Nonlinear Elasto-plastic Behavior Research Articles

Design of railway transition zones: A novel energy-based criterion

Railway transition zones (RTZs) experience higher rates of degradation compared to open tracks, which leads to increased maintenance costs and reduced availability. Despite existing literature on railway track assessment and maintenance, effective design solutions for RTZs are still limited. Therefore, a robust design criterion is required to develop effective solutions. This paper presents a two-step approach for the formulation of a preliminary-design criterion to delay the onset of processes leading to uneven track geometry in RTZs. Firstly, a systematic analysis of each track component in a RTZ is performed by examining spatial and temporal variations in kinematic responses, stresses and energies using a finite element model of an embankment-bridge transition. Secondly, the study proposes an energy-based criterion to be assessed using a model with linear elastic material behavior and states that an amplification in the total train energy in the proximity of the transition interface is an indicator of increased (and thus non-uniform) degradation in RTZs compared to the open tracks. The correlation between the total strain energy (assessed in the model with linear material behaviour) and the permanent irreversible deformations is demonstrated using a model with non-linear elastoplastic material behavior of the ballast layer. In the end, it is claimed that minimising the magnitude of total strain energy will lead to reduced degradation and a uniform distribution of total strain energy in each trackbed layer along the longitudinal direction of the track will ensure uniformity in the track geometry.

A computationally efficient coupled multi-scale model for short fiber reinforced composites

A coupled multi-scale (macro–micro) model is developed to predict non-linear elasto-plastic behavior of short fiber reinforced composites. At the microscopic level, a recently proposed micro-mechanical model, developed based on a two-step orientation averaging approach, is used. A wide range of micro-structural parameters, including matrix and fiber constitutive parameters, fiber volume fraction and fiber aspect ratio, can be accommodated in the model. Different interactions including Voigt, Reuss and a self-consistent assumption are considered in the model. This micro-mechanical model is then incorporated in a Finite Element model of the macro-scale problem, enabling coupled macro–micro simulations of real-life structures/specimens. Numerical examples and comparisons with experimental data, taken from literature, show that the model gives good predictions. Besides, several strategies and techniques are employed to improve the computational efficiency of the model. These techniques include replacing originally utilized trapezoidal integration (for fiber orientations and calculation of the Eshelby tensor) with more efficient integration schemes, and using a more efficient method for data storage. Comparisons of the computational efforts shows that these improvements substantially decreased the computational cost of the model.

Structural Stability Analysis of Eye of the Yellow Sea, a Large-Span Arched Pedestrian Bridge

To date, scholars’ research on the stability behavior of the arch structure mainly focuses on solid–web section arches, steel tubular truss arches and concrete-filled steel tubular arches, but the stability behavior of the novel spatial grid arch structure, which integrates the characteristics of grid structure and arch structure, is not yet clear. Based on the Eye of the Yellow Sea pedestrian bridge project in Rizhao, China, the stability behavior of this large-span spatial grid arch structure was studied, in this paper, by the project’s structure design team. The project is a glass covered steel arch pedestrian bridge with a span of 177 m, a height of 63.5 m, an elliptical section with a long axis of 18 m, and a short axis of 13.5 m. The elastic and the nonlinear elasto-plastic stability behavior considering different initial geometric imperfections, was analyzed by the ABAQUS finite element model. The buckling modes and the full-range load-displacement curve of the structure were analyzed, and the stress distribution, deformation mode and overall structural performance during the whole loading process were analyzed. The effects of initial imperfections, geometric nonlinearity and material nonlinearity on the ultimate load-carrying capacity of the structure were studied. The stability behavior of large-span spatial grid arch structure was studied in this paper, which provides an important reference for the design and analysis of such structures.

