Uniaxial Behavior Research Articles

Hyperelastic model for nonlinear elastic deformations of graphene-based polymer nanocomposites

Graphene-based polymer nanocomposites (PNCs) are increasingly important in engineering applications involving large deformations. However, the nonlinear behavior of these materials has not been thoroughly studied. Current models do not address the specific nonlinear effects of graphene nanofillers under large strains, lack sufficient comparison with experimental data, and primarily focus on uniaxial behavior without exploring biaxial responses, which are relevant in technological applications. This study investigates PNCs composed of silicone elastomer and graphene nanoplatelets (GNPs). We present experimental tests conducted in both simple tension and biaxial inflation on circular membranes. A homogenized hyperelastic model is developed, incorporating distinct contributions from the matrix and the nanofiller. Specifically, we introduce a novel strain energy function for the nanofiller contribution, tailored to reproduce the observed experimental behavior. The model accurately predicts the nonlinear elastic response of the studied PNCs across varying contents of GNPs. The proposed strain energy function is implemented in MATLAB to obtain an exact numerical solution for the inflation of circular PNC membranes. Finally, to demonstrate its broader applicability, the hyperelastic model is applied to additional experimental data from other PNCs found in the literature. This model contributes to establishing a robust framework for the effective use of PNCs.

Synthesis-Processing-Property Relationships in Thermomechanics of Liquid Crystal Elastomers

Liquid crystal elastomers (LCEs) are composed of rod-like liquid crystal (LC) molecules (mesogens) linked into elastomeric polymer networks. They present a nematic phase with directionally ordered mesogens at room temperature and an isotropic phase with no order at high temperatures, enabling large thermal-induced deformation. As a result, LCEs have become promising candidates for new applications in soft robotics and shape morphing. LCEs are being actively studied in both experiment and theory in recent years. However, the fundamental relationship among synthesis, processing, and thermomechanical behaviors of modern LCEs are still largely unclear. This knowledge gap is further complicated by the various LCE types, including polydomain, monodomain, nematic-genesis, and isotropic-genesis, each fabricated and used under different experimental conditions and applications. Here we explore synthesis-processing-property relationships in thermomechanics of various LCEs, by combining fabrication, characterization, and theoretical modeling. We adapt the widely used two-stage method to fabricate isotropic-genesis polydomain LCEs and nematic-genesis LCEs with varying pre-stretches during polymerization. We characterize the thermal-induced spontaneous deformation and the temperature-dependent uniaxial stress-stretch responses of the LCEs. We identify a new relationship among the soft elasticity, the thermal-induced spontaneous deformation, and the pre-stretch during polymerization, in the LCEs under study. Building on classical theories and our experimental results, we develop a constitutive model to describe the uniaxial behaviors of various LCEs. The theoretical predictions agree well with the experimental results on uniaxial stress-stretch responses at different temperatures. Finally, we discuss the remaining challenges and future opportunities in synthesis-processing-property relationships of LCEs.

A Fractal Study on Random Distribution of Recycled Concrete and Its Influence on Failure Characteristics

In order to quantitatively describe the influence of aggregate distribution on crack development and peak stress of recycled aggregate concrete, a multifractal spectrum theory was proposed to quantitatively characterize aggregate distribution in specimens. A mesomechanical model of reclaimed aggregate concrete mixed with natural aggregate and artificial aggregate was constructed. Numerical simulation tests were conducted on the uniaxial compression mechanical behavior of 25 groups of sample models with the same proportion and different aggregate distribution forms. Based on the box dimension theory, the multiple fractal spectrum method was used to quantitatively characterize the aggregate distribution form, and the key factors affecting cracks were explored based on the gray correlation degree. The research results show that the aggregate distribution in recycled aggregate concrete has multifractal characteristics. The multifractal spectrum was used to effectively characterize the aggregate distribution pattern, which can enlarge local details and provide new ideas for the quantitative analysis of the damage mode of recycled concrete. Secondly, by establishing a statistical model of the correlation between the multifractal spectrum width of the aggregate distribution pattern and the crack distribution box dimension, it was found that there was a positive correlation between the two, that is, the greater the multifractal spectrum width of the aggregate distribution pattern, the greater the crack box dimension, and the more complex the crack distribution. The complexity of aggregate distribution is closely related to the irregularity and complexity of mesoscopic failure crack propagation in recycled concrete specimens. In addition, gray correlation theory was applied to analyze the key factors affecting the formation of cracks in the specimens. The results showed that aggregate distribution had a first-order correlation with crack formation, and changes in aggregate distribution were an important factor affecting the performance of recycled concrete. Secondly, the poor mechanical properties of NAITZ led to obvious material damage, while NCA and MZ had a significant impact on the skeleton effect in the stress–strain process due to their large areas. This study deepens people’s understanding of the damage characteristics and cracking failure modes of recycled concrete. The study verifies the feasibility of the application of recycled aggregates and provides a valuable reference for engineering practice.

