastating failure occurred when the dynamic disturbance is applied in the direction of the higher static in-situ stress.

Determination of the yield loci of four sheet materials (AA6111-T4, AC600, DX54D+Z, and H220BD+Z) by using uniaxial tensile and hydraulic bulge tests

In sheet metal forming simulation, a flow curve and a yield criterion are vital requirements for obtaining reliable numerical results. It is more appropriate to determine a flow curve by using biaxial stress condition tests, such as the hydraulic bulge test, than a uniaxial test because hardening proceeds higher strains before necking occurs. In a uniaxial test, higher strains are extrapolated, which might lead to incorrect results. The bulge test, coupled with the digital image correlation (DIC) system, is used to obtain stress–strain data. In the absence of the DIC system, analytical methods are used to estimate hardening. Typically, such models incorporate a correction factor to achieve correlation to experimental data. An example is the Chakrabarty and Alexander method, which uses a correction factor based on the n value. Here, the Chakrabarty and Alexander approach was modified using a correction factor based on normal anisotropy. When compared with DIC data, the modified model was found to be able to better predict the hardening curves for the materials examined in this study. Because a biaxial flow curve is required to compute the biaxial yield stress, which is an essential input to advanced yield functions, the effects of the various approaches used to determine the biaxial stress–strain data on the shape of the BBC2005 yield loci were also investigated. The proposed method can accurately predict the magnitude of the biaxial yield stress, when compared with DIC data, for all materials investigated in this study.

Quantification of Material Constants for a Phenomenological Constitutive Model of Porcine Tricuspid Valve Leaflets for Simulation Applications.

The tricuspid valve is a one-way valve on the pulmonary side of the heart, which prevents backflow of blood during ventricular contractions. Development of computational models of the tricuspid valve is important both in understanding the normal valvular function and in the development/improvement of surgical procedures and medical devices. A key step in the development of such models is quantification of the mechanical properties of the tricuspid valve leaflets. In this study, after examining previously measured five-loading-protocol biaxial stress-strain response of porcine tricuspid valves, a phenomenological constitutive framework was chosen to represent this response. The material constants were quantified for all three leaflets, which were shown to be highly anisotropic with average anisotropy indices of less than 0.5 (an anisotropy index value of 1 indicates a perfectly isotropic response, whereas a smaller value of the anisotropy index indicates an anisotropic response). To obtain mean values of material constants, stress-strain responses of the leaflet samples were averaged and then fitted to the constitutive model (average R2 over 0.9). Since the sample thicknesses were not hugely different, averaging the data using the same tension levels and stress levels produced similar average material constants for each leaflet.

An anisotropic constitutive model for immersogeometric fluid–structure interaction analysis of bioprosthetic heart valves

This paper considers an anisotropic hyperelastic soft tissue model, originally proposed for native valve tissue and referred to herein as the Lee–Sacks model, in an isogeometric thin shell analysis framework that can be readily combined with immersogeometric fluid–structure interaction (FSI) analysis for high-fidelity simulations of bioprosthetic heart valves (BHVs) interacting with blood flow. We find that the Lee–Sacks model is well-suited to reproduce the anisotropic stress–strain behavior of the cross-linked bovine pericardial tissues that are commonly used in BHVs. An automated procedure for parameter selection leads to an instance of the Lee–Sacks model that matches biaxial stress–strain data from the literature more closely, over a wider range of strains, than other soft tissue models. The relative simplicity of the Lee–Sacks model is attractive for computationally-demanding applications such as FSI analysis and we use the model to demonstrate how the presence and direction of material anisotropy affect the FSI dynamics of BHV leaflets.

Material modeling of pure titanium sheet and its application to bulge test simulation

The hydraulic bulge test is widely used to obtain stress–strain data over large strain ranges. This study identifies plastic characteristics of pure titanium sheet by conducting several tensile tests and a hydraulic bulge test. Distortional hardening behavior of the tested material is examined experimentally by comparing the uniaxial tensile results of three specimens taken from different orientations. In addition, three stages of deformation were observed in biaxial stress–strain data obtained from the bulge test. Therefore, a constitutive model based on a non-associated flow rule is developed to describe the material characteristics. Evolution Hill’s quadratic functions are adapted to reproduce the yield surface and potential surface transients during plastic deformation. Additionally, a modified Voce hardening model is used to represent the effective stress–strain curve over large strain ranges to capture the three-stage hardening phenomenon of titanium sheet. The developed material model is then applied to simulate the bulge test to verify its accuracy. Based on simulation results, it is concluded that the distortional hardening behavior strongly affects the evaluation of apex height in the bulge test.