Post-construction safety assessment of a high concrete face rockfill dam

The most important issue regarding the safety and performance of concrete face rockfill dams (CFRDs) is to determine stresses and deformations. However, predictions of crest settlements of CFRDs are usually performed using empirical relationships. In recent years, CFRDs have been constructed much higher and at more complicated topographical and geological dam sites, so numerical analysis is required to evaluate the stress and deformations in the entire dam body. Also, assessing long-term rockfill behaviour and the concrete face membrane crack potential are important for post-construction dam safety. This study evaluates post-construction deformations and crest settlements of a high CFRD under two different loading cases, considering the non-linear elasto-plastic behaviour of the rockfill structure. As a constitutive model, the Duncan–Chang hyperbolic stress–strain model was applied in finite-element simulations considering the failure criterion is isotropic and hardening. Calibration of the rockfill's hyperbolic parameters was performed by comparing the calculated displacements with actual settlement measurements. Computed crest settlements were also compared with those of some CFRDs given in the literature. Calculated crest settlement and other deformations are in good agreement with the rockfill settlement measurements and in acceptable ranges, and do not threaten the dam's safety.

An FE-based orientation averaging model for elasto-plastic behavior of short fiber composites

A new micro-mechanical model for predicting the non-linear elasto-plastic behavior of short fiber reinforced composites is presented. The model is developed based on a two-step Orientation Averaging method, and is capable of accommodating a wide variety of micro-structural parameters. In the first step, Finite Element Analyses are performed on a unit cell (single fiber surrounded by matrix). Then, the unit cell response is up-scaled by calibrating its response to an elasto-plastic surrogate constitutive model. In a subsequent second homogenization step, a self-consistent interaction scheme is proposed. The predictive capability of the resulting two-step homogenization scheme is then evaluated, next to versions that adopt more traditional averaging schemes (Voigt and Reuss, providing upper and lower bounds, respectively), through comparisons to experiments and direct numerical simulations of realistic Representative Volume Elements. Results show that the model gives fairly good predictions. It is emphasized that the model is capable of accommodating any desired fiber orientation distribution, very large ranges of fiber aspect ratios and fiber volume fractions. Also, the model is computationally very efficient compared to the RVE computational homogenization approach, and thus, it could be conveniently used in applications possessing different fiber orientations at different points of a component.

Analysis and modeling of modified styrene–acrylonitrile/carboxylated acrylonitrile butadiene rubber nanocomposites filled with graphene and graphene oxide: Interfacial interaction and nonlinear elastoplastic behavior

AbstractNonlinear elastoplastic behavior of the nanocomposites based on the styrene–acrylonitrile/carboxylated acrylonitrile butadiene rubber (SAN/XNBR) blend was investigated using experimental and theoretical analysis. Graphene, graphene oxide nanoparticles, and glycidyl methacrylate‐grafted‐XNBR (XNBR‐g‐GMA) as a compatibilizer were incorporated in the SAN/XNBR blends. In this regard, the focus of this study is on modeling of the stress–strain behavior of these nanocomposites, considering the effect of the interfacial interactions made by compatibilizer. For this purpose, field emission scanning electron microscopy (FESEM) and transmission electron microscope (TEM) techniques were used to investigate the relationship between microstructure and mechanical properties of nanocomposites. In addition, FESEM and TEM images showed that the presence of a compatibilizer could influence the dispersion and localization of the nanoparticles. According to the tensile test results, the presence of the compatibilizer increased the mechanical properties of the nanocomposites, specifically elongation at break. Considering the nanocomposite containing compatibilizer and graphene oxide, the elongation at break increased about 570% compared with the nanocomposite without compatibilizer. Better dispersion of graphene oxide and the creation of chemical interaction among components in the presence of the XNBR‐g‐GMA compatibilizer could be the reasons for these improvements, as confirmed by TEM. The usage of the Bergstrom–Boyce model for analyzing the nonlinear elastoplastic behavior of the nanocomposites illustrated proper conformity with the experimental data in the elastic region. However, there are some deviations in the viscoplastic region, particularly close to the breaking elongation region.