Modeling nonlinear stress-strain model for sulfate dry-wet cycle erosion of concrete: considerations for the initial compaction stage

Sulfate dry-wet cycle erosion significantly affects the mechanical properties of concrete. Investigating the uniaxial compressive stress-strain relationship under these conditions is essential for developing accurate constitutive models. This study analyzes the uniaxial stress-strain curves of concrete subjected to dry-wet cycles in 5% and 15% sulfate solutions. The results show that the initial compaction phase in the stress-strain relationship is particularly pronounced under increasing sulfate concentrations and cycle counts. The concrete experiences an extended compaction phase, which accounts for up to 35.71% of the total strain process. This finding challenge traditional constitutive models, which struggle to accurately describe this phase. To address this issue, the study develops a nonlinear stress-strain model for concrete, incorporating the initial damage caused by sulfate dry-wet cycle erosion, based on Weibull statistical damage mechanics principles. The research indicates that the effects of sulfate concentration and cycle count are predominantly reflected in the pronounced nonlinearity of the skeleton strain function’s opening size (a) and shape characteristics (b), modeled using a fourth-degree polynomial. The model demonstrates an excellent fit to experimental data with an R2 value of 0.99989, showing that the proposed nonlinear stress-strain relationship effectively captures the uniaxial mechanical behavior of concrete under sulfate dry-wet cycle erosion and provides a robust framework for developing constitutive models in such environments.

Insights on the mechanical properties and failure mechanisms of calcium silicate hydrates based on deep-learning potential molecular dynamics

The molecular-scale mechanical properties of calcium silicate hydrates are crucial to the macro performance of cementitious materials, while achieving coincidence between accuracy and efficiency in computational simulations still remains a challenge. This study utilizes a deep-learning potential, specifically developed for calcium silicate hydrates based on artificial neural network, to achieve molecular dynamics simulations with accuracy comparable to first-principle methods. With this potential, the elastic properties and uniaxial mechanical behaviors are explored, wherein the anisotropy and impact mechanism of calcium ratios are analyzed. The results add to evidence that the deep-learning potential possess a higher accuracy than common force fields. The anisotropy of elastic modulus is mainly attributed to different atomic interactions in various directions, while the anisotropy of strength is additionally affected by the form of failure. This study may advance the accurate molecular-scale simulation and deepen the understanding of the strength source and cohesion mechanism of cement-based materials.

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.

A path-dependent stress-strain model of FRP-confined circular concrete columns derived from an energy balance approach

It is generally believed that the use of fibre-reinforced polymer (FRP) confinement can effectively improve the strength and ductility of concrete. Passive confinement is one of the key features of the behavior of FRP-confined concrete. Analysis-oriented models for passively confined concrete have been established on the base of the active confinement model by many researchers. Among them, a stress path-independent assumption was made for those passively confined concrete. However, in recent years, numerous researchers have found that the influence of stress path on the stress-strain relationship of confined concrete cannot be neglected. Therefore, in order to further understand and simulate the uniaxial behavior of FRP-confined concrete, this paper presents a stress path-dependent model of FRP-confined concrete based on an energy balance approach in which the extra work done by the active confining pressure in the stress path-independent model is considered. Firstly, experimental data comprising 341 sets of FRP jacket confined concrete tests and 28 sets of concrete-filled FRP tube (CFFT) tests were collected. Subsequently, the stress paths of the two types of specimens were identified based on the properties of FRP materials, and then the energy balance assumption was introduced, and finally a new stress path-dependent model was established using the energy balance approach. By comparing the predictions of the proposed model with collected experimental data and those of several existing models, it was observed that the proposed model can more accurately predict the ultimate stress of FRP-confined concrete and exhibit good agreement with the experimental stress-strain curves.

