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В работе рассматривается задача определения компонент напряжения при двуосном растяжении тонкой пластины из упругопластического материала. Пластина ослаблена круговым отверстием. В задаче рассматривается случай сопротивления отрыву, σ1 = σ2 = p, σ3 < p, p = const. Решение ищется методом разложения по малому параметру, аналогично работам [1-4]. В работе были получены выражения для определения компонент напряжения в упругой и пластической областях в первом приближении. The paper considers the problem of determining the stress components during biaxial tension of a thin plate made of elastoplastic material. The plate is weakened by the circular hole. The problem considers the case of separation resistance, σ = σ = p , σ < p , p = const . The solution is sought by the method of decomposition in a small parameter, similar to the works of [1-4]. In this work, expressions were obtained for determining the stress components in the elastic and plastic regions in the first approximation.

In this study, warp-knitted metal mesh fabric was used as the research object, and its mechanical loading behavior under uniaxial and biaxial stress loading states was studied. The relationship and connection between the effective elastic modulus of its anisotropic structure was studied with different loading angles of stress as variables. The results showed that there were differences in the mechanical properties and effective elastic modulus under these loading angles, and there was a linear relationship between the effective elastic modulus of the metal mesh with the same warp-knitted structure under different directions of stress, which will provide a theoretical basis for broadening its application in the field of anchor spray support, flexible wearable electronic devices, satellite antennas, water filter walls and other applications.

A deformation theory of gradient plasticity is employed to study elastoplastic axisymmetric boreholes subjected to far-field biaxial tension. The gradient dependence is introduced in the constituti...

Most hydraulic concrete structures are in complex stress state. In order to study the effect of dynamic action on properties of hydraulic concrete under biaxial tension-compression, hydraulic concr...

International audience; Combined cyclic tension and internal pressure tests with various proportions of each loading were run on a 2.5%Cr–1%Mo steel in air and in 3.5% NaCl solution, with and without cathodic protection to investigate the effect of positive stress biaxiality on corrosion‐fatigue lives and damage mechanisms. At free potential, a strong reduction in fatigue resistance was observed for uniaxial as well as for equibiaxial cyclic tension and attributed to multiple crack initiation from corrosion pits. Cathodic protection completely cancelled the detrimental effect of the corrosive environment on fatigue lives whatever the load biaxiality was, in spite of an obvious enhancement of intergranular fracture attributed to hydrogen embrittlement.

The mechanical response and microstructural changes under biaxial tension of two magnesium alloy sheets, ZE10 and AZ31, have been investigated. The forming limit diagram (FLD) of the two alloys was further assessed using the Marciniak–Kuczynski (M–K) model combined with two constitutive models: (a) crystal plasticity finite element (CPFE), and (b) phenomenological yield. The FLDs predicted by the combined CPFE and M–K model were in excellent agreement with the experimental data. The phenomenological yield models using the mechanical data at small plastic work led to poor prediction results. However, these could well reproduce the experimental FLDs when the mechanical data at larger plastic work were used for parameter identification. In-depth analyses revealed that the evolution of the anisotropic strain hardening during biaxial tension and significant evolution of the r-value during uniaxial tension were the main sources of the error in the predictions by the phenomenological models using the material data at smaller plastic work.

Reducing stress concentration has always been one of the main concerns for engineers, and piezoelectric patches are found to be effective in reducing this stress by altering stress flow around a notch. In this paper, the effect of using these patches around a hole in a metal sheet subjected to various ratios of biaxial tension is addressed. A quarter of a sheet with hole is modeled, and optimum arrangement of up to 12 patches in each quarter that leads to maximum stress reduction was determined using ant colony optimization algorithm. It was shown that there is no considerable stress reduction when the biaxial tension ratios are 1 and 0.9 and for tension ratio of 0.7, the stress reduction is not significant. The analysis was verified by comparing the finite element results with experimental ones.

