Continuum Finite Element Model Research Articles

Numerical analysis of group effects of a large pile group under lateral loading

Large pile group (≥100 piles) foundations supporting liquified natural gas (LNG) storage tanks and high-rise buildings are subjected to significant vertical and lateral loads, where foundation design can be governed by the required lateral resistance. A typical approach for design of laterally loaded pile groups uses the beam on Winkler foundation method, where nonlinear p-y curves are reduced by a p-multiplier to account for the group effects. Alternatively, an average p-multiplier known as a group reduction factor (GRF) can be used. There is no published guidance on these topics for large pile groups (≥100 piles) as existing design standards are premised upon smaller pile groups (<25 piles). This study uses 3D continuum finite element models to study the group effects in large pile groups using p-multipliers and GRFs. The study also looked at the effect of the circular configuration of pile groups used in LNG tank foundations. The design standards and prevailing methods are shown to overestimate trailing row p-multipliers for large pile groups, particularly with larger pile spacing. Based on the study data and published data, a predictive equation is proposed for estimating GRF of a laterally loaded large pile group.

Analytical and numerical investigation of a low-damage uplift friction damper for self-centering cross-laminated timber rocking walls

Cross-Laminated Timber (CLT) rocking wall systems have gained considerable attention in recent years as a potential Seismic-Force Resisting System for mass timber construction in regions of moderate to high seismic risk. It is well understood that CLT rocking walls do not provide any measurable amount of ductile energy dissipation on their own but instead rely on energy dissipation through their connections. A common approach has been to provide replaceable metallic yielding elements or structural fuses located at the base of the wall or the vertical interface between coupled walls. However, hysteretic yielding dampers are susceptible to both strength and stiffness degradation. To overcome these limitations, this paper presents a newly proposed Uplift Friction Damper (UFD) as an alternative to hysteretic dampers installed at the base of CLT rocking walls. The proposed UFDs provide stable energy dissipation and enhanced self-centering capability. This paper presents details of the UFD device along with analytical and continuum finite element numerical models that inform the kinematic response of the UFD. Furthermore, the tunability of the UFD device is investigated by changing select governing parameters of the UFD in a limited parametric study. First, the fundamental response of a single UFD device is presented to inform the basic local response. Next, the system response of the UFD installed on a SC-CLT wall is investigated through cyclic pushover analyses using continuum finite element models. Results show that the amount of energy dissipation depends primarily on the inclination angle of the friction interface, stiffness of the bolt-disc springs providing the normal clamping force, and coefficient of friction between the sliding interfaces.

Mesh objective stochastic simulations of quasibrittle fracture

Continuum finite element (FE) modeling of damage and failure of quasibrittle structures suffers from the spurious mesh sensitivity due to strain localization. This issue has been addressed for deterministic analysis through the development of localization limiters. This study proposes a mechanism-based model to mitigate the mesh sensitivity in stochastic FE simulations of quasibrittle fracture. The interest is placed on the analysis of large-size structures, where the mesh size is conveniently chosen to be larger than the width of the fracture process zone as well as the correlation length of the random fields of constitutive properties. The present model is formulated within the framework of continuum damage mechanics. Two localization parameters are introduced to describe the evolution of the damage pattern of each finite element. These parameters are used to guide the energy regularization of the constitutive law, as well as to formulate the mesh-dependent probability distributions of constitutive properties. Depending on the prevailing damage pattern, different energy regularization schemes and mesh dependence of the probability distribution functions are used in the constitutive law. The model is applied to simulate the stochastic failure behavior of quasibrittle structures of different geometries featuring different failure processes including damage initiation, localization, and propagation. It is shown that using fixed probability distribution functions of constitutive properties could lead to strong mesh dependence of the prediction of the mean and variance of the structural load capacity. The probability distribution functions of constitutive properties must be linked to the damage pattern, which may evolve during the failure process. Such a mechanism-based modeling of the probability distributions of constitutive properties is essential for mitigating the spurious mesh sensitivity in stochastic FE analysis of quasibrittle fracture.