Three-field mixed beam-column finite element for geometric and material nonlinear analysis

A mixed element (3fME) for geometric and material nonlinear finite element analysis of plane skeletal structures is presented, which can reach any predefined accuracy with only one element per structural member. This element is based on the 3-field approach−an application of the Hu-Washizu principle−directly approximating the fields of displacements, strains and stresses. The presented formulation considers both (i) geometrically nonlinear behavior−by including the second-order term in the strain-displacement relations and establishing equilibrium in the deformed configuration−and (ii) materially nonlinear elastoplastic behavior, at the fibre level, automatically handling the axial-bending interaction. The illustrative examples include both compression- and tension-bending interaction, and compare the accuracy of the novel finite element with published results.

An investigation into the influence of geometry on compressed earth building blocks using finite element analysis

This paper presents a parametric investigation into the influence of geometry on the compressive and flexural strength of un-stabilised compressed earth blocks (CEBs). Three CEBs with dissimilar geometric properties were manufactured and subjected to physical testing and Finite Element Analysis (FEA) using ANSYS Workbench 19.1. The compressive and flexural strength of the CEBs were shown to be dependent on their geometric properties and ranged from 3.74 to 6.73 MPa and 0.63–1.31 MPa respectively. A modified Solid65 element command was utilised within the FEA and was shown to successfully replicate the non-linear elasto-plastic behaviour observed in physical testing.

Integrated Prediction of Mechanical Behavior for the Non-Aligned Fiber Composites With Experimental Validation

Abstract This paper aims to present an integrated multi-scale method for predicting the anisotropic and nonlinear elasto-plastic behavior of short glass fiber-reinforced polymer (GFRP) materials typically produced by injection molding. The proposed method combines injection molding and microstructure together, with considering the nonaligned fibers and their corresponding anisotropy, to semi-analytically estimate the local effective mechanical properties at every point of GFRP. Micro-computed tomography measurement and injection molding simulation are used to obtain the fiber orientation tensor. The two-step mean-field homogenization method is applied to calculate the mechanical behaviors of the PA66GF30 GFRP with distributed-orientation fibers based on the fiber orientation tensor. Reverse engineering is used to obtain the optimized parameters of J2-plasticity and Tsai-Hill three-dimensional transversely isotropic stain-based failure criterion. Moreover, the integral mapping method can complete the transformation of the fiber orientation tensor from injection simulation to structure simulation model. The proposed integrated approach with the optimized parameters is verified by predicting the ring samples’ behavior from injection plates. The results from this investigation are expected to provide some design guidelines for GFRP composites.

Stochastic Analysis of Adjacent Structures Subjected to Structural Pounding under Earthquake Excitation

Seismic pounding occurs as a result of lateral vibration and insufficient separation distance between two adjacent structures during earthquake excitation. This research aims to evaluate the stochastic behavior of adjacent structures with equal heights under earthquake-induced pounding. For this purpose, many stochastic analyses through comprehensive numerical simulations are carried out. About 4.65 million time-history analyses were carried out over the considered models within OpenSees software framework. Various separation distances effects are also studied. The response of considered structures is obtained by means of Hertzdamp contact element. The models have been excited using 25 earthquake records with different peak ground accelerations. The probability of collision between neighboring structures has been evaluated. An efficient combination of analytical and simulation techniques is used for the calculation of the separation distance under the assumptions of non-linear elasto-plastic behavior for the structures. The results obtained through Monte Carlo simulations show that use of the current provision’s rule may significantly overestimate or underestimate the required separation distance, depending on the natural vibration periods of adjacent buildings. Moreover, based on the results, a formula is developed for stochastic assessment of required separation distance.

Fast simulation of stent deployment with plastic beam elements.

Coronary stent deployment is a reference cardiology intervention, used to treat atherosclerosis and prevent heart attacks. The outcomes of the intervention highly depend on the accuracy of the stent apposition, which could benefit from per-operative prediction tools. In this paper, we propose a fast and mechanically realistic 3D simulation of a coronary stent expansion. Our simulation relies on the finite element method and involves serially linked beam elements to model the slender geometry of a stent. The elements are implemented with a non-linear elasto-plastic behavior, describing realistically the complex deformation of a balloon-expandable stent. As a proof of concept, we simulated the free expansion of a coronary stent. The simulation output was compared with micro-CT data, acquired experimentally during the device expansion. Results show that the plastic beam model is able to reproduce successfully the final geometry of the stent. In addition, the use of 1D elements allows to achieve a significantly lower computational time than for equivalent literature simulations, based on 3D elements. This preliminary work highlights the compatibility of our method with clinical routine in terms of execution time. Further developments include the application of the method to more advanced simulation scenarios, with the addition of a personalized artery model.