Stress-strain curve estimation from micropillar compression with transverse contraction effect

The Focused Ion Beam (FIB) technique and the associated compression testing capabilities provide versatile access to understanding the microstructural behaviour of materials. Among many objectives, determining the stress-strain relationship from experimental or numerical force-displacement data remains a fundamental challenge. However, for micropillers under compression, the inside deformation constraint is complex like in components and the transformation of a measured force-displacement curve into an accurate uniaxial stress-strain curve is not straightforward. In this context, in a previous numerical based analysis for perfect volume constancy or incompressibility the determination of reliable and accurate stress-strain curves from nonlinear load-deformation curves of micropillers was already verified. In the case of transverse contractions, however, numerical simulations of micropillers provide unexpected force-displacement behaviour, i.e. their force-displacement curves are almost superimposing and are very close to the force-displacements for incompressibility. This effect implies, that transverse contraction would have no contributions in micropillar compression. In contrast, independent simulations using a single finite element accurately explore the true uniaxial stress-strain behaviour for the whole range of transverse contractions. These are considered as the reference behaviour and are also treated by an analytical expression. With the presented new stress-strain estimation approach, including transverse contraction, any force-displacement curve from a micropillar under compression can be stepwise corrected. The first step of the new stress-strain curve estimation method, including transverse contraction, is carried out in the same way as in the preceding analysis for incompressibility, followed by further steps to obtain the final true stress-strain curve. Although the presented numerical analysis is exemplarily performed for the behaviour of fused silica, but the stress-strain approach is in the same manner generally applicable for a material behaviour with other stress-strain curves. The assumption behind is isotropic and nonlinear material behaviour.

Prediction of Biaxial Properties of Elastomers and Appropriate Data Processing.

An equibiaxial tension test could be necessary to set up hyperelastic material constants for elastomers exactly. Unfortunately, very often, only uniaxial tension experimental data are available. It is possible to use only uniaxial data to compute hyperelastic constants for a hyperelastic model, but the prediction of behavior in different deformation modes (as is equibiaxial or pure shear) will not work correctly with this model. It is quite obvious that there is some relation between uniaxial and equibiaxial behavior for the elastomers. Thus, we could use uniaxial data to predict equibiaxial behavior. If we were able to predict (at least approximately) equibiaxial data, then we could create a hyperelastic model usable for the general prediction of any deformation mode of elastomer. The method of the appropriate processing of experimental data for such prediction is described in the article and is verified by the comparison with the experiment. The presented results include uniaxial and equibiaxial experimental data, the created average curve of both the deformation modes, and the predicted equibiaxial data. Using Student's t-test, a close coincidence of the real and predicted equibiaxial data was confirmed.

A Component Method for Full-Range Behaviour of Embedded Steel Column Bases

This paper introduces a component model for analysing embedded column bases to predict rotational stiffness, moment resistance, and the full-range moment–rotation response. The key components identified include the embedded column, concrete in compression on the column side, concrete in compression beneath the base plate, concrete in punching shear above the base plate, and anchor bolts. The embedded column is modelled as a Timoshenko beam, considering both shear and flexural deformations, while other components are represented by springs. Methods are provided for determining their uniaxial constitutive behaviour. A simplified iterative solution method is proposed, where the embedded column is further simplified into three rigid segments to specifically address shear and bending deformations. A corresponding simplified finite element model is developed for accurate numerical solutions. The validity of the component model is confirmed through comparisons with the results of existing tests and refined solid finite element analysis for H-steel column bases. The simplified iterative solution method effectively predicts strength but underestimates the stiffness of deeply embedded column bases. This is due to the trilinear deformation pattern simplification, which concentrates flexural deformation at the upper bearing stress resultant force point, leading to an overestimation of steel column rotation on the foundation surface.

Harnessing ion beam erosion engineering for controlled self-assembly and tunable magnetic anisotropy in epitaxial films

The engineering of the surface morphology and the structure of the thin film is one of the essential technological assets for regulating the physical properties and functionalities of thin film-based devices. This study presents an easy and handy approach to tailor the surface structure of epitaxial thin films utilizing low-energy ion beam. Here, we investigate the evolution of the surface structure and magnetic anisotropy (MA) in epitaxial Fe/MgO (001) model systems subjected to multiple cycles of ion beam erosion (IBE) after thin film growth. The growth of Fe film occurs in the form of three–dimensional islands and exhibits intrinsic biaxial MA. Following a few cycles of IBE, an induced uniaxial magnetic anisotropy leads to a split in the hysteresis loop, and the film displays almost uniaxial magnetic switching behavior. More distinctly, we present a clear and conclusive evidence of (2 × 2) reconstruction of the Fe surface due to the atomic rearrangement by IBE. Furthermore, 57Fe isotope sensitive nuclear resonance scattering measurement provides insight into the depth-resolved magnetic information due to the modified surface topography. We also demonstrate that thermal annealing can reversibly tune the surface reconstruction and induced UMA. The feasibility of the IBE technique by adequately selecting IBE parameters for surface structure modification has been highlighted apart from conventional tailoring of the morphology for the tuning of UMA and introduces a new dimension to our understanding of self-assembled surface morphology evolution by IBE.