Finite element modeling and behavior of dissipative embedded column base connections under cyclic loading

This paper explores, by means of continuum finite element (CFE) analysis, a recently developed concept that promotes controlled inelastic energy dissipation within the embedded portion of column base connections rather than in steel columns of conventional embedded column bases. As such, dissipative embedded column base connections become resilient to local buckling. Several loading and geometric parameters are interrogated through parametric simulations with a high-fidelity CFE model, which is thoroughly validated with available experimental data. The simulation results suggest that steel columns in conventional embedded bases are prone to local buckling even at modest lateral drift demands (i.e., 2% rad), thereby exhibiting 10 to 30 mm of axial shortening in the presence of constant compressive axial load. On the other hand, dissipative bases are resilient to local buckling till at least 4% rad lateral drift demands regardless of the column cross-sectional characteristics and loading parameters. At larger lateral drift demands, the use of horizontal stiffeners in dissipative bases alleviates localized flange deformations attributable to bearing of the embedded column flange with the reinforced concrete foundation. Axial shortening in dissipative base connections is only attributable to inelastic cyclic straining within the dissipative zone and is up to 60% less than that of steel columns in conventional bases at lateral drift demands of 2% rad. The CFE simulations reveal that the hysteretic response of dissipative bases is insensitive to bidirectional loading.

Predictive equations and continuum FE models for self-centering response of SMA-based steel beam-column connections with steel angles

The main objective of this study is to develop predictive equations for characterizing the cyclic response of steel beam-to-column connections with superelastic Shape Memory Alloy (SMA) bolts and steel angles. High-fidelity continuum finite-element (FE) models are developed to simulate the cyclic behavior and limit states of steel beam-column connections with combined SMA bolts and steel angles. The simulation results are then validated against a set of seven full-scale connection specimens from a previous experimental study. The validated models are then used to perform sensitivity and response surface studies. The sensitivity analysis results with sixteen design factors indicate that the beam web slenderness ratio, SMA bolt diameter, and angle thickness are the most significant design factors influencing the cyclic response of SMA connections. The results also indicate that permanent deformation in the connection subassembly is confined to steel angles, confirming the robust damage-avoidance design of the beam-column connections with SMA bolts and steel angles. Beams of lower depth are recommended to prevent early bolt fracture and minimize residual deformations in SMA connections. The developed surrogate models can be used to accurately predict the cyclic and self-centering response of the SMA connections. A design example is also presented to illustrate the use of the surrogate models.

Hysteretic Behaviour of Shear Stud Connectors in Composite Steel Moment‐Resisting Frames

AbstractIn steel moment resisting frames (MRFs) with composite floor slabs, seismic loads are transmitted from the slab into the beam through shear studs. Shear strength degradation of the studs due to cyclic loading results into the loss of the load transfer mechanism and composite action. To date, several low‐cyclic, high‐amplitude push‐out tests have been conducted to characterize the shear stud hysteretic behaviour. These isolated tests showed considerable degradation in the shear stud resistance; nevertheless, they do not simulate the actual hysteretic behaviour of shear studs within a composite steel beam. To elaborate, conventional cyclic push‐out tests do not replicate the actual stress state in the concrete slab, nor do they account for the force redistribution between the shear studs. This paper investigates the hysteretic behaviour of shear studs in steel MRFs with composite floor slabs. The load‐slip hysteretic behaviour of the shear studs is examined through continuum finite element (CFE) models of 2‐bay sub‐systems and their corresponding cruciform subassemblies. Moreover, shear force and interlayer slip envelopes are obtained along the composite steel beams. Results of the CFE models are used to propose new design recommendations for shear studs in composite‐steel MRFs.

An anisotropic elastoplastic Cosserat continuum model for shear failure in stratified geomaterials

In this article, we formulate an anisotropic elastoplastic Cosserat continua model for shear failure in stratified geomaterials. Considering the dip angle between local and global coordinates of a formation, a Cosserat elastic anisotropy constitutive matrix under plane strain condition is derived, and cohesion anisotropy is reflected using a microstructural tensor combined-stress invariant method. A Cosserat continuum finite element model and consistent algorithm are developed to consider the characteristics of elastic anisotropy, strength anisotropy, and strain softening. The simulation of a stratified geomaterial sample under uniaxial compression condition shows that the elastic anisotropy has an evident influence on the deformation pattern. It is also demonstrated that dip angle could significantly impact macroscopic failure modes, uniaxial compressive strength, and macroscopic equivalent elastic modulus. The stability analysis of a layered slope demonstrates that the strength anisotropy has a considerable influence on the overload safety factor of the slope and can be a trigger of the formation of shear bands in such slopes. Furthermore, the dip angle of the structural plane also affects the stability of the stratified slope, which is controlled by both the block and structural surface. By comparing the numerical results of the classical continuum model and the Cosserat continuum model, it is proved that the numerical model considering the elastoplastic anisotropy and strain softening under the Cosserat continuum theory overcomes the ill-posedness of mesh sensitivity and maintains the well-posedness of the strain localization problem. Thus, the proposed model is useful for modeling shear failure in stratified geomaterials.

