Effects Of Material Nonlinearity Research Articles

Capacity of axially loaded RC columns with arbitrary cross sections to Eurocode 2

Unlike older design codes, Eurocode 2 does not provide a procedure for calculation of the capacity of axially loaded columns. For that purpose, a general algorithm is developed, using the principles of structural mechanics and mathematics: It starts with constructing the P-Δ relationship (buckling curve) for the element, accounting for initial imperfections, minimum eccentricity, material nonlinearity and second order effects. Then, the respective bending moments are determined from the displacements and the P-M relationship is obtained. Finally, the axial load capacity in planar domain is determined by intersecting the P-M diagram with the interaction curve for the RC section. In spacial domain, the P-Δ relationship is defined by the respective “buckling surface”. Its intersection with the interaction surface represents a spacial curve in the (P, Mx, My) coordinate system. The axial capacity is determined as the minimum of P values along the curve. The solution is performed by numerical methods.

A finite element study on the effects of thickness and material nonlinearity on the equilibrium path of axially loaded circular cylindrical shells

Research has been carried out in recent years dealing with Lighter than Air Structures (LTAS), in which the innermost volume is taken to be a vacuum. Variations of a thin membrane over a frame were considered in order for such structures to have buoyancy potential while being capable of sustaining atmospheric pressures. The need for extremely thin membranes became evident as a result of the weight constraint The potential for the development of a viscoplastic stress field and instability led to the study of a classical problem: the instability of circular cylindrical shells under compressive loading. Thus, in order to obtain information related to the nonlinear geometric and material effects that can eventually be used in the LTAS, this study focused on what increasingly smaller membrane thicknesses and changes in the modulus can have on the equilibrium path of circular cylindrical shells. Considering shell thicknesses from 1E−3 to 1E−6m and using the Johnson-Cook constitutive relationship, results show that (1) the equilibrium path is highly dependent on shell thickness, and (2) inelastic strains drive path deviations and distinct post-collapse shapes. Furthermore, a reduction in the yield stress can result in plasticity before collapse, effectively changing the path of equilibrium and the post-collapse shape. Solutions were found using SIMULIA® Abaqus finite element (FE) software. At the present time these membrane thicknesses and material properties are not available. It is felt that, with the advancement of material science, they will become available in the immediate future.

Numerical modeling and nonlinear analysis of semi-rigid jointed steel frames

This paper investigates the effect of semi-rigid connection, geometric nonlinearity and material nonlinearity in steel frame analysis. To study the independent and combined effects of different nonlinearities, elastic and inelastic analyses are carried out using general purpose finite element software SAP2000. Connections are modeled as rotational springs and frame as one dimensional beam element. Verification and application of the simplified numerical model developed in the present study is demonstrated by considering different examples and comparing the results of present study with those available in the published literature. Numerical alternatives, key features about modeling and necessary input parameters are discussed in detail. Rotational springs are characterized by linear, bilinear, multi-linear or nonlinear moment-rotation relationships of the connection. Results in terms of beam moment and nodal displacement are presented for both elastic and inelastic analyses. With the increase in connection flexibility, beam mid-span moments and displacements increase, but beam-end moments decrease. It is observed that the influence of connection nonlinearity dominates over material and geometric nonlinearities.

The performance of vertically perforated clay block masonry in fire tests predicted by a finite-element model including an energy-based criterion to identify spalling

Fire tests on masonry are one of the most expensive experiments in developing new vertically perforated clay block geometries. Numerical simulations might be a reasonable substitute for such experiments, leading to a significant cost reduction in the development phase. However, the prediction of such tests with numerical modeling concepts is challenging due to large temperature and stress gradients, highly non-linear material effects, and the complex geometry of the blocks. Herein, we present a finite-element-based concept, including thermal and mechanical simulations, a unit-cell approach, a smeared damage model, and a novel energy-based spalling criterion to describe the structural and material behavior of a masonry wall in a fire experiment. We could predict the obtained spalling times of longitudinal webs and the total endurance of a masonry wall without any empirical fitting parameters in good agreement with experimental data. These results show that we can use our modeling approach for simulating such fire tests, enabling a much cheaper and more efficient development of block geometries.

