Inelastic Behavior Research Articles

Structural performance of split orthogonal beam joints in continuous beam‐type circular concrete‐filled steel tubular beam‐to‐column connections

AbstractA continuous beam‐type connection has been proposed as a new type of concrete‐filled steel tubular beam‐to‐column connection without a diaphragm exhibits good seismic performance. However, in a 2‐way configuration, the performance of the connection in a direction orthogonal to the continuous beam may be suboptimal due to beam splitting. In this study, a new detail of a split orthogonal beam joint was proposed and 4 specimens were constructed and tested under quasi‐static conditions. All the specimens attained the full‐plastic flexural strength for the beams and exhibited a stable inelastic behavior. The specimen in which the depth of the orthogonal continuous beam was 100 mm greater than that of the split beam exhibited good inelastic cyclic behavior, whereas two other specimens with a split beam exhibited slipping and pinching. Minor fractures were observed in the tube wall; however, the strength and stiffness did not deteriorate significantly, though a slight pinched hysteresis was observed. In addition, a finite element analysis was conducted. The split beam was largely rotationally constrained by the bearing pressure of the concrete above and/or below the beam flange. If the split beam's flange was sufficiently inserted into the connection panel, the stiffness and strength were ensured.

Evaluation of Link Overstrength Factor for the Seismic Design of Eccentrically Braced Frames

In eccentrically braced frames (EBFs), inelastic behavior is only permitted in the links. All members, except for the links, are designed according to the capacity design concept by using the link overstrength factor, Ω, so that they remain elastic even when the links develop their ultimate strength (including the strain-hardening effect). AISC 341 specifies that the Ω factor of link members must be 1.25 for beam and brace design and 1.1 for column design. In this study, the relevance of the current Ω factor was investigated. A total of 471 K-braced EBF systems with various conditions were designed using a multi-objective optimization technique, and nonlinear dynamic analyses were performed to evaluate the Ω factor. The results indicate that it is reasonable to use the current Ω factor for the design of beam outside link and brace; however, it leads to an overestimation of axial force in columns, especially in the lower stories of tall buildings. From the analysis results, a new Ω factor equation for column design was proposed. It was demonstrated that the structural quantities of 15-story frames designed using the proposed equation decreased by an average of 19% compared to those designed using the current Ω factor.

Constant-ductility inelastic displacement ratio spectra for design of superstructures in seismically isolated buildings

Constant-ductility inelastic displacement ratio (Cμ) spectra can be utilized for the estimation of peak inelastic structural displacements in the seismic design procedure. Currently, suitable analytical estimates of Cμ are lacking for base-isolated buildings with inelastic behavior of superstructures in a beyond design basis earthquake. This paper attempts to fill this research gap and hence conducts parametric studies on the Cμ spectra of base-isolated inelastic superstructures with lead-rubber bearings (LRBs). For that purpose, the inelastic model and equations of motion, boundary conditions of the analytical formulation of Cμ, and controlling parameters for the two-degree-of-freedom (2DF) superstructure-isolator system with LRBs are presented first. Subsequently, by analyzing the parameterized 2DF systems using an ensemble of strong earthquake records representative of a site with stiff soil conditions, the influence of controlling parameters, namely, displacement ductility ratios, superstructure periods, post-yielding stiffness ratios of superstructures, mass ratios, isolation periods and normalized isolator strength, on the mean and dispersion of Cμ are discussed, and the boundary conditions of Cμ are validated based on the calculated data. Comparisons of how the controlling parameters influence the Cμ and earlier investigated CR (i.e. constant-strength inelastic displacement ratio) spectra are also presented. Lastly, a predicting equation with reasonable accuracy is proposed for the mean Cμ using the nonlinear multivariable regression analysis method. The outcome of this study allows the application of displacement-based design via inelastic displacement ratio for new base-isolated structures under beyond design basis earthquakes.

