Biaxial Behavior Research Articles

Biaxial Behavior of Steel Fiber–Reinforced Recycled-Aggregate Concrete Subjected to Dynamic Compression

Biaxial Behavior of Steel Fiber–Reinforced Recycled-Aggregate Concrete Subjected to Dynamic Compression

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.

A rheological constitutive model to predict the anisotropic biaxial bending behavior of spiral strands subjected to variable axial force

Spiral strands exhibit dissipative bending behavior when subjected to external axial force. To the best of the authors’ knowledge, only the uniaxial bending behavior of spiral strands subjected to constant axial force has been studied in the literature so far. Thanks to a recently developed mixed stress–strain driven computational homogenization for spiral strands, this paper is the first to study the biaxial bending behavior of spiral strands subjected to variable tensile force. Based on the observed anisotropic behavior, a rheological constitutive model equivalent to multilayer spiral strands is proposed to predict their behavior under such loading. For an Nl-layer strand, the proposed model consists of several angularly distributed uniaxial spring systems, referred to as a multiaxial spring system, where each uniaxial spring system consists of a spring and Nl slider-springs. In a uniaxial spring system, the spring represents the slip contribution of all wires to the bending stiffness of the strand, while each slider-spring represents the stick contribution of each layer. A major advantage of the proposed scheme is its straightforward parameter identification, requiring only several monotonic uniaxial bendings under constant axial force. The proposed rheological model has been verified against the responses obtained from the mixed stress–strain driven computational homogenization through several numerical examples. These examples consist of complex uniaxial and biaxial load cases with variable tensile force. It has been shown that the proposed scheme not only predicts the response of the strand, but also provides helpful insight into the complex underlying mechanism of spiral strands. Furthermore, the low computational cost of the proposed models makes them perfect candidates for implementation as a constitutive law in a beam model. Using a single beam with the proposed constitutive law, spiral strand simulations can be performed in a few seconds on a laptop instead of a few hours or days on a supercomputer.

Characterization of pediatric porcine pulmonary valves as a model for tissue engineered heart valves

Heart valve tissue engineering holds the potential to transform the surgical management of congenital heart defects affecting the pediatric pulmonary valve (PV) by offering a viable valve replacement. While aiming to recapitulate the native valve, the minimum requirement for tissue engineered heart valves (TEHVs) has historically been adequate mechanical function at implantation. However, long-term in situ functionality of TEHVs remains elusive, suggesting that a closer approximation of the native valve is required. The realization of biomimetic engineered pediatric PV is impeded by insufficient characterization of healthy pediatric tissue. In this study, we comprehensively characterized the planar biaxial tensile behaviour, extracellular matrix (ECM) composition and organization, and valvular interstitial cell (VIC) phenotypes of PVs from piglets to provide benchmarks for TEHVs. The piglet PV possessed an anisotropic and non-linear tension-strain profile from which material constants for a predictive constitutive model were derived. The ECM of the piglet PV possessed a trilayer organization populated by collagen, glycosaminoglycans, and elastin. Biochemical quantification of ECM content normalized to wet weight and DNA content of PV tissue revealed homogeneous distribution across sampled regions of the leaflet. Finally, VICs in the piglet PV were primarily quiescent vimentin-expressing fibroblasts, with a small proportion of activated α-smooth muscle actin-expressing myofibroblasts. Overall, piglet PV properties were consistent with those reported anecdotally for pediatric human PVs and distinct from those of adult porcine and human PVs, supporting the utility of the properties determined here to inform the design of tissue engineered pediatric PVs. Statement of significanceHeart valve tissue engineering has the potential to transform treatment for children born with defective pulmonary valves by providing living replacement tissue that can grow with the child. The design of tissue engineered heart valves is best informed by native valve properties, but native pediatric pulmonary valves have not been fully described to date. Here, we provide comprehensive characterization of the planar biaxial tensile behaviour, extracellular matrix composition and organization, and valvular interstitial cell phenotypes of pulmonary valves from piglets as a model for the native human pediatric valve. Together, these findings provide standards that inform engineered heart valve design towards generation of biomimetic pediatric pulmonary valves.