Ultimate bearing capacity of UHPC-encased CFST medium-long columns under axial compression

To study the effect of slenderness ratio on the ultimate bearing capacity of UHPC (ultra-high performance concrete)-encased concrete-filled steel tubular (UC-CFST) columns, a total of nine specimens under axial compression were tested. A finite element model, considering the effects of material nonlinearity and interaction between concrete and steel tube, was developed. A full-range analysis was carried out on the typical load–deformation response of the UC-CFST medium-long columns. The experimental and numerical analysis results showed that with the increase in slenderness ratio, the deformation capacity of the UC-CFST columns increased, the ultimate bearing capacity decreased, and the failure mode changed from exceedance of compressive strength to loss of stability. The internal forces and stress distributions at the mid-height section of the columns at different stages were also investigated. Finally, the applicability of various methods for calculating the ultimate bearing capacity of ordinary concrete-encased CFST (OC-CFST) columns to UC-CFST columns was discussed, including the methods recommended by Chinese standard T/CECS 188-2019, European standard Eurocode 4, Australian/New Zealand joint standard AS/NZS 5100.6 : 2017 and American standard ANSI/AISC 360-16. It was found that the method recommended in AS/NZS 5100.6 : 2017 was suitable for calculating the ultimate bearing capacity of UC-CFST medium-long columns.

Stress–strain model and design strength of cold-formed steel non-slender elliptical tubular stub columns

This paper aims to propose a stress–strain model for the stub column behavior of cold-formed steel non-slender elliptical hollow sections (EHS) under axial compression by considering the post-local buckling behavior and taking into account the effects of local imperfection, material nonlinearity and residual stresses. The proposed model is applicable to the sections of both high strength and normal grade steels; and is mainly defined by four key parameters, including the 0.2% proof stress, the local buckling stress and buckling strain, as well as the post-peak residual strength of a stub column. Equations are also proposed to express these key parameters in terms of the basic input cross-section parameters and virgin material properties. In order to determine these key parameters, existing test and numerical results on the structural behavior of cold-formed steel EHS stub columns were collected and analyzed, which covered a wide range of steel grades (up to 960 MPa) and section sizes. Existing design methods, which have not yet been calibrated for cold-formed high strength steel EHS, were first evaluated by comparing their predicted stub column strengths (i.e., local buckling stresses) with the collected test and numerical data. The Continuous Strength Method (CSM) was found to provide better predictions than other examined design methods. Modified CSM base curves were then developed to further improve the accuracy of the existing CSM for both the local buckling strains and design strengths of cold-formed EHS with steel grades up to 960 MPa. In addition, a theoretical framework is proposed to develop the semi-empirical equations for both the 0.2% proof stresses and local buckling stresses of stub columns by incorporating the modified CSM base curves, whereas one curve based on the conventional equivalent diameter and one curve based on equivalent diameter of the four-arc approximation. A predictive expression of the post-peak residual strengths is also presented. Predictions from the proposed stress–strain model were in a good agreement with the collected test and numerical results, which can demonstrate its accuracy and validity.

Power characteristics of vibration-based piezoelectric energy harvesters: the effect of piezoelectric material nonlinearity

Piezoelectric energy harvesting has received tremendous interests in the past two decades as a viable solution to self-powered electronics and devices. Recently, significant emphasis has been given to nonlinear energy harvesters driven by the desire for broadband, high-performance energy harvesting. Numerous efforts have been devoted to the understanding and modeling of the electromechanical coupling and the effect of nonlinearities introduced by mechanical and electrical aspects of the system. However, very few works in the literature considered the effect of piezoelectric material nonlinearity on the system power performance. Nevertheless, it has been found that piezoelectric nonlinearity is significant even at low to moderate excitation level. This paper is motivated to study the power behavior of piezoelectric energy harvesters with piezoelectric nonlinearity, most importantly, the power limit and electromechanical coupling. For this purpose, an approximate model is developed from the nonlinear model in the literature to derive the closed-form expressions of important power characteristics. Analytical analysis shows that the effect of piezoelectric material nonlinearity results in a nonlinear damping term and a nonlinear stiffness term in the approximate model. The approximate solutions of optimal load resistance, maximum power, power limit, and critical electromechanical coupling are obtained and validated by numerical simulations first. The induced nonlinear damping reduces the power limit of the system compared to its linear counterpart. Interestingly, a harvester that exhibits strong electromechanical coupling under small excitation could become weakly coupled under large excitation. The analytical analysis and numerical results are validated by experiments.

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.