Nonlinear elastoplastic formulation for tunneling effects on superstructures

The paper presents a formulation for evaluating the effect of tunneling on existing buildings. The formulation involves the matrix condensation method to represent the response of a linear elastic building and macroelements to represent the nonlinear elastoplastic soil behavior. The formulation includes new features that allow interaction between macroelements, both through the soil continuum and the structure, to result in the final displacements of the foundations due to tunneling. One of the advantages of the formulation is its ability to incorporate a general input of a greenfield field displacement for the interaction analysis, allowing consideration of various tunneling scenarios. The formulation is evaluated by a comparison with a continuum-based solution obtained using the finite difference method. The formulation is then used to conduct a parametric analysis of tunneling–soil–superstructure interaction, considering three different approaches: (i) the suggested elastoplastic formulation, (ii) purely elastic analysis, and (iii) simplified analysis in which the foundations are forced to displace as a greenfield. It is shown that the vertical settlements of the foundations, due to tunneling, are the greatest when the first approach is considered. This is an outcome of the combined vertical and horizontal yielding, depicted in the formulation by the coupled yield function and plastic flow potential. Yet damage, which relates to differential settlement, appears to be smaller in the elastoplastic formulation.

Nonlinear elastoplastic behavior induced by multiwalled carbon nanotubes in the compatibilized low density polyethylene/poly(methyl hydrogen siloxane)-grafted perlite nanocomposites

The effect of various concentrations of multiwalled carbon nanotubes (MWCNTs) on the elastoplastic behavior, thermal and rheological properties of compatibilized nanocomposites based on low density polyethylene containing poly(methyl hydrogen siloxane)-grafted perlite was explored through using experimental and theoretical analysis. The nanocomposites were prepared by using melt mixing procedure and characterized by various experimental measurements including scanning electron microscopy (SEM), differential scanning calorimeter (DSC), thermogravimetric analysis (TGA), Dynamic mechanical thermal analysis (DMTA), tensile test and rheological measurements. The experimental analyses revealed that the MWCNTs can raise the Young's modulus of prepared nanocomposites up to 63% depending on the nanotubes concentration and dispersion state. Thermal decomposition investigations demonstrated a higher thermal stability up to 10 °C for nanocomposites containing 2 wt% of MWCNTs. The large strain elastoplastic behavior of prepared nanocomposites was elucidated by application of Bergström-Boyce model to the resulted stress-strain curves. Generally, theoretical analyses could appropriately predict nonlinear elastoplastic behavior of nanocomposites, even though some deviations were detected at yielding and necking regions, especially at higher nanotube concentrations. The analytical stiffness analysis through using Christensen-Lo model with emphasizing the effect of interphase region could accurately predict the effect of various MWCNTs loading onto the Young's modulus.

Binary-medium-based constitutive model of frozen soils subjected to triaxial loading

To model the elastoplastic behaviors of frozen soils, a binary-medium-based constitutive model is developed and validated by a series of cryotriaxial compressive tests. In the framework of the proposed model, frozen soils are conceptualized to consist of structural blocks and weakened bands. Herein, the structural blocks are idealized as bonded elements with elastic-brittle deformational behaviors. Moreover, the weakened bands are conceptualized as frictional elements whose deformational characteristics are described by a nonlinear Duncan–Chang hyperbolic model. The bonded elements are found to gradually break up and transfer into frictional elements, which collectively contribute to the resistance capability against external loading. From the micro perspective and in the representative volume element (RVE) of the soil specimen, nonuniform strain distributions and particle slippage mechanisms are considered in the strain concentration coefficient and breakage ratio to formulate a constitutive model. Predictions are calibrated with available laboratory results, demonstrating that the proposed model can reasonably account for a breakage mechanism and can quantitatively simulate the nonlinear elastoplastic behavior of frozen soils.