Self-centering of steel braced frames equipped with Fe-SMA TADAS dampers

This study proposes a novel triangular added damping and stiffness (TADAS) damper that uses the shape memory effect of iron-based shape memory alloy (Fe-SMA) to provide a self-centering system to recover the initial shape of a structure after significant inelastic deformation induced by nonlinear response of fused elements, without the need for difficult and expensive replacement procedures of conventional TADAS systems. Unlike most studies which consider simplified uniaxial behavior of Fe-SMAs, the present non-linear finite element simulations cover the full 3D material non-linearity of Fe-SMA component based on the SMA constitutive law to capture both flexural and shear behavior in various coupled thermomechanical loadings, including the mechanical loading/unloading, the heating, and the final cooling (as the recovering process). Simulations performed on a one-bay steel frame for different drift ratios reveal that although the dissipation energy of the new device is at most 10% less than the ordinary one, it enjoys the self-centering property to recover the initial shape of the frame before loading, showing that the proposed damper is an effective alternative to ordinary TADAS yielding dampers to achieve the self-centering characteristics.

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.

Uniaxial deformation behaviors and mechanism of Ti–6Al–4V alloy with bi-oriented grains

It is of great importance to investigate the deformation and damage mechanisms of polycrystalline materials with soft crystal orientations, considering the soft grains are usually the fatigue crack initiation sites. In this study, a Ti–6Al–4V alloy fully consisted of <01 1‾ 0> and <1‾ 21‾ 0> α (soft) grains was prepared and its uniaxial deformation behavior was investigated. Interestingly, no significant asymmetry on the tension-compression yield strength was found in this alloy with bi-grain orientations, though mechanical asymmetry was generally found in the traditional Ti alloys with strong texture. After high temperature solution treatment, the preferred bi-orientations were retained and the asymmetry degree of yield strength did not change, showing an excellent stability in texture and mechanical performance. Deformation mechanisms during tension and compression were studied and discussed. This work provides a new understanding on the deformation and damage mechanisms in the grains with soft crystal orientations, and may guide the microstructural design of Ti alloy for pursuing high mechanical and fatigue performances in the future.

Uniaxial behavior of UHPC under cyclic compression: Experimental investigation and constitutive model

The compressive behavior of ultra-high performance concrete (UHPC) is experimentally investigated in this paper for three different micro steel fiber volume fractions (Vf= 1.0%, 1.5% and 2.0%) under uniaxial monotonic and cyclic compression. The cube specimens are loaded and fully unloaded twice per displacement increment to track the evolution of damage. Cycles are included till the peak load and after attaining the peak load, all the way till the load carrying capacity becomes marginal. A one dimensional (1D) elastoplastic damage constitutive model is proposed to simulate the damage of UHPC under uniaxial cyclic compression, incorporating the damage parameters within a damage function deduced from the tests. Damage is incorporated as a nonlinear function and thus the hysteresis behavior (distinguishable unloading and reloading paths) is adequately captured in the model. The experimental results from this study and the accompanying model demonstrate that the strength and stiffness degradation in UHPC due to low cycle fatigue stabilize at higher fiber dosage levels.

Using spherical indentation to determine creep behavior with considering empirical friction coefficient

Indentation testing is a common technique for characterizing the mechanical properties of materials. When it comes to assessing the yield behavior of metals, conical indentation is often favored due to its ability to induce significant plastic deformation at relatively shallow indentation depths. On the other hand, spherical indentation is typically chosen for evaluating metal creep behavior, as it helps minimize the influence of plastic deformation on creep measurements. In spherical indentation tests, the friction at the contact interface is particularly crucial, given the larger contact area and more pronounced slip zones. However, accurately determining the friction coefficient at the contact interface is a complex multi-scale challenge, with the exact coefficient varying based on specific testing conditions and surface treatments. Consequently, empirical friction coefficients are frequently employed, often without thorough justification. In this work, we proposed Bayesian inference method for obtaining the creep constitutive behavior of alloys through spherical indentation tests. Our model considers not only the complexity of creep law, but also the indentation friction, which is unable to consider in most spherical indentation tests with traditional treatment. By using experimental data of spherical indentation tests on 310S stainless steel and pure nickel alloy from literature, present study demonstrates the effectiveness of the Bayesian inference approach, with the inferred constitutive models exhibiting well agreement with uniaxial creep behavior. Furthermore, the method considers the friction coefficient as an extra factor in inferring creep constitutive behavior from indentation tests.