Seismic behaviour and design of a tall mixed reinforced concrete–steel structure supporting an oil refinery reactor

AbstractThis study investigates the seismic behaviour of a special mixed reinforced concrete-steel structure that supports an oil refinery reactor. The structure is 64.90 m tall and consists of three parts: (a) a reinforced concrete frame basement; (b) a steel braced frame that supports the oil reactor and (c) the steel reactor itself. A three-dimensional model of the structure is created to perform static non-linear (pushover) analyses in order to obtain the capacity curves and understand the overall inelastic behavior of the structure. The results of the pushover analyses reveal that the structure exhibits similar inelastic behavior in both horizontal directions and satisfies the capacity design principles. The structure exhibits limited ductility considering the fact that has been designed with a behavior factor of q = 1.5 and primary damages are expected mainly in concrete members. Subsequently, dynamic non-linear time-history (NLTH) analyses are performed utilizing the three translational components of three seismic motions recorded during past earthquakes. These results involve: (i) the maximum values for displacements, accelerations and base shears; (ii) the maximum stresses at critical points of the oil refining reactor and (iii) the formation of plastic hinges at columns, beams and braces of the structure. Contrary to pushover analyses, NLTH analyses revealed the development of plastic hinges, hence seismic damage, that do not follow the desirable formation pattern. Moreover, the accelerations and displacements observed are expected to cause failure of the piping and mechanical equipment, while local failure of the high-stress areas of the shell of the reactor may be possible. Localized strengthening might be necessary to avoid repair works and downtime after such seismic event.

Predicting the non-linear behaviour of cross laminated timber shearwalls with cut-out openings

The behaviour and failure mode expected in Cross Laminated Timber (CLT) shearwalls when either window or door openings are incorporated into the shearwalls may be considerably different than that of shearwalls without openings. Despite clear theoretical and experimental evidence of the possible occurrence of significant increase in the deformation contribution of the CLT panels and induce high stress concentrations around openings, limited studies have been conducted on the effect of crack propagation in CLT shearwalls with cut openings. The current study presents two modelling techniques to account for the crack propagation around openings, through concentrated plastic hinge (PHM) and continuous post-elastic (CPEM) models. The proposed models are validated using available experimental results obtained from six full-scale shearwalls in the literature while input parameters, such as the mechanical properties of the CLT panels, are obtained, in part, from component-level experimental investigation on CLT beams conducted by the authors as part of the current study. The impact and advantages of accurately predicting the non-linear behaviour of the CLT panels are investigated through a numerical analysis on a case-study representing a multi-storey shearwall with multiple openings. The results showed the inability of elastic models to predict the inelastic behaviour in the CLT shearwall after the crack opening, and this the study recommends the inclusion of stress redistribution near crack openings and subsequent inelastic behaviour in the analysis.

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

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

Hyperinelasticity. Part II: A stretch-based formulation

A generalisation of the hyperinelasticity modelling framework devised in Part I of this sequel is formulated here, by presenting a (principal) stretches-based hyperinelastic deformation energy function WF. This generalisation is based on the premise that the (principal) stretches λj may assume any arbitrary real-valued exponents, rather than being restricted to the prescriptive powers 2 and −2, as in principal invariants-based models. The motivation behind this extension is to reduce the overall number of model parameters and thereby increase the versatility of the application of the hyperinelasticity framework, as well as to provide a more universal model. The ensuing hyperinelastic model is then applied to a wide range of extant experimental datasets encompassing foams, glassy and semi-crystalline polymers, hydrogels and liquid crystal elastomers, over both elastic and inelastic deformation ranges including yield, softening and plateau, and hardening behaviours, under tensile and compressive deformations. Upon demonstrating the favourable simulation of the foregoing behaviours by the model, its application is then extended to account for other nuanced aspects of inelasticity such as the effects of rate of deformation, crystallinity volume and angle of printing in 3D printed lattice structures. This augmentation is done via devising a generalised modelling framework which allows for the incorporation of a generic tensorial (including rank zero scalar) field of inelasticity-inducing factors into the core model, resulting in the model parameters to evolve with an appropriate measure of the factor of interest; e.g., deformation rate, crystallinity volume ratio etc. The proposed modelling framework will be shown to capture these effects proficiently. Given the simplicity of this modelling approach, as essentially an extension in the application of hyperelasticity, its versatility of implementation, and the favourable capturing of both elastic and inelastic behaviours, the devised hyperinelasticity framework is presented for application to the large elastic and inelastic deformation of polymers and elastomers.