Numerical modelling and analysis of post-tensioned timber beam-column joint

As a part of sustainable development initiatives, post-tensioned timber structural systems have been developed in recent years with the intention of implementation in seismically active regions. Ductility is achieved through rocking connections between members and optional steel yielding elements. Numerical investigations on such systems have been mostly limited to macro-modeling to avoid complexities arising from the wood anisotropy. This paper examines the lateral cyclic behavior of post-tensioned Laminated Veneer Lumber (LVL) beam-column subassemblies using three-dimensional continuum finite element (FE) modeling. The results of a testing program on full-scale interior joints with unreinforced and steel reinforced configurations at the connection interface are presented. A description of the pre-processing and solution of the FE models, including material, geometric and contact nonlinearities, element mesh, and analysis is provided. The FE results are then validated against the experiments through a verification study. Focus is placed upon the anisotropy of the material as well as the difficulties emerging from performing the nonlinear analysis for such systems.

Strength and Plastic Rotation Capacity of I-Shaped Beams with Grid-Purlin System Subjected to Cyclic Loading

This paper introduces a grid-purlin system, which was composed of secondary rectangular-hollow-section grids welded onto the top flange of I-shaped beams of moment frames. The welded grid-purlin itself may play a role of a lateral bracing member for the welded beam. However, the ultimate strength, plastic rotation capacity, or other structural characteristics of this grid-purlin system remain poorly understood. This paper presents two full-scale cyclic loading tests on specimens with I-shaped beams 700 mm deep, 240 mm wide, and 13 m long. The diagonal length of grids in the square grid-purlin of the specimen was 1.3 m on-center, and two different depths of the sections were selected for the purlin sections. Both specimens successfully achieved fully plastic moments at a plastic rotation exceeding 0.04 rad. This shows that the grid-purlin system provides reliable lateral bracing. Continuum finite-element (CFE) analysis was performed to simulate the hysteretic experimental response of the grid-purlin system. This CFE model was used to examine the plastic rotation capacity for a variety of combinations of I-shaped beams and grid-purlins.

Experimental Database for Steel Flush End-Plate Connections

A comprehensive experimental database of bare steel and composite flush end-plate (FEP) connections, covering tests conducted within the last 50 years, was collated and made public. The database includes deduced and tabulated parameters defining the configuration, geometric and material properties, and observed deformation and failure modes for more than 360 test specimens. The database also includes the specimens’ monotonic/cyclic responses in the form of digital moment versus rotation data. The database will aid researchers and engineers in benchmarking empirical, mechanical, or continuum finite-element models; assessing the robustness of existing numerical modeling and designing methodologies for end-plate connections; and developing new predictive models or damage fragility functions. The database also serves as an exemplar for the systematic development of similar databases for other types of semirigid connections. A graphical interface was developed to aid users in exploring, filtering, and assessing the database.

Comparisons between beam and continuum models for modelling wheel-rail impact at a singular rail surface defect

A singular rail or wheel surface irregularity, such as a squat, insulation joint or wheel flat, can cause large wheel-rail impact force. Both the magnitude and frequency content of the impact force need to be correctly modelled because they are closely related to the formation, deterioration and detection of such irregularities. In this paper, we compare two types of commonly used wheel-track interaction models for wheel-rail impact problems, i.e., a beam and a continuum finite element model. We first reveal the differences between the impact forces predicted by the two models due to a typical rail squat using a time-frequency analysis. Subsequently, we identify the causes for the differences by evaluating the effects of different model assumptions, as well as different model parameters. Results show that the impact force consists of a forced vibration peak M1 followed by free vibration related oscillations with three dominant frequencies: f1 (340 Hz), f2 (890 Hz) and f3 (1120 Hz). Compared with the continuum model, the beam model with a Hertzian contact spring overestimates the M1 peak force. The discrepancy can be reduced by using a Winkler bedding contact model. For the track model, the beam model is comparable to the continuum model up to about 800 Hz, beyond which the track damping starts to deviate. As a result, above 500 Hz, the contact forces dominate at f2 for the beam while at f3 for the continuum model. Finally, we show that the continuum model is more accurate than the beam model by comparing to field observations. The effects of stress wave propagation on the differences are also discussed.