Determination of in-situ engineering properties of soil using an inverse solution technique and limited field tests

The goal of this research is to develop a response surface based inverse solution technique to determine in-situ engineering properties of soil for use in mobility and traction prediction models from the force displacement data generated by a cone penetrometer device. The nonlinear elasto-plastic behavior of soil was characterized by a six-parameter constitutive model – two elastic parameters (i.e., bulk modulus, K and the Poisson’s ratio, υ), three plastic parameters (i.e., angle of internal friction φ, cohesion c, and soil hardening parameter λ), and one soil physical condition parameter (i.e. initial void ratio, e∗). Soil failure was represented by the Drucker-Prager yield criterion and associated flow rule. LS-DYNA FEM software package was used to model the soil-cone interaction problem. FEM simulations were conducted for a set of soil properties properly selected within the defined parameter space. The analysis of FEM simulations indicated that the cone penetration force-displacement curves could be represented by two piecewise smooth functions – a parabola followed by a straight line. The coefficients of these two curves were used to create fourth order response surfaces using a stepwise multiple linear regression technique. The results showed both cohesion and soil hardening parameter could be predicted using this methodology.

Isostrain elastoplastic model for prediction of static strength and fatigue life of fiber metal laminates

In this paper, the new analytical prediction models were proposed for assessment of static strength and fatigue life of Fiber Metal Laminates (FMLs). The proposed static model combines composites mechanical linear-elastic behavior with non-linear elastoplastic behavior of metals, including curing stresses in laminae. Based on determined internal stress distribution through the thickness of the laminate, the fatigue life of FML is modeled at the lamina level, based on S-N mother curves of monolithic materials. The new criterion for prediction of residual fatigue life period in FMLs was proposed. Theoretical work was experimentally validated with good convergence of results.

Finite Element Modeling and Simulations to Investigate the Relationship between the Cone Index Profile and Draft Requirements of a Compaction Profile Sensor with Depth

Abstract. Previous research conducted using a compaction profile sensor and a standard cone penetrometer over a wide range of soil types and conditions found that the unit pressure acting on the cutting edge, defined as the cone index equivalent (CIE), at a specific depth (d) was related to the cone index (CI) value at that depth, the depth of the cutting edge (d), and the interaction between CI and the depth of the cutting edge (i.e., CI × d) with a very high coefficient of multiple determination irrespective of the soil type and conditions. The objective of this study was to provide an analytical basis for the relationship between CIE and CI. A two-dimensional axisymmetric model for soil-cone interaction and a three-dimensional model for soil-tine interaction were developed using a finite element method (FEM). A non-linear elasto-plastic constitutive behavior along with the Drucker-Prager yield criterion were used to represent the soil cutting process. Simulations studies were conducted in 25 distinct soil types and conditions, and the results indicated a similar relationship between CIE and CI, as observed in the previous research. These results support the existence of a strong theoretical basis for the empirical relationship observed in the previous research. Keywords: Cone index, Compaction profile sensor, Finite element modeling, Soil penetration resistance.

Computational Study of the Effects of Processing Parameters on the Nonlinear Elastoplastic Behavior of Polymer Nanoclay Composites