Uniaxial material model with softening for simulating the cyclic behavior of steel tubes in concrete‐filled steel tube beam‐columns

AbstractThis paper presents a new uniaxial constitutive material formulation with softening for simulating the inelastic behavior of steel rectangular tubes in concrete‐filled steel tube (CFST) members. The primary behavioral characteristics of the steel tube in CFST members are isolated and pronounced through a carefully designed experimental campaign with CFST specimens subjected to uniaxial strain‐based loading protocols. The model is expressed in an effective stress–strain domain, where the effective uniaxial strain is defined as the uniaxial displacement within a dissipative zone over a predefined length. In the pre‐peak state, the proposed model can effectively capture the combined kinematic/isotropic hardening and Bauschinger effect—characteristic of mild structural steels—within the framework of rate‐independent plasticity. In the post‐peak state, the proposed model traces strength deterioration due to outward local buckling, which is a characteristic nonlinear geometric instability in CFST members due to the presence of the filled concrete in the steel tube. The proposed constitutive formulation incorporates a softening branch that exponentially decays to trace the stabilization of the outward buckling wave within the buckling region in successive inelastic loading cycles. Cyclic deterioration of the effective stress is explicitly considered via an energy‐based rule. The proposed model is calibrated to a CFST dataset. Regression equations are proposed for predicting the input model parameters. These equations cover a wide range of geometric parameters and structural steel materials in CFST members. Comparisons with prior tests on actual CFST beam‐columns under planar symmetric cyclic loading suggest that conventional 2‐dimensional displacement‐based beam‐column elements can predict the full‐range of the hysteretic behavior of the CFST members with the proposed constitutive formulation including cases where the post‐peak response of CFST members exhibits negative stiffness.

Compaction and Permeability Evolution of Tuffs From Krafla Volcano (Iceland)

AbstractPressure and stress perturbations associated with volcanic activity and geothermal production can modify the porosity and permeability of volcanic rock, influencing hydrothermal convection, the distribution of pore fluids and pressures, and the ease of magma outgassing. However, porosity and permeability data for volcanic rock as a function of pressure and stress are rare. We focus here on three porous tuffs from Krafla volcano (Iceland). Triaxial deformation experiments showed that, despite their very similar porosities, the mechanical behavior of the three tuffs differs. Tuffs with a greater abundance of phyllosilicates and zeolites require lower stresses for inelastic behavior. Under hydrostatic conditions, porosity and permeability decrease as a function of increasing effective pressure, with larger decreases measured at pressures above that required for cataclastic pore collapse. During differential loading in the ductile regime, permeability evolution depends on initial microstructure, particularly the initial void space tortuosity. Cataclastic pore collapse can disrupt the low‐tortuosity porosity structure of high‐permeability tuffs, reducing permeability, but does not particularly influence the already tortuous porosity structure of low‐permeability tuffs, for which permeability can even increase. Increases in permeability during compaction, not observed for other porous rocks, are interpreted as a result of a decrease in void space tortuosity as microcracks surrounding collapsed pores connect adjacent pores. Our data underscore the importance of initial microstructure on permeability evolution in volcanic rock. Our data can be used to better understand and model fluid flow at geothermal reservoirs and volcanoes, important to optimize geothermal exploitation and understand and mitigate volcanic hazards.