The main objective of this paper is to provide a reliable experimental methodology that utilizes biaxial tension and shear loading combined with appropriate butterfly specimens for characterizing forming limits at fracture (FLF) for aluminum alloy 6K21-T4 sheets over a wide range of strain paths. To realize the goal, the performance of an existing butterfly specimen for fracture testing of the aluminum sheet is first experimentally and numerically studied. Experimental and numerical results show that premature edge fracture may easily occur on the aluminum sheet specimen under combined tension and shear loading, which would lead to a high degree of uncertainty for the measured limit strains at fracture. To solve the problem and provide a reliable testing method, optimized butterfly specimens are proposed, and their performance for fracture testing of the aluminum sheet is numerically evaluated. Subsequently, verification experiments on the optimized butterfly specimens extracted from the aluminum sheet are conducted under seven different combined tension and shear loading conditions and a strain-rate-based time-dependent method combined with the image inspection of specimen surface is presented to determine the onset of fracture. Experimental results show that the forming limit strains at fracture in arbitrary strain paths between simple shear and plane strain can be accurately obtained by using the proposed experimental methodology. In addition, three newly proposed ductile fracture criteria (Lou−Huh 2012, MMC3, and Hu−Chen) are employed to predict the FLF for the aluminum 6K21-T4 sheet over a wide range of strain paths. It is found that the Hu−Chen model exhibits the best prediction capability for the FLF.

The utilization of Asymmetric stent for recovering atherosclerotic diseases, particularly non-symmetric obstruction, is a quite challenging breakthrough treatment. In terms of eccentric plaque, the non-uniform stiffness of arterial layer causes the increasingly complex issues of vulnerability. This study investigated the vulnerability of the interaction between the Asymmetric stent and the surrounding arterial layer using structural transient dynamic analysis in ANSYS. Four combinations of stent deployment, i.e. the Sinusoidal stent expanded by the offset balloon, the Sinusoidal stent expanded by the ordinary cylindrical balloon, the Asymmetric stent expanded by the offset balloon, and the Asymmetric stent expanded by the ordinary cylindrical balloon, are generated for this comparative study. Multilayer material properties from recent in vitro experiments are adopted for the surrounding arterial layer, such as a fibrous cap, lipid core, diseased-healthy intima, and diseased-healthy media. In order to address plaque vulnerability, the Cauchy stresses and Hencky strains are used for stress measure because of convenience in comparison with the uniaxial/biaxial tension test data. The location-specific threshold value from the diseased human carotid artery is adopted for rupture criteria. The simulation indicated that as regards the eccentric plaque, the plaque vulnerability is caused by the plaque shape and components rather than caused by the geometrical structure of the stent or balloon expansion method. Nevertheless, the non-symmetric inflation of balloon, which leads against the plaque, contributed to an increase in the vulnerability of fibrous cap of fibroatheroma plaque.

The method and unit for experimental research of membrane formation from titanium alloys under conditions of superplastic is developed, which allows to determine necessary parameters of deformation. The unit is designed to deform titanium sheets in isothermal conditions by applying a uniform distributed load. When membrane is formed by a gas medium, a biaxial tension is realized. This type of test is used to assess the plastic properties of metals. In this work, the limiting deformations of the sheet titanium alloy OT4-0 have been evaluated in the formation of the membrane. Installed during the process of superplastic deformation the connection between the external parameters of deformation (force, temperature) with the depth of formation of the membrane in time and strain distribution along its generatrix.

A mesoscale finite element model is presented for calculating the deformation and initial strength of angle-ply laminates subjected to biaxial tension and biaxial tension–compression. Using the concept that the whole laminate structure can be represented by a rhombohedral unit cell, predictions of the mechanical behavior for various biaxial loading ratios are made. Damage by microcracking at the fiber–matrix interface and shear band formation in the matrix are incorporated into the numerical simulations. The failure locus calculated from the mesoscale model is found to agree with experimental data available in the literature better than do theoretical predictions. Results of this study indicate that computational micromechanics can be used for detecting leakage failure in filament wound tubes.

Most of the elements in structural design are subjected to the complex loading conditions that need to be predicted in advance for a reliable design. The failure prediction of these structural elements is based on the failure theories that employ the experimental data of the uniaxial, the biaxial and the shear tests. Among these tests, the biaxial testing is used to model the behavior of the structure loaded in more than one direction. In this study, we discover an interesting fact for the biaxial tension specimen that the thickness reduction of the measuring region cannot increase the stress to a high level. This behavior of the biaxial testing is different from the uniaxial testing where the thickness reduction of the measuring region always increases its stress to a higher level. Therefore, we further investigate the biaxial testing specimen via related fundamental problem, i.e., an axisymmetric plate with varying thickness under axisymmetric tension. We perform the shape optimization based on our analytical solution and the FEM results. For an infinite axisymmetric disk, the optimized design should include a low slope diverging section connecting the inner to outer region. On the contrary, the larger inner measuring region for finite axisymmetric disk would result in higher corresponding stress. These conclusions can be used as a guideline for the design of a biaxial testing specimen.