Processing parameters (e.g., exfoliation extent and volume fraction) of clay particles in polymeric resins play a crucial role in the mechanical properties of polymer nanoclay composites (PNCs). This paper is aimed to investigate the effects of clay aspect ratio and volume fraction on the global mechanical properties (e.g., effective stiffness, yield strength, and ultimate tensile strength) of PNCs. During the process, computational micromechanics models are adopted to simulate the nonlinear elastoplastic behavior of the PNCs of varying clay particle volume fractions and aspect ratios subjected to uniaxial tension. A representative volume element (RVE) of the PNCs is employed for the finite-element-method (FEM) based computational simulations. The polymeric matrix is treated as an idealized elastoplastic solid with isotropic hardening behavior, and the clay particles are treated as stiff elastic platelets distributed evenly in the stack and stagger configurations in the matrix. Seven volume fractions (Vf = 0.5%, 1%, 2%, 5%, 7.5%, 10%, and 15%) and seven aspect ratios (the ratio of platelet length over thickness ρ = 1, 2, 5, 10, 20, 50 and 100) of the reinforcing clay particles are utilized. Numerical experiments show that the effective modulus of the PNCs at small strains increases with the increase of either the clay volume fraction or the platelet aspect ratio largely following those predicted by classic micromechanics models. However, at the low particle aspect ratios (e.g., ρ = 1, 2, 5 and 10), the ultimate tensile strength of the clay composite is nearly independent of the clay volume fraction up to 5% in the present study, i.e., the polymeric matrix governs the PNC strength; at the large particle aspect ratios (e.g., ρ = 20 and 50), the ultimate tensile strength is significantly enhanced with growing clay volume fraction higher than 5% and reaches ~150% of that of the polymeric matrix at ρ = 50 and Vf = 10%. A comparative study is conducted for stack and stagger models for the prediction of the mechanical properties of PNCs. It shows that the stack model predicts slightly larger values of the effective stiffness and tensile strength than the stagger model. The numerical study shows that a large platelet aspect ratio through full exfoliation of the clay particles in matrix is crucial to achieving the preferable mechanical properties of PNCs as evidenced in experiments. The present results can be utilized to quantitatively explain the mechanical properties of clay particle-reinforced composites and PNCs within the framework of classic micromechanics, and provide guidelines for computer-aided nanocomposites design for processing property-tailorable PNCs.

Modeling and analysis of nonlinear elastoplastic behavior of compatibilized polyolefin/polyester/clay nanocomposites with emphasis on interfacial interaction exploration

Analysis of mechanical properties of compatibilized polymer pairs comprising clay nanoplatelets was the subject of numerous works, however nonlinear elastoplastic behavior of such nanocomposites has rarely been addressed in the literature. Though localization of nanofiller within one or at the interface of two phases was occasionally dealt with, there often were serious complexities with the lack of knowledge about the interface region. This work focuses on modeling of stress-strain behavior of the compatibilized polyolefin/polyester/clay nanocomposites to give some more lights on the interfacial interaction in such complex system, and clay localization analysis. The use of two kinds of organomodified clays as well as two compatibilizers having different chemical affinity to polymers, and using different amount of compatibilizers led to localization of clay either in the polyester or at the polyolefin/polyester interface region, as confirmed by X-ray diffraction, transmission electron microscopy and uniaxial tensile strength measurements. The mechanical properties analyses revealed a rise in both Young's modulus and tensile strength of composites with clay loading. Application of Bergström-Boyce model brought about a deeper understanding of the effect of compatibilizer and organoclay on large deformation mechanical behavior of polyolefin/polyester/clay nanocomposites. Overall, theoretical analyses could appropriately predict nonlinear elastoplastic behavior of nanocomposites, even though some deviations were detected at yielding and necking regions.

Two-phase model for nonlinear elasto-plastic behavior of reinforced soil structures using Pastor-Zienkiewicz-Chan model for matrix phase

The present study proposes a two-phase model to predict nonlinear elasto-plastic behavior, including deformation patterns and large displacements of geosynthetic-reinforced soil structures under monotonic loading. The two-phase model considers reinforced soil as the superposition of two mutually-interacting continuous phases; the matrix (soil) and the reinforcement (inclusion). The Pastor-Zienkiewicz-Chan model is implemented in a two-phase model as the constitutive law for the matrix phase by which the hardening–softening behavior of the two-phase medium can be considered. The model is applicable for granular soils under drained conditions. Inclusions are treated as linearly-elastic perfectly-plastic material. The perfect bonding hypothesis is assumed between the matrix and reinforcement phases. The approach was validated by comparison of the results with those of plane strain element testing and layered simulation models. Two centrifuge tests on geosynthetic-reinforced soil slopes were then simulated. The settlement, deformation pattern and potential failure surface of the slopes are also investigated. The results indicate satisfactory performance of the model for investigation of the nonlinear behavior of reinforced soil slopes.