Data-driven continuum damage mechanics with built-in physics

Soft materials such as rubbers and soft tissues often undergo large deformations and experience damage degradation that impairs their function. This energy dissipation mechanism can be described in a thermodynamically consistent framework known as continuum damage mechanics. Recently, data-driven methods have been developed to capture complex material behaviors with unmatched accuracy due to the high flexibility of deep learning architectures. Initial efforts focused on hyperelastic materials, and recent advances now offer the ability to satisfy physics constraints such as polyconvexity of the strain energy density function by default. However, modeling inelastic behavior with deep learning architectures and built-in physics has remained challenging. Here we show that neural ordinary differential equations (NODEs), which we used previously to model arbitrary hyperelastic materials with automatic polyconvexity, can be extended to model energy dissipation in a thermodynamically consistent way by introducing an inelastic potential: a monotonic yield function. We demonstrate the inherent flexibility of our network architecture in terms of different damage models proposed in the literature. Our results suggest that our NODEs re-discover the true damage function from synthetic stress-deformation history data. In addition, they can accurately characterize experimental skin and subcutaneous tissue data.

Effect of Infilled Frames on Reduction Factor (R) for RC Irregular Structure

Investigating the modification factors as a critical seismic design tool, delineating the anticipated level of inelastic behavior within structural systems during seismic events. Both damping and ductility are included in this factor, particularly at movement nearing maximum capacity. Moreover, it offers valuable insights into buildings' response during earthquakes and the anticipated behavior of structures compliant with building codes during design earthquakes. Essentially, it mirrors the structure's capacity to dissipate energy via an inelastic mechanism. In this research, the infill (RC) structures with various structural irregularities were focused. The selected irregularities included dimension, elevation, and mass. Infill location, number of bays, and seismic zone were the expected R factors for RC frames. Non-linear static pushover analysis was adopted in numerical simulation. The available data gathered from the literature was used to validate the outcomes of the developed models. Additionally, the effects of different types of soil were taken into consideration, and the research results demonstrated that the value of the modification factor (R) for change in stiffness and mass of high-rise buildings for bare and infill (RC) structures is less compared to irregular (RC) structures. It was concluded that the same structure with different types of soil and different parameters has a great effect on the value of R for bare and infill regular and irregular (RC) structures. Furthermore, recommendations for accurate R estimation for RC structures were discussed. Doi: 10.28991/CEJ-2024-010-08-09 Full Text: PDF

Hyperinelasticity: An energy-based constitutive modelling approach to isothermal large inelastic deformation of polymers. Part I

The foundation of a new concept, coined here as hyperinelasticity, is presented in this work for modelling the isothermal elastic and inelastic behaviours of polymers. This concept is based on the premise that both the elastic and inelastic behaviours of the subject specimen in the primary loading path may be characterised by a single constitutive law derived from a comprehensive deformation energy W, akin to hyperelasticity, whose constitutive parameters determine and capture both the elastic and inelastic behaviours without the need for additional flow/yield/damage parameters. This core hyperinelastic model captures the elastic and inelastic behaviours in the primary loading path. It is then further specialised, by augmenting the embedded constitutive parameters in the core model, for capturing the inelasticity of the unloading behaviour and the rate of deformation effects. The former is done by devising and incorporating a discontinuous inelasticity variable into the core function, and the latter is achieved by considering that the core model parameters can evolve with, i.e., be a function of, the deformation rate. Examples of the application of the core and augmented hyperinelastic models to a wide range of extant experimental datasets will be presented, ranging from foams, glassy and semi-crystalline polymers to hydrogels and liquid crystal elastomers. The loading modes encompass both tensile and compressive deformations. With a reduced set of number of model parameters (compared with the existing models in the literature), simplicity of implementation (as essentially a straightforward extension to hyperelasticity), and encouraging accuracy in the modelling results, the concept of hyperinelasticity together with the presented hyperinelastic model are proposed as a unified modelling means for capturing the elastic and inelastic behaviours of polymers.

