Nonlinear Stress-strain Model Research Articles

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.

Multi-scale coupling numerical modeling of metallic strip flexible pipe during reel-lay process

Complex plastic deformation and local buckling may occur due to the nonlinear contact between the pipe and drum in the offshore pipeline laying by reel-lay method. In this paper, material performance tests are carried out to obtain the nonlinear stress-strain constitutive models for high density polyethylene (HDPE) material and steel strip. Meanwhile, full-scale tensile tests are also conducted to acquire the tension-strain correlation of metallic strip flexible pipe (MSFP). Then, shell element and solid element are combined to establish an ABAQUS multi-scale finite element model (FEM) for MSFP under the coiled laying condition. The proposed multi-scale FEM consists of three components, i.e. two simplified components and one fine component, which could accurately and efficiently simulate the mechanical properties of flexible pipe under the coiled laying condition. The results indicate that: due to the radial extrusion restriction of spiral steel strips, the Mises stress distribution of inner HDPE layer shows a more uniform spiral strip distribution than outer HDPE layer; the most dangerous condition for MSFP may be when it is just partially wound up on the drum; the effect of friction coefficient on the spiral steel strips seems obviously larger than the effects of traction force and drum diameter.

Characterization studies on calcium silicate boards and fibre cement boards used as sheathing in light gauge steel framed systems

This paper presents a systematic mechanical characterization study on two types of board materials reinforced with lignocellulosic fibres used as sheathing in light gauge steel framed building, namely calcium silicate board (CSB), and fibre cement board (FCB), under tensile, compressive and shear loading. The ASTM and EN standards for wood-based panels recommend the preparation of the test specimen by bonding additional numbers of boards along thickness to eliminate global buckling under compression and shear loading. However, it is observed that the FCB and CSB specimens still suffers premature bearing failure at the loaded ends and delamination of the boards at the glued interface which often fails to characterize the actual material behaviour. To overcome this limitation, the paper proposes a unified coupon made of single (virgin) thick board and the use of combined loading compression fixtures and large panel–shear test fixtures to simulate the desired failure modes and obtain complete stress–strain response under compression and shear loading, respectively. The scope of the work majorly encompassed an extensive experimental program comprising of total 115 specimens made of FCB and CSB of thicknesses 8 mm, 10 mm and 12 mm, tested along both longitudinal and transverse directions to evaluate the constitutive properties and strength limit states. The results show that the FCB exhibits higher strength and stiffness than the CSB specimens. Further, a nonlinear stress–strain model was established to represent the response of the board material under compression.

Mechanical Constitutive and Seepage Theoretical Model of Water Storage Media Based on Fractional Derivative

Using an abandoned underground goaf in coal mines as water reservoirs has been successfully applied for protecting mine water resources in western China. The water storage media are composed of broken rock masses and the voids between the rock masses. It is critical for reservoir capacity calculation that the deformation characteristics and seepage evolution of the water storage media under triaxial stress are theoretically described. In this study, broken rock masses and the space among the rock masses are simplified as two springs in a series. The mechanical behavior of the broken rock mass is described by Hooke’s law of linear elasticity, and the deformation characteristics of the space among the rock masses are represented by a nonlinear elastic constitutive model. The nonlinear stress-strain constitutive model of the water storage media is established by combining Hooke’s law and the fractional derivative stress-strain model. Similarly, a non-Darcy seepage model of the water storage media is obtained. The nonlinear stress-strain model is verified by mechanical experiments, physical simulation tests, and field measured data, and parameter sensitivity analysis is performed. The non-Darcy seepage equation is fitted and analyzed by using the seepage experimental data of the broken rock mass under triaxial compression conditions. The fractional non-Darcy model rather than the Forchheimer equation can more accurately describe the nonlinear seepage process in water storage media.