An anisotropic damage visco-hyperelastic model for multiaxial stress-strain response and energy dissipation in filled rubber

In this article, we introduce a novel physically-based anisotropic damage visco-hyperelastic model designed to predict the history-dependent inelastic behavior of multiaxially stretched filled rubber. The model integrates both the anisotropic Mullins effect and intrinsic viscosity through the consideration of internal physics, represented by two distinct networks: an elastic ground network and a superimposed viscous network. The rupture of molecular bonds within the elastic network chain backbone is modeled using statistical mechanics, while the effects of anisotropy-induced chain orientation at the upper scale are addressed through a microsphere-based scale transition method. The intrinsic viscosity is represented by the viscous network, which is governed by time-dependent equations to account for the viscous overstress. The influence of fillers is captured through the concept of strain amplification, applied to the two networks within the rubber matrix. The effectiveness of the model in capturing the biaxial behavior of filled rubber is evaluated by comparing its outputs with experimental data from a filled rubber system. This assessment specifically considers the impact of pre-stretching under various loading conditions and across a wide range of filler concentrations. Notably, it successfully predicts anisotropic stress-strain response and energy dissipation, and the coupled effects of damage and viscosity.

Numerical prediction of beam capacity using the new constitutive model based on concrete biaxial behavior

The biaxial strength of concrete exhibits intriguing nonlinearity and scattering, posing challenges to the assessment of building structural safety. Experiments have confirmed that biaxial strength envelopes can manifest concave, quasi-linear, and convex shapes. Despite various empirical formulas being proposed to describe this behavior, they cannot be applied to finite element simulations due to the absence of a constitutive perspective. To study the mechanisms forming the shape of strength envelopes, a novel three-invariant model constitutive model is proposed, which reveals the characteristics of the envelopes resulting from the coupling effect of hydrostatic pressure and Lode angle. By adjusting the model parameters, it effectively describes concave, quasi-linear, and convex envelopes. The model's accuracy and compatibility were validated against experimental data spanning various concrete types, with compression strengths ranging from 19.29 to 96.5 MPa and tension-compression ratios form 0.056 to 0.095. To investigate how biaxial strength impacts the capacity of beams, numerical experiments were conducted on notched and intact beams based on the proposed model. The results underscored that beams prepared using concrete with convex envelopes exhibited higher capacity compared to those with quasi-linear envelopes. Therefore, conducting biaxial tension-compression experiments is recommended to accurately evaluate beam bearing capacity. The proposed model is expected to have further applications in the safety evaluation of building structures.

In-plane biaxial low-cycle dwell fatigue behavior of CP-Ti based on DIC method

This study investigates the biaxial dwell fatigue behavior of commercial pure titanium (CP-Ti) under different load ratios and dwell times. The evolution of mean strain, ratcheting strain, and creep strain was systematically analyzed. The findings reveal that with the decrease of load ratio or the increase of dwell time, both ratcheting and creep strain exhibit an upward trend. The interaction between ratcheting strain and creep strain promotes crack initiation and propagation. The statistical analysis of crack paths by the digital image correlation (DIC) method indicates that crack initiation occurs between 0.7Nf and 0.8Nf, and fatigue failure is governed by the maximum principal strain. Moreover, the electron backscatter diffraction (EBSD) analysis results indicate that as the load ratio increases, the activity of prismatic slip systems decreases, while the activities of other slip systems and twinning modes increases. To enhance predictive accuracy, a modified SWT model by incorporating time-dependent creep damage and anisotropy is proposed for life prediction under biaxial dwell fatigue conditions.

Load history dependency of stiffness properties of PTFE-coated glass fibre membranes

The aim of this contribution is to investigate whether the order of load ratios applied to a textile structure impacts the biaxial stiffness behaviour of the structural textile itself. These investigations are performed based on biaxial tests on an architectural woven glass fibre fabric, a representative of such membranes. The first part of the paper investigates the existence and extent of load history dependency in the material response. Biaxial test results show that effects of a previous load history on the weave geometry cannot be eliminated by further load cycling in all biaxial stress ratios. Moderate to strong effects are recognized in two stress ratios, although not in both weave directions.The second part of the paper examines how these effects influence material stiffness parameters and structural calculations. Two boundary value problems are investigated: a pressure chamber test and a roof structure. Parameters obtained by fitting biaxial tests with or without history are considered. By incorporating an adaptive load-ratio dependent scheme, highly predictive numerical results are obtained, showing that while the effect of load history may appear small in the biaxial tests and pressure chamber test, it can be significant in complex structural problems like roof structures.

Independent Control of the Width and Length of Semiconducting 2D Nanorectangles via Accelerated Living Crystallization-Driven Self-Assembly.