Simulation and parameterization of nonlinear elastic behavior of cables

AbstractThis work contributes to the simulation, modeling, and characterization of nonlinear elastic bending behavior within the framework of geometrically nonlinear rod models. These models often assume a linear constitutive bending behavior, which is not sufficient for some complex flexible slender structures. In general, nonlinear elastic behavior often coexists with inelastic behavior. In this work, we incorporate the inelastic deformation into the rod model using reference curvatures. We present an algorithmic approach for simulating the nonlinear elastic bending behavior, which is based on the theory of Cosserat rods, where the static equilibrium is calculated by minimizing the linear elastic energy. For this algorithmic approach, in each iteration the static equilibrium is obtained by minimizing the potential energy with locally constant algorithmic bending stiffness values. These constants are updated according to the given nonlinear elastic constitutive law until the state of the rod converges. To determine the nonlinear elastic constitutive bending behavior of the flexible slender structures (such as cables) from the measured values, we formulate an inverse problem. By solving it we aim to determine a curvature-dependent bending stiffness characteristic and the reference curvatures using the given measured values. We first provide examples using virtual bending measurements, followed by the application of bending measurements on real cables. Solving the inverse problem yields physically plausible results.

Numerical examination on seismic response behavior of a piping system considering the plastic deformation of supports

A previous study proposed a passive safety structure to mitigate severe damage to crucial components under the beyond design basis event (BDBE). To examine the applicability of this concept to the piping system, the effect of the elastic-plastic behavior of the piping support structure on the seismic response of the piping system was investigated through elastic-plastic time history response analyses on a piping system model with multiple support structures. The numerical analyses considered the elastic-plastic behavior of supports and/or the inelastic characteristics of pipe material. The analysis results confirmed that the response of the piping system can be suppressed by adequately introducing the inelastic behavior of support structures. The results show the possibility of realizing of passive safety structure in piping systems and addressing some issues, such as changing vibration modes due to the elastic-plastic deformation of the support or the order of generation of inelastic behavior of pipe material and supports.

A mesh‐in‐element method for the theory of porous media

AbstractWhile direct homogenisation approaches such as the FE method are subject to the assumption of scale separation, the mesh‐in‐element (MIEL) approach is based on an approach with strong scale coupling, which is based on a discretization with finite elements. In this contribution we propose a two‐scale MIEL scheme in the framework of the theory of porous media (TPM). This work is a further development of the MIEL method which is based on the works of the authors A. Ibrahimbegovic, R.L. Taylor, D. Markovic, H.G. Matthies, R. Niekamp (in alphabetical order); where we find the physical and mathematical as well as the software coupling implementation aspects of the multi‐scale modeling of heterogeneous structures with inelastic constitutive behaviour, see for example, [Eng Comput, 2005;22(5‐6):664‐683.] and [Eng Comput, 2009;26(1/2):6‐28.]. Within the scope of this contribution, the necessary theoretical foundations of TPM are provided and the special features of the algorithmic implementation in the context of the MIEL method are worked out. Their fusion is investigated in representative numerical examples to evaluate the characteristics of this approach and to determine its range of application.

Cyclic inelastic behaviour of a bonded patch repair system used for pipes with through-wall corrosion damage

Repairs of through-wall corrosion damage in pipes conveying liquids using bonded metallic patches are becoming common in the oil and gas industry. Usually, this kind of patch is used in association with a composite sleeve, and it is essential to assure that the repair wońt leak. The use of bonded metallic patches associated with the composite sleeve is not forbidden in the standards for the design of composite repair systems (such as ASME PCC-2 and ISO 24817). However, they do not address this very frequent practice adopted in industry. Since the patch is responsible for sustaining most of the pressure of the repair, it becomes necessary to further understand its behaviour. This paper investigates the cyclic inelastic behaviour of a metal patch/adhesive system and its effect on the failure pressure. Hydrostatic tests were performed regarding how pressure variations can generate cyclic inelastic strains in the adhesive layer that bonds the metal patch to the pipe, and how this cyclic loading–unloading process ultimately affects the failure pressure. The failure pressure in monotonic burst tests can be reasonably modelled using basic concepts of linear elastic fracture mechanics. Although the assumption of a brittle-elastic behaviour of the repair system seems adequate in the case of monotonic loading, it is not in the case of cyclic tests with high pressure amplitudes. Repairs in steel pipes under pressure with a 25 mm diameter hole failed after a very small number of cycles with pressure amplitude of 80% of the average failure pressure obtained in monotonic burst tests. To help understanding the behaviour of the system, single lap joints were studied. The patch and pipe are not subjected to significant permanent deformations, while the adhesive layer has an inelastic behaviour. Results show that the lap joints present a rate-dependent behaviour in tensile tests and may present highly different cyclic responses which are quite sensitive to very small perturbations in the manufacturing process.