On the Biaxial Mechanical Response of Porcine Tricuspid Valve Leaflets.

Located on the right side of the heart, the tricuspid valve (TV) prevents blood backflow from the right ventricle to the right atrium. Similar to other cardiac valves, quantification of TV biaxial mechanical properties is essential in developing accurate computational models. In the current study, for the first time, the biaxial stress-strain behavior of porcine TV was measured ex vivo under different loading protocols using biaxial tensile testing equipment. The results showed a highly nonlinear response including a compliant region followed by a rapid transition to a stiff region for all of the TV leaflets both in the circumferential and in the radial directions. Based on the data analysis, all three leaflets were found to be anisotropic, and they were stiffer in the circumferential direction in comparison to the radial direction. It was also concluded that the posterior leaflet was the most anisotropic leaflet.

Microstructure and Mechanical Property of Glutaraldehyde-Treated Porcine Pulmonary Ligament.

There is a significant need for fixed biological tissues with desired structural and material constituents for tissue engineering applications. Here, we introduce the lung ligament as a fixed biological material that may have clinical utility for tissue engineering. To characterize the lung tissue for potential clinical applications, we studied glutaraldehyde-treated porcine pulmonary ligament (n = 11) with multiphoton microscopy (MPM) and conducted biaxial planar experiments to characterize the mechanical property of the tissue. The MPM imaging revealed that there are generally two families of collagen fibers distributed in two distinct layers: The first family largely aligns along the longitudinal direction with a mean angle of θ = 10.7 ± 9.3 deg, while the second one exhibits a random distribution with a mean θ = 36.6 ± 27.4. Elastin fibers appear in some intermediate sublayers with a random orientation distribution with a mean θ = 39.6 ± 23 deg. Based on the microstructural observation, a microstructure-based constitutive law was proposed to model the elastic property of the tissue. The material parameters were identified by fitting the model to the biaxial stress-strain data of specimens, and good fitting quality was achieved. The parameter e0 (which denotes the strain beyond which the collagen can withstand tension) of glutaraldehyde-treated tissues demonstrated low variability implying a relatively consistent collagen undulation in different samples, while the stiffness parameters for elastin and collagen fibers showed relatively greater variability. The fixed tissues presented a smaller e0 than that of fresh specimen, confirming that glutaraldehyde crosslinking increases the mechanical strength of collagen-based biomaterials. The present study sheds light on the biomechanics of glutaraldehyde-treated porcine pulmonary ligament that may be a candidate for tissue engineering.

On the determination of the work hardening curve using the bulge test

Hydraulic bulge test represents nowadays an important means to obtain higher accuracy on material characterization. One reason is the possibility of using the obtained biaxial stress–strain data to largely extend the hardening information extracted from the tensile test. The other reason is the use of biaxial data as input information when determining parameters for current most advanced yield criteria.This contribution aims to obtain the material stress–strain hardening curve from the bulge test using a simpler experimental equipment, in which the output data is the hydraulic bulge pressure and the pole bulge height. This information is used to determine the sheet thickness and corresponding radius of curvature at the pole of the cap, which is the needed data to calculate the biaxial stress–strain curve, the stress being determined based on Laplace׳s equation from the membrane theory, a standard approach for this kind of analysis.Analytical models are proposed relating the radius of curvature and the sheet thickness with the pole bulge height. These models are based in an extensive analysis of different material behaviors, which in turn are related to characteristic properties of sheet metals, as well as different geometries of bulge test. Geometric variables include bulge die diameter and the fillet radii located at the entrance of the die. The analytical formulas also include the material variables associated with the hardening behavior and the sheet anisotropy, with different interaction and weighting impact.The extensive study also permits a deeper theoretical understanding of relations among the interconnecting variables and their influence on the accuracy of sheet thickness and radius of curvature determination, which directly influences the obtained biaxial stress–strain curve. This means, for example, the understanding between sheet thinning evolution or bulge curvature evolution during bulging and the corresponding relation with material plastic properties, hardening and anisotropy.The validation of the methodology and the proposed analytical models is performed with experiments, both from developed experimental system and also from literature with different bulge geometric relations.