Design analysis and testing of flat sandwich panels under bird strike

A non-linear energy-based analytical approach to design flat sandwich panels resistant to bird strike is presented. The approach is then complemented by numerical simulation in Abaqus using smooth particle hydrodynamics to model the bird and a non-linear stress-strain model for the core material. Flat sandwich panels were designed to deform and just fail when the maximum deflections are reached for given strike energies. The panels designed with this approach were tested using gelatin birds and two different material combinations with non-toughened and toughened facesheet and core materials. The analytical and numerical approaches were found to be conservative as they predicted failure onset for the bird energies selected while the tests showed no damage. The maximum deflection and maximum strains at different locations of the panels were well predicted by the numerical analysis, but the predictions departed significantly from the tests after the first peak was reached.

Microstructure and modeling of uniaxial mechanical properties of Polyethersulfone nanocomposite ultrafiltration membranes

Polyethersulfone (PES) nanocomposite membranes are some of the emerging ultrafiltration technologies that have promising applications in gas separation and wastewater treatment due to their unique microporous structure and cheapness. However, the effect of nanofiller additives on their mechanical and viscoelastic properties is still missing and these fundamentals should be known to designers and manufacturers for potential upscaling. In this context, this research aims to study the uniaxial mechanical behaviors of PES membranes and their nanocomposites (CNTs/PES and Graphene/PES), and then to model their mechanical characteristics based on the results of mechanical experiments. In order to achieve that, four batches from CNTs/PES and Graphene/PES nanocomposite membranes with different concentrations of nanofillers (0.01-0.04 wt.%) were prepared using a solution casting method and a tape casting process. Also, another neat PES batch was prepared for comparison. The pore topology of the synthesized membranes was observed using SEM. Afterwards, the mechanical tensile specimens were cut from the synthesized membranes and tested according to standard ASTM 638M-3 using a uniaxial universal testing machine. Finally, a nonlinear uniaxial stress-strain model was built to simulate the mechanical performance of the fabricated membranes using the generalized Maxwell model. The results showed that the mechanical properties of the membranes were reduced significantly by additives (up to 26% for CNTs and 57% for GA compared with neat batch) because of the changes in the pore topology (orientation, size, and distribution) of the prepared membranes,whereas the modeling results showed that the constitutive model is valid for deducing the uniaxial stress-strain curves of PES membrane and its nanocomposites membranes with a high predictability and average deviation estimated at 0.715% (PES), 0.302% for CNTs/PES and 0.164% for GA/PES membranes.

The nonlinear stress-strain curve model as a solution of the fourth order differential equation

The idea that the stress-strain curve satisfies different ordinary differential equations in its different segment is proposed and implemented. In contrast to the classical Ramberg-Osgood law, the model establishes the dependence of stress on deformation. For each segment of the deformation curve, a differential equation is formulated that corresponds to the physics of deformation in this section. The curve is divided into two segment: linear and nonlinear. In the first segment, a second-order differential equation of the simplest type is postulated. In the second segment, a fourth-order differential equation is postulated. The boundary value problem in each segment is formulated from the requirement of continuity and differentiability of the deformation curve. The resulting solution has the advantage that, in contrast to the empirical Ramberg-Osgood law, it has a strictly linear part of the stress-strain curve. The proposed model was tested on modeling the elastoplastic properties of four Russian steels. The standard deviation of the theoretical curves from the samples of the experimental points did not exceed 2.5% for all materials.

Applicability of 2360 MPa grade prestressing steel strand: Performance of material, bond, and anchorage system

A 2360 MPa grade PS strand has been developed with the tensile strength increased by about 27% compared to the existing 1860 MPa grade PS strand. In order to apply this new material to prestressed concrete (PSC) structures, the material performance and characteristics have to be identified, while the conformity to the existing design criteria must also be variously evaluated and investigated. The study conducted a series of material performance evaluations to apply the newly developed 2360 MPa grade PS strand to a real structure. Firstly, the study evaluated the material properties of the 2360 MPa grade strand itself for all criteria; secondly, the evaluation of the bond performance between 2360 MPa grade strand and concrete; and thirdly, the performance of the anchorage system for 2360 MPa grade strand. As a result, the material performance, bond performance, and anchorage system performance for the 2360 MPa grade PS strand satisfied all specified performance criteria. Thereby the 2360 MPa grade strand could be applied directly to pre-tensioned and post-tensioned PSC structures. However, it was also found that the method of calculating the yield strength for the PS strand of ASTM A416 is unsuitable for higher strength PS strand than the 1860 MPa grade PS strand. In addition, non-linear and bilinear stress-strain models of 2360 MPa grade PS strand for analysis and design of PSC structures were presented.