Nonlinear finite element analysis of reinforced concrete flat plate punching using a thick-shell modelling approach

The punching shear resistance of reinforced concrete flat plates is an area where design is typically done in a highly-idealized manner, using provisions developed from experimental results of isolated slab-column connections; yet, involves structures where performance may be greatly impacted by system-level response. This paper presents the development and application of a practical thick-shell finite element-based nonlinear modelling procedure for reinforced concrete flat plate slab systems. Cracked concrete material modelling based on the formulations of the Disturbed Stress Field Model is employed in conjunction with computationally-efficient layered thick-shell finite elements that accommodate through-thickness shearing effects and are shown to be capable of capturing brittle punching-governed failure modes. A simple low-cost sectional analysis modification procedure is proposed to incorporate strength enhancements attributed to confining effects stemming from disturbances in slab-column connection regions. Load-displacement responses and failure modes developed using the proposed modelling procedure are shown to capture observed experimental responses and provide response estimates similar to those obtained using more costly three-dimensional solid continuum finite element modelling techniques. Finally, the analysis results presented were developed using simple-to-define concrete property input without the need for supplemental material model or analysis parameter calibration.

Failure Mechanisms of Equal and Unequal Wall Thickness Hybrid Maraging Steel-P20 Tubular Joints: Effects of Welding Residual Stresses

Abstract Joining an additively manufactured component to a forged or cast part through welding processes has recently attracted the attention of engineers and scientists. This technique integrates the technical benefits of additive manufacturing (AM) technology with conventional processes that may be more cost-efficient. In this paper, the effect of residual stresses on the mechanical performance of a hybrid welded pipe joint connecting an additively manufactured maraging steel (MS1) pipe segment with a conventional P20 steel tube having an equivalent outside diameter was studied. A sequentially coupled thermo-mechanical continuum finite element (FE) modeling procedure to predict the residual stress state on circumferential pipe hybrid MS1-P20 joints subjected to multi-axial loads was developed and validated. Available experimental data on a welded pipe joint with conventional stainless steel (SUS304) were used to calibrate the model. The FE modeling procedures were further validated for the hybrid MS1-P20 joint. The predicted residual stress state was mapped on the pipe joint with equal and unequal wall thickness joint transitions. The mechanical performance of these pipe joints was evaluated with the application of internal pressure, uniaxial tension, and flexural loads. The major contribution of this study was the proposition of a new concept of hybrid joints, where a significant transition of the load was expected. The new hybrid joint concept was presented to meet the existing design criteria requirements without sacrificing other parameters (e.g., component weight and manufacturing expense) and facilitate the production of hybrid components using AM techniques.

Multiscale modelling of soft lattice metamaterials: Micromechanical nonlinear buckling analysis, experimental verification, and macroscale constitutive behaviour

Soft lattice structures and beam-metamaterials made of hyperelastic, rubbery materials undergo large elastic deformations and exhibit structural instabilities in the form of micro-buckling of struts under both compression and tension. In this work, the large-deformation nonlinear elastic behaviour of beam-lattice metamaterials is investigated by micromechanical nonlinear buckling analysis. The micromechanical 3D beam finite element model uses a primary linear buckling analysis to incorporate the effect of geometric imperfections into a subsequent nonlinear post-buckling analysis. The micromechanical computational model is validated against tensile and compressive experiments on a 3D-printed sample lattice structure manufactured via multi-material jetting. For the development and calibration of macroscale continuum constitutive models for nonlinear elastic deformation of soft lattice structures at finite strains, virtual characterization tests are conducted to quantify the effective nonlinear response of representative unit cells under periodic boundary conditions. These standard tests, commonly used for hyperelastic material characterization, include uniaxial, biaxial, planar and volumetric tension and compression, as well as simple shear. It is observed that besides the well-known stretch- and bending-dominated behaviour of cellular structures, some lattice types are dominated by buckling and post-buckling response. For multiscale simulation based on nonlinear homogenization, the uniaxial standard test results are used to derive parametric hyperelastic constitutive relations for the effective constitutive behaviour of representative unit cells in terms of lattice aspect ratio. Finally, a comparative study for compressive deformation of a sample sandwich lattice structure simulated by both full-scale beam and continuum finite element models shows the feasibility and computational efficiency of the effective continuum model.