Gray correlation analysis between mechanical performance and pore characteristics of permeable concrete

Pervious concrete is a type of sustainable construction material used in pavement engineering due to its advantages in water permeability, skid resistance, and sound absorption performance. This study investigated the pore characteristics of five types of pervious concrete, along with the uniaxial compression behaviors and semi-circular bending (SCB) fracture performance. The critical stress intensity factor was obtained using the equivalent energy approach. Gray relational analysis was conducted between the mechanical performance and the pore characteristics. Pore indicators include the effective porosity, 2D porosity along the specimen height, 2D coordination number (CN) along the specimen height, 2D pore radius, 2D specific surface area, 3D CN, 3D pore radius, and 3D virtual porosity. Results indicated that from M1 to M3, when cement mortar content decreased from 520 kg/m3 to 408 kg/m3, the effective porosity increased from 18.95% to 27.43%, and the compressive strength and fracture toughness decreased obviously. For the same type of pervious concrete mixture, with the increase of notch length, the critical stress intensity factor decreased accordingly. The 2D porosity distribution, 2D pore size distribution, and 2D CN distribution presented a symmetrical trend of decreasing, then increasing, and then decreasing with the increase of specimen height. Aggregate with the gradation within the range of 9.5 mm to 19.0 mm generated a higher compressive strength, larger effective porosity and larger pore size compared to the gradation of 4.75 mm∼9.5 mm. The results of CN and pore radius generated from the 3D pore network model were larger than the corresponding 2D values. The gray correlation analysis revealed that 2D pore radius and 3D pore radius played critical effects on the uniaxial compressive strength and fracture resistance, while 2D CN and 3D CN were the least significant factors affecting the mechanical performance.

DEM study on the micromechanical behaviour of sand-clay mixtures

A DEM model incorporating realistic sand shape was developed to simulate sand-clay mixture (SCM) behaviour based on CT images acquired during uniaxial compression of a SCM containing quartz sand (SCM_R) and a SCM containing glass beads (SCM_S) with in-situ X-ray micro-tomography scanning. The influences of shape, size and content of sand grains on the uniaxial behaviour of SCM were studied. SCM_R revealed a higher peak strength and elastic modulus than SCM_S with the same sand content, sand size and initial void ratio. Increasing sand content led to significantly reduced peak strength for both SCM, and remarkably increased and unnoticeably changed elastic modulus for SCM_R and SCM_S, respectively. Meanwhile, increasing sand size resulted in dramatically decreased yet insignificantly varied peak strength and elastic modulus for SCM_R and SCM_S, respectively. The different phenomenon between SCM_R and SCM_S were attributed to the significantly different sand-clay bond intensities and interface interlocking effects between them.

Analysis of the uniaxial fatigue behaviour of 42CrMo4 Q&amp;T steel specimens extracted from the big end of a marine engine connecting rod using the heat dissipation approach

Analysis of the uniaxial fatigue behaviour of 42CrMo4 Q&amp;T steel specimens extracted from the big end of a marine engine connecting rod using the heat dissipation approach

Compositional dependence of uniaxial zero thermal expansion and zero linear compressibility in metal-organic framework MIL-122 (Al, Ga, In).

The responses of MIL-122(Al, Ga, In) to pressure or temperature have been investigated. The findings suggest that the a-axis in the lattice exhibits minimal compressibility, particularly zero linear compressibility (ZLC) behavior observed in MIL-122(In), consistent with experimental reports. Additionally, as the radius of metal atoms increases, the compressibility of the b-axis and c-axis gradually strengthens. There is a notable compositional dependence on volume thermal expansion in MIL-122(Al, Ga, In), where an increase in the metal atom radius leads to gradual weakening of volume thermal expansion. In particular, MIL-122(In) demonstrates pronounced volume negative thermal expansion (NTE) behavior, with the a-axis displaying zero thermal expansion (ZTE) behavior and both the b-axis and c-axis exhibiting NTE behavior. The temperature-dependent relative change in the bulk modulus of MIL-122(Al, Ga, In) has also been explored, revealing abnormal thermal hardening specifically within MIL-122(Ga, In). We attribute these unique uniaxial ZTE and ZLC behaviors in MIL-122(In) to its distinctive wine-rack topology, anomalous phonons (negative Grüneisen parameters), and internal structural flexibility.