A nonlinear uniaxial stress-strain constitutive model for viscoelastic membrane materials

Membrane materials with the excellent thermal, optical, electrical and chemical properties have attracted significant attention in numerous research fields recently. However, while being used to construct the membrane structures, the mechanical behaviors of membrane materials are more foundational than the other properties in evaluating the structure safety. This paper thus proposes a nonlinear stress-strain constitutive model for revealing the viscoelastic behaviors of membrane materials under uniaxial tensile loading. To this end, the constitutive equations for expressing the uniaxial tensile stress-strain relationships of viscoelastic materials are established gradually from the kinematic equations of the generalized Maxwell model that includes several basic Maxwell models and one basic spring element. Meanwhile, the uniaxial tensile tests of two typical viscoelastic membrane materials were carried out in order to examine the proposed constitutive model. The constitutive model parameters of the stress-strain properties of both membrane materials are accurately identified using the least square method. By comparing the true stress-strain curves between experimental results and constitutive models, good agreements with the maximum differences of 4.67% and 3.41% are acquired for the two employed viscoelastic membrane materials, respectively. These observations are able to validate the accuracy and efficiency of this proposed constitutive model in predicting the uniaxial stress-strain behaviors of viscoelastic membrane materials, which are significant in the nonlinear structural analysis of membrane structures.

Nonlinear Stress-Strain Model for Confined Well Cement.

The cement sheath is the key for providing the zonal isolation and integrity of the wellbore. Oil well cement works under confining pressure, so it exhibits strong nonlinear and ductile behavior which is very different from that without confining pressure. Therefore, for the accuracy of the simulation and the reliability of well construction design, a reliable compression stress–strain model is essential for confined well cement. In this paper, a new axial stress–strain model for confined well cement is developed based on uniaxial and triaxial test data, examinations of failure mechanisms, and the results of numerical analysis. A parametric study was conducted to evaluate and calibrate the model. The model is simple and suitable for direct use in simulation studies and well design. Results from this study show the nonlinear compressive behavior of confined well cement can be predicted using the traditional uniaxial compressive strength test measurements.

Analysis of laterally loaded piles in sloping ground using a modified strain wedge model

This paper proposes a modified strain wedge model for the analysis of laterally loaded piles in sloping ground. The proposed model allows the assessment of the soil resistance along the pile and describes the stress-strain behaviour of the soils using a nonlinear stress-strain model. The modified strain wedge is divided into two parts: an upper soil wedge and a modified lower strain wedge. Two calculation methods for the two parts are discussed, and an in-situ test is used to verify the validity and accuracy of the proposed method.

ARCS: A one dimensional nonlinear soil model for ground response analysis

This paper presents a one dimensional nonlinear stress-strain model called ARCS (Axis Rotation and Cubic Spline) capable of reproducing any user-input modulus reduction and damping curve. Unlike many previous nonlinear models, the ARCS model does not utilize Masing's rules, nor does it require a specific functional form for the backbone curve such as a hyperbola. Rather, the model matches the desired modulus reduction curve by fitting cubic splines to the implied stress-strain curve, and matches the damping curve by utilizing a coordinate transformation technique in which one axis lies along the secant shear modulus line with the other axis in the orthogonal direction for a particular unload-reload cycle. Damping is easily controlled in the transformed coordinate space. An inverse coordinate transformation returns the desired stress. The integration algorithm is independent of strain step size, meaning that the returned stress for a large strain increment is identical to the stress that would be returned by subdividing the strain increment into smaller increments. Small-strain damping may be modeled hysteretically, avoiding the need for supplemental viscous damping. The model is shown to match the results of laboratory cyclic simple shear tests involving deliberately irregular stain histories. The performance of the model is illustrated in a set of ground response simulations where its predictions are compared with those of existing models. The ARCS model does not explicitly account for rate effects, cyclic degradation, or pore pressure generation. However, the equations can potentially be adapted in more advanced constitutive models to capture these effects. Such implementations are reserved for future publications.