Zusammenfassung Seit ungefähr sechs Jahren gibt es auf europäischer und nationaler Ebene die Bestrebungen das Prüfverfahren zur Untersuchung des zweiachsigen Spannungs-Dehnungs-Verhalten beschichteter Gewebe in ein Standardwerk zu fassen. Hierzu gehört das Bestimmen von Werkstoff-Parametern in ebenen Spannungs-Verzerrungs-Zustand als Eingabegröße in jede numerische Strukturanalyse und für die Ermittlung von Zuschnitten. Zur Bestimmung der Zugsteifigkeiten für einen ebenen Spannungs-Verzerrungs-Zustand von beschichteten Geweben liegt seit Februar 2019 eine nationale Norm vor. In dieser stehen Versuchseinrichtungen und Verfahren nebeneinander, denen eine Einordnung in die Grundlagen der Mechanik und Strukturanalyse fehlt. Beschichtete Gewebe sind inhomogene und anisotrope Verbundwerkstoffe, bestehend aus einzelnen Fadenscharen, die über Webtechniken im losen Verband gehalten und durch Beschichtungen gegen Umwelteinflüsse geschützt werden. Werkstoff-Parametern werden in biaxialen Zugversuchen bestimmt, indem die Eigenschaften für die jeweilige Fadenrichtung homogeniert und linearisiert werden. Es wird aufgezeigt wie sich die homogenen Werkstoff-Parameter des unbeschichteten Gewebes aus dem Fadenverhalten ableiten. Der Einfluss der Probengeometrie auf das Last-Verformungs-Verhalten wird an zwei Beispielen dargestellt. Abschließend werden vier Verfahren zur Bestimmung der Werkstoff-Parameter nach der aktuellen Norm an den derselben Versuchsreihe gegenübergestellt und interpretiert.

Common practice for the integrity assessment of structures, follows the use of Fitness for Service procedures, such as BS 7910/R6. There are many common structures (e.g. pipes) that are under biaxial loading. Even though the load biaxiality has been proven experimentally to have an effect on both the fracture toughness and the limit load of a component, the influence of biaxial stresses is not always directly addressed in the procedures. In order to address the effect of biaxiality on engineering critical assessments, BS 7910 and R6 fitness for service procedures are applied to four biaxially loaded wide plate tests previously conducted on A533B steel. The plates had been loaded in biaxial tension, with different biaxiality ratios, while the temperatures of the plates tested correspond to lower transition fracture toughness. The assessments include failure assessment lines created using Option 1, which requires the knowledge of the yield stress and tensile strength, Option 3 which is a material, structure and load dependent option, as well as a constraint modified Option 3 failure assessment line. To obtain Option 3 failure assessment lines, finite element analyses are conducted for the specimens. The tests are first assessed with the proximity to plastic collapse (Lr) and fracture (Kr) being calculated with the use of the main fracture clauses of BS 7910/R6, which do not take into account the effects of biaxiality. The conventional assessment is then followed by a more detailed assessment using the values calculated from Finite Element Analyses (FEA).

Intracranial aneurysms (ICAs) are focal dilatations that imply a weakening of the brain artery. Incidental rupture of an ICA is increasingly responsible for significant mortality and morbidity in the American’s aging population. Previous studies have quantified the pressure-volume characteristics, uniaxial mechanical properties, and morphological features of human aneurysms. In this pilot study, for the first time, we comprehensively quantified the mechanical, collagen fiber microstructural, and morphological properties of one resected human posterior inferior cerebellar artery aneurysm. The tissue from the dome of a right posterior inferior cerebral aneurysm was first mechanically characterized using biaxial tension and stress relaxation tests. Then, the load-dependent collagen fiber architecture of the aneurysm tissue was quantified using an in-house polarized spatial frequency domain imaging system. Finally, optical coherence tomography and histological procedures were used to quantify the tissue’s microstructural morphology. Mechanically, the tissue was shown to exhibit hysteresis, a nonlinear stress-strain response, and material anisotropy. Moreover, the unloaded collagen fiber architecture of the tissue was predominantly aligned with the testing Y-direction and rotated towards the X-direction under increasing equibiaxial loading. Furthermore, our histological analysis showed a considerable damage to the morphological integrity of the tissue, including lack of elastin, intimal thickening, and calcium deposition. This new unified characterization framework can be extended to better understand the mechanics-microstructure interrelationship of aneurysm tissues at different time points of the formation or growth. Such specimen-specific information is anticipated to provide valuable insight that may improve our current understanding of aneurysm growth and rupture potential.