Self-assembly of conjugated polymers offers a powerful method to prepare semiconducting two-dimensional (2D) nanosheets for optoelectronic applications. However, due to the typical biaxial growth behavior of the polymer self-assembly, independent control of the width and length of 2D sheets has been challenging. Herein, we present a greatly accelerated crystallization-driven self-assembly (CDSA) system of polyacetylene-based conjugated polymer to produce 2D semiconducting nanorectangles with precisely controllable dimensions. In detail, rectangular 2D seeds with tunable widths of 0.2-1.3 μm were produced by changing the cosolvent% and grown in the length direction by uniaxial living CDSA up to 11.8 μm. The growth rate was effectively enhanced by tuning the cosolvent%, seed concentration, and temperature, achieving up to 27-fold increase. Additionally, systematic kinetic investigation yielded empirical rate equations, elucidating the relationship between growth rate constant, cosolvent%, seed concentration, and seed width. Finally, the living CDSA allowed us to prepare penta-block comicelles with tunable width, length, and height.

The effect of starch types on extensional, linear and nonlinear rheological properties of starch cracker dough

Cracker is a popular snack, and their quality depends on the rheological properties of the dough during production. This study focused on the impact of different starch types (tapioca, corn, and potato) used in the same amount (30 g) on the rheology of starch cracker dough. Various rheological tests were conducted to assess the dough's properties. Linear viscoelastic properties were determined using oscillatory frequency and temperature sweep tests, while the nonlinear viscoelastic behavior was characterized through stress relaxation and creep recovery tests. Extensional rheological behavior was also examined. Additionally, the textural and thermal properties of the dough were monitored to understand starch gelatinization and its interactions with other components. In the linear viscoelastic region, no significant differences were found between different dough formulations. However, in the nonlinear viscoelastic region, the potato starch-containing formulation exhibited different viscoelastic and textural properties. Biaxial extensional rheological behaviors showed no significant variations between formulations. The temperature sweep test data from differential scanning calorimetry measurements were consistent with temperature sweep data. In summary, this study provides valuable insights into how different starches influence the rheological behavior of starch cracker dough, considering various degrees of deformation and temperature. These findings have implications for cracker production parameters.

Biaxial tensile behavior of CoCrFeNi high-entropy alloy under dynamic and proportional loadings

The dynamic failure behavior of CoCrFeNi High-Entropy Alloy (HEA) under plane biaxial stress was investigated in detail. The dynamic biaxial tensile tests were conducted using an Electromagnetic Biaxial Split Hopkinson Tensile Bar (EBSHTB) system. For comparison, the quasi-static uniaxial and biaxial tensile tests, as well as dynamic uniaxial tensile tests, were performed respectively. A cruciform specimen suitable for large plastic deformation was designed and employed in the experiments. The Finite Element Method (FEM) verified that the improved cruciform specimen could satisfy the basic requirements. The feasibility of the proposed specimen was further confirmed through loading tests. Finally, the quasi-static and dynamic yield loci of the HEA in the first quadrant of the principal stress space were plotted. The results indicate that the alloy exhibits obvious strain hardening effect and strain rate strengthening effect, the yield locus and plastic work contours can be accurately described by Hill’48 criterion.

Stability and Biaxial Behavior of Fresh Cheese Coated with Nanoliposomes Encapsulating Grape Seed Tannins and Polysaccharides Using Immersion and Spray Methods.

In the food industry context, where fresh cheese stands out as a highly perishable product with a short shelf life, this study aimed to extend its preservation through multi-layer edible coatings. The overall objective was to analyze the biaxial behavior and texture of fresh cheese coated with nanoliposomes encapsulating grape seed tannins (NTs) and polysaccharides (hydroxypropyl methylcellulose; HPMC and kappa carrageenan; KC) using immersion and spray methods, establishing comparisons with uncoated cheeses and commercial samples, including an accelerated shelf-life study. NT, HPMC, and KC were employed as primary components in the multi-layer edible coatings, which were applied through immersion and spray. The results revealed significant improvements, such as a 20% reduction in weight loss and increased stability against oxidation, evidenced by a 30% lower peroxide index than the uncoated samples. These findings underscore the effectiveness of edible coatings in enhancing the quality and extending the shelf life of fresh cheese, highlighting the innovative application of nanoliposomes and polysaccharide blends and the relevance of applying this strategy in the food industry. In conclusion, this study provides a promising perspective for developing dairy products with improved properties, opening opportunities to meet market demands and enhance consumer acceptance.