Performance-Based Wind Design of Tall Buildings Considering Corner Modification and Inelastic Behavior

Performance-Based Wind Design of Tall Buildings Considering Corner Modification and Inelastic Behavior

Molecular Dynamics Simulation of Cumulative Microscopic Damage in a Thermosetting Polymer under Cyclic Loading.

To develop durable composite materials, it is crucial to elucidate the correlation between nanoscale damage in thermosetting resins and the degradation of their mechanical properties. This study aims to investigate this correlation by performing cyclic loading tests on the cross-linked structure of diglycidyl ether bisphenol A (DGEBA) and 4,4'-diaminodiphenyl sulfone (44-DDS) using all-atom molecular dynamics (MD) simulations. To accurately represent the nanoscale damage in MD simulations, a bond dissociation algorithm based on interatomic distance criteria is applied, and three characteristics are used to quantify the microscopic damage: stress-strain curves, entropy generation, and the formation of voids. As a result, the number of covalent bond dissociations increases with both the cyclic loading and its amplitude, resulting in higher entropy generation and void formation, causing the material to exhibit inelastic behavior. Furthermore, our findings indicate the occurrence of a microscopic degradation process in the cross-linked polymer: Initially, covalent bonds align with the direction of the applied load. Subsequently, tensioned covalent bonds sequentially break, resulting in significant void formation. Consequently, the stress-strain curves exhibit nonlinear and inelastic behavior. Although our MD simulations employ straightforward criteria for covalent bond dissociation, they unveil a distinct correlation between the number of bond dissociations and microscale damage. Enhancing the algorithm holds promise for yielding more precise predictions of material degradation processes.

Inelastic behavior of diagonally reinforced coupling beams confined with steel fibers

Experimental studies were conducted to analyze the plastic rotation capacity and the effect of replacing transverse reinforcements with steel fibers in diagonal reinforced concrete coupling beams. Six specimens were planned, and the steel fiber reinforcing index and total area of transverse reinforcements were the main variables. Reverse cyclic loading tests were conducted to confirm the seismic performance of the coupling beam. The results showed that the plastic hinge rotation capacity increased and the buckling point of the diagonal reinforcing bars was delayed as the steel fiber reinforcing index increased. An analysis of 78 specimens and the results of previous studies confirmed that ductility improved when the confinement effect of the steel fiber was considered. Application of an equation for ductility requirements reflecting the confining stress of steel fiber reinforced concrete confirmed that the amount of transverse reinforcement could be reduced.

Mechanical behavior and apparent stiffness of flax, hemp and nettle fibers under single fiber transverse compression tests

While plant fibers find extensive use across numerous applications, their transverse behavior and mechanical properties lack direct and fiber-scale characterization, posing a significant knowledge gap. This paper investigates, for the first time, the transverse behavior of flax, hemp and nettle fibers through Single Fiber Transverse Compression Tests (SFTCTs). Finite element analysis is used to study the influence of time-dependent and irreversible inelastic behavior on the fiber’s response and identify configurations fit for the identification of apparent elastic properties. SFTCTs are performed experimentally with a repeated progressive loading protocol using a custom micro-mechatronic setup. An apparent fiber transverse elastic modulus of 1 to 3 GPa is identified by inverse method for all tested fibers, demonstrating high fiber anisotropy. Important inelastic features are also observed on fiber behavior. Their origin is discussed with both material behavior and structural mechanisms such as lumen collapse, identified as the main potential causes.