In the present paper, a new type of micro-mechanically motivated chain network model for rubber-like materials is proposed. The model captures topological constraints of polymer network chains, in particular, entanglements. The model demonstrates how the local molecular packing constraints modify under deformation and shows the impact of these changes on the macroscopic elasticity of the material. To this end, we combine concepts of a confining tube and a slip-link (reptation) model. In these models, entanglements of polymer chains play an important role. The nature of entanglements is discussed, and relationships governing entanglements are formulated in terms of molecular physics. In the context of nonlinear elasticity, we apply a non-affine concept which captures the liquid-like behavior of polymer networks at smaller scales in a more realistic way. Model predictions show good agreement with experimental results from uniaxial and biaxial tension tests.

Biaxial behavior of various types of concrete is essential to be considered in construction design because construction structures normally experience multiaxial stresses rather than uniaxial stress. Research on biaxial behavior of steel fiber-reinforced concrete (SFRC) has been conducted in the past decades. Most of the research, however, is only limited to biaxial compression, whereas information regarding biaxial tension and biaxial tensioncompression on SFRC is relatively scarce. This study presents a simple biaxial experimental setup to investigate the biaxial behavior of SFRC with 0.5, 1.0, and 1.5% steel fiber under biaxial tension and biaxial tension-compression. It is found that the smaller stress ratio enhanced the deformability and tensile capacity of SFRC under biaxial tension-compression, whereas the effect of stress ratio on biaxial tensile behavior of SFRC is negligible. The addition of steel fiber eventually enhanced the concrete strength by 15 to 41% under tension-compression compared with plain concrete.

In tissue engineering (TE) strategies, cell processes are regulated by mechanical stimuli. Although TE scaffolds have been developed to replicate tissue-level mechanical properties, it is experimentally prohibitive to measure and prescribe the cellular micromechanical environment (CME) generated within these constructs. Accordingly, this study aimed to fill this lack of understanding by modelling the CME in TE scaffolds using the finite element method. A repeating unit of composite fiber scaffold for annulus fibrosus repair with a fibrin hydrogel matrix was prescribed a series of loading, material, and architectural parameters. The CME was predicted and the corresponding cell phenotypes were predicted based on previously hypothesized criteria. Scaffold multi-axial loading was demonstrated as the most pertinent parameter contributing to the CME criteria being satisfied. Specifically, radial-direction compression with biaxial tension lead to a prediction of regeneration for 66.5% of the cell volumes. Additionally, the architectural scale had a moderate influence on the CME with minimal change in the tissue-level properties of the scaffold. All other scaffold materials and architectures considered had secondary influences on the predicted regeneration by modifying the scaffold loading. By predicting the regeneration potential of different scaffold designs, the developed high-fidelity computational tool described in this study enables for a more comprehensive understanding of the relationship between tissue-level and cell-level mechanics for a broad range of tissue engineering applications.

Wedge-splitting test is widely used fracture mechanical test for its stability in measurement during the testing and many papers were published. However, the biaxial wedge-splitting test is relatively a new method and the numerical stress analysis of such test is necessary. Especially the investigation of the stress fields in the vicinity of the crack tip. In this contribution, influence of various biaxial stress level is discussed on values of first and second terms of William’s expansion.

The work is dedicated to determination of stress-strain behavior of Ti6Al4V alloy deformed in conditions of biaxial tension provided by free bulging testing. The dome height during each test was continuously measured and recorded using a magnetostrictive position transducer. All the tests were performed using stepped pressure regime with jump pressure changing between two values at evenly spaced time moments. This experimental technique provides the possibility to study strain rate sensitivity index variation during the test and subsequently construct strain and strain rate dependent material model. The output data of each test include the evolution of dome height, subsequent pressure regime and final thickness of the specimen at the dome pole. In the framework of this study the processing of such data in order to evaluate the material behavior is discussed. Inverse analysis with different material models was implemented as well as special direct technique allowing one to construct stress-strain curves based on the results of free bulging tests with pressure jumps. The obtained material model was verified by finite element simulation.