Stability of geometrically imperfect struts with Ramberg–Osgood constitutive law

Both the initial geometrical imperfections and material nonlinearity have great influence on the stability of the struts. In this paper, an analytical approximate solution of the post-buckling behavior of the geometrically imperfect struts with pinned–pinned ends under axial compression is obtained. The struts are made of aluminum alloys, and its constitutive relation conforms to the Ramberg–Osgood law. The Ramberg–Osgood type constitutive relation is extended by Taylor series to facilitate its application. A theory based on Euler–Bernoulli hypothesis is applied to establish the nonlinear equilibrium equations of the aluminum alloy struts. The analytical approximate solutions of the nonlinear equilibrium equations are derived by the harmonic balance method for the first time. Moreover, numerical solutions are obtained by finite element analysis for comparison. By comparing with the numerical solution, the accuracy of the analytical approximate solution proposed in this paper is verified in the case of small strain. The effects of material nonlinearity and initial geometrical imperfections on the post-buckling equilibrium path of the aluminum alloy struts are analyzed by the proposed analytical approximate solution.

A dual-scale elasto-viscoplastic constitutive model of metallic materials to describe thermo-mechanically coupled monotonic and cyclic deformations

Thermo-mechanical coupling effect often occurs during the deformation of the metallic materials, especially when they are subjected to cyclic loadings at a high loading rate. On one hand, the internal heat generation and accumulation originated from the energy dissipation during plastic deformation lead to the change of temperature field in the material. On the other hand, the variation of temperature field further changes the dissipation property of the material, since the stress-strain response depends on the temperature. These two factors influence with each other and result in a complex thermo-mechanical coupling effect. In this work, a dual-scale thermo-mechanically coupled elasto-viscoplastic constitutive model is developed to predict the monotonic, cyclic deformation and temperature field evolution of metallic materials under monotonic and cyclic loadings. At the mesoscopic scale, the polycrystalline representative volume element (RVE) is considered as an aggregation of individual grains. For an individual grain, a crystal plasticity model accounting for the internal heat generation is developed based on the fundamental laws of irreversible thermodynamics. A nonlinear kinematic hardening rule extended from the Ohno-Abdel-Karim model is adopted to capture the evolution of resolved shear back stress for each slip system, and the classical Bassani-Wu latent hardening rule is utilized to describe the interaction of dislocation slipping. To calculate the thermo-mechanical interactions among the grains, and obtain the overall responses of the polycrystalline RVE, a self-consistent (SC) homogenization scheme accounting for material nonlinearity and thermo-mechanical coupling effect is developed. At the macroscopic scale, the thermo-mechanical responses for the specimen are obtained by solving the equations of force balance, deformation compatibility, thermodynamic equilibrium and constitutive relationship through an approximation method. Finally, the proposed model is validated by predicting the monotonic, cyclic stress-strain responses and temperature evolution of 316L stainless steel.

Accurate Modeling of Material Nonlinearities in a Wind Turbine Spar Cap

This study presents component-level testing of carbon fiber sandwich beams and the effect of carbon fiber material nonlinearity in its strain response in bending. A simple material model is presented and validated that accurately captures the carbon fiber longitudinal nonlinearity in both the tensile and compressive response. This material model is implemented in a finite element model of the BAR-DRC reference wind blade, a downwind 100-meter rotor blade, and the effects of the nonlinearity on ultimate limit states of the blade are analyzed. The material nonlinearity has negligible effect on the deflection, and material failure predictions. The buckling analysis revealed significant reductions in buckling load factor in the controlling flap direction caused by the material nonlinearity, revealing the importance of including this material model for buckling analyses of wind blade with carbon fiber reinforced spar caps.

Dynamic Response of Some Noncarbon Nanomaterials Using Multiscale Modeling Involving Material and Geometric Nonlinearities

Abstract Nonlinear dynamic response of some noncarbon nanomaterials, involving material and geometric nonlinearities under different types of dynamic loads, is investigated using computationally efficient multiscale modeling. Multiscale-based finite element model is developed in the framework of the Cauchy–Born rule, which couples the deformation at the atomic scale to deformation at the continuum scale. The Tersoff–Brenner type interatomic potential is employed to model the atomic interactions. The governing finite elemental equations are derived through Hamilton's principle for a dynamic system. The linearization of nonlinear discrete equations is done using Newton–Raphson method and are solved using Newmark's time integration technique. The effects of material and geometric nonlinearities, inherent damping, different types of dynamic loads, and initial strain on the transient response of noncarbon nanosheets with clamped boundary conditions are reported in detail. The present results obtained from the multiscale-based finite element method are compared with those obtained from molecular dynamics (MD) simulation for the free vibration analysis, and the results are found to be in good agreement. The present results are also compared with the results of those obtained from Kirchhoff plate model for some cases.