Analytical Model of Nonlinear Stress-Strain Relation for a Strand Made of Two Materials.

Unlike conventional steel strands, the smart strand supports strain-measuring function and adopts different materials for its core wire and helical wires. This study intends to analytically derive the nonlinear stress-strain model of this strand made of two materials. The effect of the bending moment and torsional moment of the helical wires on the overall load within the range of geometric shapes shown by actually used strands is verified to be negligible and is thus ignored in order to simplify the analytical model. Moreover, the slight difference between the actual and analytic behaviors, which only appears in the slope varying part in the case of bilinear behavior, such as that of steel, is also ignored. The proposed constitutive model of the smart strand obtained by introducing the experimental stress-strain relation between the carbon fiber reinforced polymer core wire and the helical steel wires is in good agreement with the experimental data. The previous analytical models are applicable only to strands made of a unique linear material, whereas the model proposed in this study is also applicable to strands in which the core wire and the helical wires are made of two different materials, exhibiting nonlinear behavior.

Fiber finite element in nonlinear analysis of square CFT columns

The paper presents nonlinear analysis of square CFT columns using distributed plasticity fiber elements. Behaviour of CFT columns is nonlinear and it is necessary to include different nonlinear effects into the numerical model in order to simulate their behaviour properly. Model proposed in this work considers: nonlinear behaviour of concrete and steel using nonlinear stress-strain models, confinement effect and geometrical nonlinearities. Tests exposed to static loading with different slenderness, different D/t ratio (where D is the total dimension of a cross section and t is the thickness of steel tube) and different loading conditions are analyzed. Stress-strain models that best approximate the behaviour of CFT columns are determined from a detailed parametric study. The proposed numerical model is validated by comparing numerical with experimental results available in the literature.

Consideration of Variability of Concrete Characteristics in Calculation of Reinforced Concrete Structures

The objective of this study is to analyze the effect of variability of concrete stress-strain characteristics on the bearing capacity of eccentrically compressed reinforced concrete elements. Relevance of this issue is caused by wide application of the nonlinear stress-strain model for calculations of reinforced concrete structures. A distinctive feature of calculations with the use of the nonlinear stress-strain model is the need of joint use of concrete strength and stress-strain characteristics. In addition to that, valid regulations of Russian Federation deal with the average values of stress-strain characteristics, and there are no information on their variability.

Experimental characterization of Italian composite adobe bricks reinforced with straw fibers

Adobe buildings are located in many countries and are often constructed with fiber reinforced bricks, which are composite materials made of soil, water, and natural or artificial fibers. This study presents experimental findings for straw fiber reinforced adobe bricks typically used in Sardinia (Italy) and produced according to traditional worldwide handcrafted manufacturing procedures. A large number of compression and three-point bending tests were carried out on cubic and prismatic specimens, respectively. The identification of significant scatter in experimental data sets due to handcrafted manufacturing motivated the estimation of mechanical parameters at different percentile levels, in order to provide their characteristic and median values. The geometry of straw fibers was statistically characterized in terms of mean, standard deviation and probability distribution of their diameter and length. The mechanical characterization in compression included the estimation of fracture energy. Bending test data were processed to estimate Young’s modulus in tension, highlighting the bimodularity of the earthen composite material. Finally, both elastic–perfectly plastic and nonlinear stress–strain models are proposed for design/assessment purposes.