Uniaxial and multiaxial cyclic deformation behavior prediction of Z2CN18.10 austenitic stainless steel based on Transformer deep learning method

In this study, the experimental study of cyclic deformation behavior of Z2CN18.10 austenitic stainless steel under uniaxial, cross, rhombus and circular paths is investigated. Based on Transformer deep learning method, three models are built to predict the cyclic deformation behavior of the material. One is the single input–single output model, which is used to predict the uniaxial cyclic deformation behavior. The second is the double input–single output model, which is used to predict the biaxial cyclic deformation behavior. The third is the time series multi-step model, which is used to predict the stress evolution under all paths. The Cross-Entropy loss function is adopted to train the models and the rationality of its application in the regression model is deduced from the theoretical point of view. Transformer deep learning method is based on attention mechanism, which can focus on the historical effect of Z2CN18.10 stainless steel cyclic deformation and accurately describe the uniaxial and multiaxial cyclic deformation behavior of the material.

Plane-Stress Deformation Behavior of CoCrFeMnNi High-Entropy Alloy Sheet under Low Temperatures.

High-entropy alloys are promising candidates expected to be applied in transportation equipment serving in extreme environments due to their excellent properties. CoCrFeMnNi high-entropy alloy is a typical representative of them, and its low temperature performance is excellent. In this study, to evaluate the feasibility of forming HEA shells, the deformation behavior of CoCrFeMnNi under a plane-stress state at lower temperatures was thoroughly studied. Firstly, a thin-walled HEA tube was fabricated using hot extrusion and further formed into a thin shell for uniaxial tensile and biaxial bulging tests. Subsequently, uniaxial tensile tests at cryogenic temperatures were conducted. Both the strength and the ductility improves as the temperature decreases from -160 °C to -196 °C. Then, a systematic low-temperature bulging test was performed using isothermal dome tests and the thickness uniformity analysis of the bulged specimens was carried out. In addition, grain microstructural observation using EBSD was characterized analyze the possible deformation mechanism at the cryogenic temperature under the biaxial stress state. This study, for the first time, investigated the biaxial deformation behavior of HEA. Considering the plane-stress state deformation is the dominant type in the thin-walled shell deformation, this study enables us to provide direct guidance for various sheet-forming processes of HEAs.

Study on the biaxial mechanical behavior of steel fiber reinforced recycled aggregate concrete

Steel fiber reinforced recycled aggregate concrete (SFRAC) was proposed considering the enhancement of mechanical properties by incorporating steel fibers and the reduction of environmental impacts and cost due to the addition of recycled aggregates. To better understand the mechanical properties of SFRAC under biaxial compression and its failure criteria, 150 SFRAC specimens were prepared with different replacement ratios of recycled coarse aggregate (50%, 75%, 100%) and volume fractions of steel fibers (0%, 0.6%, 1.2%, 1.8%). In addition, various stress ratios were considered in the biaxial compression test (σ1:σ2=0:1.0, 0.2:1.0, 0.5:1.0, 0.7:1.0, 1.0:1.0). The results indicated that the failure of SFRAC was observed as columnar and splitting modes depending on the biaxial stress ratio. The impacts of the considered variables on the biaxial peak strength were studied. The increasing volume fraction of steel fibers tended to improve the biaxial peak strength of SFRAC within a threshold beyond which the impact was negative. Similarly, the biaxial strength of most SFRAC samples showed a pessimum effect when the biaxial loading stress ratio was higher than 0.7, though they were still higher than the uniaxial compressive strength. A failure criterion for SFRAC under biaxial compression loading is proposed, in which four parameters are included. The calculations are in good agreement with the experimental results.

Mechanical Behavior of Lithium-Ion Battery Separators under Uniaxial and Biaxial Loading Conditions.

The mechanical integrity of two commercially available lithium-ion battery separators was investigated under uniaxial and biaxial loading conditions. Two dry-processed microporous films with polypropylene (PP)/polyethylene (PE)/polypropylene (PP) compositions were studied: Celgard H2010 Trilayer and Celgard Q20S1HX Ceramic-Coated Trilayer. The uniaxial tests were carried out along the machine direction (MD), transverse direction (TD), and diagonal direction (DD). In order to generate a state of in-plane biaxial tension, a pneumatic bulge test setup was prioritized over the commonly performed punch test in an attempt to eliminate the effects of contact friction. The biaxial flow stress-strain behavior of the membranes was deduced via the Panknin-Kruglov method coupled with a 3D Digital Image Correlation (DIC) technique. The findings demonstrate a high degree of in-plane anisotropy in both membranes. The ceramic coating was found to negatively affect the mechanical performance of the trilayer microporous separator, compromising its strength and stretchability, while preserving its failure mode. Derived from experimentally calibrated constitutive models, a finite element model was developed using the explicit solver OpenRadioss. The numerical model was capable of predicting the biaxial deformation of the semicrystalline membranes up until failure, showing a fairly good correlation with the experimental observations.