Advanced high-strength steel has great potential for application in automotive and high-speed rail industries owing to its excellent mechanical properties. To predict the forming limit of dual-phase 500 steel sheets (DP500), Banabic’s innovative hydraulic bulging test was conducted on them, and the Gurson–Tvergaard–Needleman (GTN) ductile damage model was used to determine their failure under different strain paths. GTN damage parameters were identified using a hybrid experimental–numerical method based on the equal biaxial hydraulic bulging test. The results show that fracture of all of the DP500 specimens occurred in their polar region in experiments under different strain paths from uniaxial to equal biaxial tension. Moreover, the GTN ductile damage model could not only provide an accurate prediction of the fracture position, but also give an appropriate evaluation of the sheet forming limit under different loading paths.

Compared with conventional monolithic material, an aluminum-polymer sandwich sheet possesses advantageous strength/stiffness versus weight ratio and has received increasing attention in aeronautical, automotive, marine, and civil engineering industries. In the present study, limiting draw ratio (LDR) and other cylindrical cup-drawing characteristics of aluminum-polymer sandwich sheets were investigated by experiments and numerical simulations. Deformation behaviors of skin layer and core polymer layer were analyzed respectively. It was demonstrated that the deformation mode of exterior sheet tends to biaxial tension state and that of interior sheet tend to compression state. The LDR of aluminum-polyethylene sandwich sheet was well predicted, and influences of core layer thickness and mechanical properties of skin sheet on the LDR of sandwich sheet were analyzed. Research results show that the drawability of the aluminum-polymer sandwich sheet becomes poor with increasing the thickness of the polymeric core and the strength of core polymer. The LDR of the sandwich sheet mainly depends on the drawability of the skin sheet.

In many engineering applications, 3D braided composites are designed for primary loading-bearing structures, and they are frequently subjected to multi-axial loading conditions during service. In this paper, a unit-cell based finite element model is developed for assessment of mechanical behavior of 3D braided composites under different biaxial tension loadings. To predict the damage initiation and evolution of braiding yarns and matrix in the unit-cell, we thus propose an anisotropic damage model based on Murakami damage theory in conjunction with Hashin failure criteria and maximum stress criteria. To attain exact stress ratio, force loading mode of periodic boundary conditions which never been attempted before is first executed to the unit-cell model to apply the biaxial tension loadings. The biaxial mechanical behaviors, such as the stress distribution, tensile modulus and tensile strength are analyzed and discussed. The damage development of 3D braided composites under typical biaxial tension loadings is simulated and the damage mechanisms are revealed in the simulation process. The present study generally provides a new reference to the meso-scale finite element analysis (FEA) of multi-axial mechanical behavior of other textile composites.

The relationship between void size/location and mechanical behavior under biaxial loading of copper nanosheets containing voids are investigated by molecular dynamics method. The void location and the void radius on the model are discussed in the paper. The main reason of break is discovered by the congruent relationship between the shear stress and its dislocations. Dislocations are nucleated at the corner of system and approached to the center of void with increased deformation. Here, a higher stress is required to fail the voided sheets when smaller voids are utilized. The void radius influences the time of destruction. The larger the void radius is, the lower the shear stress and the earlier the model breaks. The void location impacts the dislocation distribution.

This paper investigates the failure behavior of three-dimensional (3D) braided composites subjected to biaxial tension and compression through an improved micromechanical computational method and the finite element (FE) method. The yarns and the out-of-yarn matrix in the composites are modeled by an extended Hashin criterion and an extended Drucker-Prager criterion, respectively. The uniaxial mechanical properties are analyzed based on the available experimental data as a verification of the models. The biaxial progressive damage and failure behavior are investigated using the models. The braiding structure, whose diversity results in the difference in failure modes during damage evolution, has significant influence on the biaxial failure correlation of the composites. The predicting formulae for failure envelopes are suggested in this study. The failure envelopes of 3D four-directional and five-directional braided composites can be described by quadratic tensor theories, and the envelopes of 3D six-directional and seven-directional braided composites can be predicted by the maximum strain criterion.