Experimental stress–strain analysis of tapered silica optical fibers with nanofiber waist

We experimentally determine tensile force–elongation diagrams of tapered optical fibers with a nanofiber waist. The tapered optical fibers are produced from standard silica optical fibers using a heat and pull process. Both, the force–elongation data and scanning electron microscope images of the rupture points indicate a brittle material. Despite the small waist radii of only a few hundred nanometers, our experimental data can be fully explained by a nonlinear stress–strain model that relies on material properties of macroscopic silica optical fibers. This is an important asset when it comes to designing miniaturized optical elements as one can rely on the well-founded material characteristics of standard optical fibers. Based on this understanding, we demonstrate a simple and non-destructive technique that allows us to determine the waist radius of the tapered optical fiber. We find excellent agreement with independent scanning electron microscope measurements of the waist radius.

Seismic response and simulations of reinforced concrete bridge using OpenSees on high performance computing

Nonlinear seismic analysis is becoming increasingly significant to grasp the performance of structures under earthquake. A nonlinear finite element model of existing bridge at Karad, India, including the bridge structure, pile groups, and the supporting foundation soil, is developed under 2D and 3D conditions in Gid (a pre and postprocessor software). The computational model is analyzed using Parallel OpenSees. OpenSees is open source software for carrying out earthquake engineering simulations, developed by Pacific Earthquake Engineering Research Centre, USA. The earthquake simulations were carried out using C-DAC’s high performance computing facilities. The ground motion selection and modification technique-predicting median interstory drift response of building, ground motions are selected by M and R and scaling to Sa(T1), is used for seismic response of combined large scale soil-structure interaction of Karad bridge. The idealized model properly represents the actual geometry; boundary conditions, gravity loads and mass distribution. Nonlinear modeling and analysis allows more accurate determination of stresses, strains, deformations and forces of critical components. The present work involves the effects of specially varying input excitation (earthquakes) at an existing bridge site. A nonlinear finite element model of this bridge site including the bridge structure, pile group and supporting foundation soil is developed in 2D plane strain conditions and in 3D 20 noded brick element. Carefully calibrated nonlinear stress–strain models are employed for both bridge and soil materials, in order to realistically reproduce actual site conditions. Seismic input motions are defined as forces using the boundary layer force method (zero length element approach). The earthquake simulation of bridge structure includes large scale interaction between structure–foundation–soil system and deformations at various locations of the bridge. The results include deformations at base of piers and at various spans of the bridge. Performing the bridge simulation on C-DAC’s Param Yuva facility results in accuracy and saving in computing efforts.

A New Nonlinear Stress-Strain Model for Soils at Various Strain Levels

Soils have nonlinear stiffness and develops irrecoverable strains even at very small strain levels. Accurate modeling of stress-strain behaviour at various strain levels is very important for predicting the deformation of soils. Some existing stress-strain models are reviewed and evaluated firstly. And then a new simple non-linear stress-strain model is proposed. Four undetermined parameters involved in the proposed model can be obtained through maximum Young’s module, deformation module, and limit deviator stress and linearity index of soils that can be measured from experiment directly or calculated by empirical formulas indirectly. The effectiveness of the proposed stress-strain model is examined by predicting stress-strain curves measured in plane-strain compression test on Toyota sand and undrained triaxial compression test on London clay. The fitting results of the proposed model are in good agreement with experimental data, which verify the effectiveness of the model.

Determination, Derivation, Influence and Discussions of Parameters for Deformation Analyses with Duncan-Chang Modified E-B Model

This paper presents a study on influence of model parameters on deformation analyses with Duncan-Chang Modified Nonlinear Stress-strain (E-B) model for an ore mining tailings located in Chengde, Hebei Province of China. How to determine and derive these parameters from the laboratory experimental results was introduced first. Findings from numerical analyses performed with Midas GTS indicate that model parameters K and n most significantly affect the vertical and horizontal deformation respectively. Based on the analysis, the accuracy and effectiveness of these parameters were discussed further. Principles of the model and the parameter derivations suggest the model and parameters work better for small strain cases, hence model parameters shall be better determined with laboratory tests with low confining pressures or using new apparatus to measure small strain behavior of soil to ensure analysis results reliable.