Fractional-order Bouc-wen hysteresis model for pneumatically actuated continuum manipulator

Continuum manipulators with pneumatic actuators are designed for large-scale movements with high dexterity. However, during applications, such manipulators suffer control inaccuracies due to material nonlinearities. Thus, this paper proposes a generalized forward kinematic and forward dynamic model based on Cosserat-rod theory for a pneumatically actuated multi-segment conic manipulator. The model includes the effect of material nonlinearities and reduces the steady-state absolute error. Moreover, the model also considers the self-weight and external loadings to determine the manipulator backbone shape. Explicit fractional-order Bouc-Wen model is used in the constitutive laws to model the effect of material hysteresis in the developed partial differential equations for the manipulator. The developed mathematical model is solved numerically for possible backbone shapes. The results of the model are validated experimentally on the trunk of the Robotino-XT, which is a two-segment pneumatically actuated conic manipulator. The validation results show that the absolute pose error between the experimental and the proposed model for the manipulator tip at steady-state is very small, which is a far superior result to the other existing models for the same system.

Finite element computational development for thermo-mechanical analysis of plane steel structures exposed to fire

This article presents a numerical formulation based on finite element procedures for application in nonlinear thermo-mechanical analyses of steel planar structures under fire condition. The mechanical properties of structural elements degrade when subjected to high temperatures, resulting in significant reductions in strength and stiffness. Under these conditions, the structures present complex behaviors associated with nonlinear models, requiring an advanced mathematical analysis. As such, a computer program called NASEN has been developed to investigate the behavior of steel structures subjected to fire, considering the effects of geometric and material nonlinearity, as well as the thermal gradients acting on the cross-section. The solution strategy is based on sequential coupling of numerical processes. Initially, the two-dimensional thermal field is determined, followed by an assessment of structural behavior. In each solution step, corrective processes are implemented to ensure convergence of the temperature and displacement nodal vectors. Numerical experiments are performed in order to evaluate the accuracy and capacity of the computer program. Results are compared with experimental tests and computer simulations found in pertinent literature. The program shows good agreement with reference solutions, indicating its accuracy and applicability for the cases studied.

Experimental Study on Stability of Long‐Span PC Cable‐Stayed Bridge during the Construction Periods

With the increasing span of cable‐stayed bridges, the towers are getting higher and higher, and the stiffening beams are becoming more and more slender. The increase in span causes the axial pressure of the beams and towers to increase rapidly, and the sag effect of the cables, geometric nonlinearity, and material nonlinear effects are significantly increased. The influence of these disadvantages greatly reduces the stability of the cable‐stayed bridge, and the stability of the cable‐stayed bridge becomes prominent. In this paper, the finite element method is used to analyze the first kind of stability problem and the second kind of stability problem of cable‐stayed bridges. On this basis, a large‐span prestressed concrete (PC) cable‐stayed bridge is taken as an example to analyze and compare the two types of stability problems of the bridge during the construction phase and the operation phase. Besides, the model experimental study on the stability of the bridge during the maximum double cantilever construction period was carried out. The theoretical values and the model test results are compared to verify the correctness of the calculation method and design theory, which may provide a reference for the design, construction, and scientific research of cable‐stayed bridges.

Nonlinear Numerical Simulation of Finite Elements Based on Fiber Beam Elements With Shear Effects for Structures

The classical fiber beam model based on the Euler-Bernoulli beam theory ignores the influence of shear deformation on the section. To get a more accurate beam element model, based on the fiber beam element with shear effects and the Timoshenko beam theory, the stiffness matrix of the fiber beam element was deduced, and the dual effects of geometric nonlinearity and material nonlinearity were considered at the same time, combined with the elastoplastic incremental theory. Then, the nonlinear finite element analysis theory for the structure under the complex stress state of compression, bending and shear was established. Finally, a program was coded on MATLAB to conduct finite element numerical simulation of the typical compression-bending-shear members of reinforced concrete and rectangular concrete-filled steel tube, and the nonlinear full-process load-displacement curves were obtained. The analysis of the numerical examples show that, the established nonlinear finite element analysis theory is universal, feasible and correct.