Softened membrane model for shear of ultra-high-performance concrete (SMM-UHPC)

Understanding the shear behavior of Ultra-High-Performance (UHPC) is crucial to prevent undesired responses that could be induced by diagonal shear cracks. Hence, the ability of analytical models to predict shear responses of UHPC members is of paramount importance, which is addressed in this paper by the Softened Membrane Model (SMM). Since the SMM is a two-dimensional shear modeling framework developed for reinforced concrete, a parametric investigation was conducted to assess its suitability for UHPC, namely SMM-UHPC. Through this assessment, a softening coefficient for the biaxial behavior of UHPC was developed and new constitutive laws were integrated in SMM. Comparisons with shear panel tests were used to evaluate the accuracy of SMM-UHPC and quantify the significance of key model parameters. Sensitivity analyses showed that the decomposition between biaxial and uniaxial strain fields, which is used in SMM to capture the Poisson effect, has a negligible influence on UHPC shear. Combining experimental and analytical data, the tensile localization strain was identified to be of most significance for predicting the shear stress-strain response of UHPC.

Meso-FE modelling for homogenization of the nonlinear orthotropic behavior of PTFE-coated fabric based on virtual fiber method

Compared to traditional textile composites, the coated fabric used in fabric membrane structures is much more flexible. Its macroscopic mechanical behavior is highly nonlinear, anisotropic, and shows stress ratio dependence during the loading process. The main reason is that the yarns within the coated fabric are not completely solidified, and there is a significant crimp interchange process in the yarns under load. This paper proposes a novel mesoscopic finite element (FE) model to predict the nonlinear orthotropic mechanical behavior of PTFE-coated fabric using the virtual fiber method (VFM). By comparing with experimental data, it is shown that the virtual fiber defined by the truss element can visually and effectively simulate the mechanical behavior of the internal fibers and reflect the crimp interchange process between two-way yarns. Combined with PBCs, it can effectively predict the uniaxial and biaxial tensile behaviors of the PTFE-coated fabric. Moreover, a new multi-scale model suitable for structural scale analysis of fabric membrane structures has been attempted by combining the direct FE2 (D-FE2) method with the proposed mesoscopic FE model. Local deformation mechanisms and macro response of fabric membrane structures can be observed simultaneously from these analyses, which provide a better understanding of the mechanical behavior of the fabric membrane structures.

Deformation characterization of multi-morphology composite cellular hyperelastic structure under biaxial tension: Analytic approaches for sensor applications

As a preliminary study to develop an effective stretchable sensor, we implemented multi-morphology cellular structures in the gauge area of a biaxial tensile specimen to obtain the desired biaxial mechanical behaviour. A numerical parametric study was conducted by considering the unit cell geometries, four biaxial tension conditions, and three groups of unit cells. The parametric study reveals that a multi-morphology composite cellular (M2C2) specimen with compliant unit cells near the centre and stiff unit cells along the border of the gauge area shows high linearity between the force and displacement relationships and high compliance. M2C2 specimens optimised using the Bayesian optimisation process share similar geometric patterns found in the parametric study and show enhancements in linearity and compliance up to 40.4 % and 65.6 %, respectively, compared with those of a conventional solid specimen.

Study on biaxial tensile failure behavior of ultra-thin-ply carbon fiber reinforced composites

The superior mechanical properties of ultra-thin-ply carbon fiber reinforced composites under uniaxial stress have been widely recognized. However, composite structures are often subjected to multiaxial loading in practical applications. Therefore, this study focuses on investigating the mechanical properties of ultra-thin-ply carbon fiber reinforced composites under biaxial stress conditions. Firstly, the geometric structure of a cruciform biaxial test specimen for composites is designed, and its rationality is demonstrated. Subsequently, cruciform biaxial test specimens with ply thicknesses of 24 μm and 100 μm are prepared for quasi-isotropic laminated plates, and biaxial tensile experiments with stress ratios of 0:1, 1:1, and 2:1 are conducted. This study establishes the failure envelope of ultra-thin-ply composites under biaxial tensile conditions and compare it with the experimental results of standard-ply composites. Finally, the fracture surfaces of the specimens and acoustic emission signals are analyzed to reveal the failure mechanisms of the composites under biaxial stress conditions. The results indicate that ultra-thin-ply carbon fiber reinforced composites exhibit higher interaction degree under biaxial stress, and their ability to suppress delamination is stronger.