Cable structures: An exact geometric analysis using catenary curve and considering the material nonlinearity and temperature effect

Structures formed by cables constitute structural systems of great practical application in engineering, such as suspension bridges, cable-stayed bridges, cable cars, transmission lines in which case they are used as supporting elements that conduct electricity, overcoming the spans between the towers or in stays for the so-called cable-stayed towers, among other applications. Cable structures have a highly non-linear behavior both from a geometric point of view, arising from their initial equilibrium configuration, and from a material point of view, since the constitutive laws of the cables present an elastoplastic behavior. The objective of this work is to present a geometrically exact formulation for static analysis of cable structures considering the catenary configuration. For this, both geometric and material nonlinearities are included in the development of the the catenary cable element formulation. The effect of temperature variation is also considered. A rigorous updated Lagrangian description combined with the corotational approach is employed to obtain the consistent tangent stiffness matrix of the exact cable element. The proposed methodology was implemented in the software program called Advanced Structural Analysis System (ASTRAS), which is an academic software based on the Finite Element Method (FEM). Finally, numerical examples are analyzed using the present procedure and the obtained results are compared with those found in the literature and given by commercial softwares in order to demonstrate the consistency and precision of the formulation.

Nonlinear buckling analysis of a semi-elliptical dome: Numerical and experimental investigations

In this paper, non-linear buckling performance of a semi-elliptical steel dome under uniform external pressure is investigated numerically and experimentally. Numerical buckling analysis is performed on an ellipsoidal dome with various nonlinearities including geometric (GN) and material non-linearity (MN) to obtain the critical pressure. The option “Arc length method” available in ANSYS is implemented to solve the non-linear differential equations. Further, an experimental testing is performed on the prototype ellipsoidal dome subjected to external hydrostatic pressure to obtain the critical pressure. The effectiveness of the developed numerical modelling is demonstrated by comparing the critical buckling load evaluated using the present non-linear analysis with those available in literature and experimental analysis. Imperfections such as Force Induced Dimple (FID) and eigen affine imperfections are considered in the ellipsoidal dome to investigate their effects on collapse load. Non-linear (NL) buckling analysis of stringer reinforced semi-elliptical dome is performed to investigate the effect of stringers on critical buckling pressure. Various parametric studies are also performed to study the effect of the nature of imperfection, location of imperfection, aspect ratio on critical buckling pressure of the dome. It was observed that an increase in the amplitude of eigen affine imperfection significantly reduces the critical buckling pressure. FID at an apex of the dome causes a reduction in buckling pressure whereas FID located at the middle and bottom of dome do not affect the critical load significantly. It was also demonstrated that stringer reinforcement on semi-elliptical dome without modifying the mass of overall structure significantly increases the critical buckling pressure. The effect of geometric nonlinearity and material nonlinearity on the critical buckling pressure of the semi-elliptical dome is observed to be more significant in stringer reinforced domes.

Analysis method of isolation layer composed of high damping rubber bearings based on deformation history integral type model

As the high damping rubber bearings (HDRBs) presents stronger nonlinear material effects, the deformation history integral type model (DHI model) validated to well simulate the mechanical behaviors was adopted instead of traditional bilinear model. While considering the computational cost of the nonlinear time history (NLTH) analyses, simplified analysis methods represented by the equivalent linearization (EL) method has been widely applied to estimate the structural response, especially in the cases where isolated structures can be simplified to single-degree-of-freedom systems. The EL parameter calculation formulas based on the DHI model was derived to realize the equivalent linearization analysis of isolation layer composed of HDRBs, and the formulas were applied to an iterative process for calculating the maximum deformation of the isolation layer. A six-story isolated building was taken as an example to verify the accuracy of the proposed method. It was shown that the estimated results of the iterative approach have limited difference with the structure responses obtained from NLTH analyses. Therefore, the established model can be further applied for the assessment of the seismic demands of structures isolated by HDRBs.

Size effect in single layer graphene sheets and transition from molecular mechanics to continuum theory

The size-dependent mechanical response of graphene is investigated with an entirely nonlinear molecular mechanics approach. Finite element (FE) simulations under uniaxial and equibiaxial tensile loads are carried out on graphene sheets with increasing size. It is found that the response of graphene remains unchanged after a threshold size. Furthermore, anisotropy is observed for large deformations and a negative Poisson’s ratio is found after a critical strain for the zigzag uniaxial load case. The threshold size defines the transition to the continuum theory, which is developed as a membrane model in the fully nonlinear context of finite elasticity. The constitutive parameters of the model are calibrated by fitting the results of the FE simulations. The proposed model represents the basis for accurate predictions of the response of graphene subjected to large in-plane deformations. Nonlinear laws for the size-dependent elastic properties of graphene are derived. These laws can be used in linear elasticity-based models to take into account for material nonlinearity, anisotropy and size effect. Finally, a sensitivity analysis of the molecular mechanics model to the parameters of the interatomic potentials is carried out. The discussion of the results gives insights into the influence of each parameter and useful remarks for the molecular mechanics modeling of graphene.