Numerical Investigation on the Deformational Behavior of Continuous Buried Pipelines Under Reverse Faulting

Steel pipelines are vulnerable to the movements of active faults. Few studies focused on reverse faults. The deformational behavior of buried steel pipelines crossing an active reverse fault is investigated in this paper by applying 3D continuum finite element modeling. Numerical simulations indicate that local buckling (or wrinkling) mode of failure is more sensitive to the pipeline rather than tensile failure mode. The results were also confirmed by the experiment. Based on parametric studies, the pipeline capacity against failure can be significantly improved by reducing the burial depth and the pipe thickness ratio. Besides, the soil consistency around the pipe has a great effect on the behavior of buried pipelines. Furthermore, it is found out that the failed pipeline sections would be generated in longer distance from the fault plane as the soil behaves more softly or the pipeline is more flexible. These findings can lead the designers to have a safer and economic design of pipelines crossing reverse faulting zones.

Estimating tissue-level properties of porcine talar subchondral bone

Tissue-level properties of bone play an important role when characterising apparent-level bone biomechanical behaviour and yet little is known about its effect at this hierarchical level. In combination with trabecular morphological data these properties can be used to predict bone strength, which becomes an invaluable tool for clinicians in patient treatment planning.This study developed specimen-specific micro-finite element (μFE) models using validated continuum-level models, containing grayscale-derived material properties, to indirectly establish tissue-level properties of porcine talar subchondral bone.Specimen-specific continuum finite element (hFE) models of subchondral trabecular bone were setup using μCT data of ten cylindrical specimens extracted from juvenile porcine tali. The models were validated using quasi-static uniaxial compression testing. Validated hFE models were used to calibrate the tissue modulus of corresponding μFE models by minimising the difference between the μFE and hFE stiffness values. Key trabecular morphological indices (BV/TV, DA, Conn.D, Tb.Th, EF) were evaluated.Good agreement was observed between hFE models and experiment (CCC = 0.66). Calibrated Etiss was 504 ± 37.65 MPa. Average BV/TV and DA for μFE specimens were 0.37 ± 0.05 and 0.68 ± 0.11, respectively. BV/TV (r2 = 0.667) correlated highly with μFE stiffness.The small intra-specimen variation to tissue-level properties suggests that variations to apparent-level stiffness originate from variations to microarchitecture rather than tissue mechanical properties.

Hysteretic Behavior of Moment-Resisting Frames Considering Slab Restraint and Framing Action

This paper examines the influence of framing action and slab continuity on the hysteretic behavior of composite steel moment-resisting frames (MRFs) by means of high-fidelity continuum finite-element (CFE) analyses of two-bay subsystems and typical cruciform subassemblies. The CFE model, which is made publicly available, was thoroughly validated with available full-scale experiments and considers variations in the beam depth and the imposed loading history. The simulation results suggest that beams in subsystems may experience up to 25% less flexural strength degradation than those in typical subassemblies. This is because of local buckling straightening from the slab continuity and framing action evident in subsystems. For the same reason, beam axial shortening attributable to local buckling progression is up to five times lower in subsystems than in subassemblies, which is consistent with field observations. While the hysteretic behavior of interior panel zone joints is symmetric, exterior joint panel zones in subsystems experience large asymmetric shear distortions regardless of the employed lateral loading history. From a design standpoint, it is found that the probable maximum moment in deep and slender beams (db≥700 mm) may be up to 25% higher than that predicted by current design provisions with direct implications to capacity design of steel MRFs. The 25% reduction in the shear stud capacity as proposed by current seismic provisions is not imperative for MRFs comprising intermediate to shallow beams and/or featuring a high degree of composite action (η>80%) as long as ductile shear connectors are employed.

Estimating the evolution of strain induced by inelastic cyclic local buckling in steel beam-columns

Steel beam-columns subjected to seismic loading often experience inelastic cyclic local buckling, which leads to strain amplification within the locally buckled region. These strains are ultimately responsible for Ultra Low Cycle Fatigue or fracture. An approach is presented to estimate the evolution of local buckling induced strain at critical locations in steel wide-flanged members subjected to cyclic loading. The main scientific basis for the approach is a series of 26 Continuum Finite Element (CFE) models that investigate a range of configurations (member cross section, axial load, loading history). Based on these simulations, a 3-dimensional post-buckling mechanism defined by yield lines, rigid facets, and yielding zones is proposed. This mechanism provides a bridging relationship between member plastic hinge rotations and local buckling induced strains at the continuum level. Guidelines for estimating various parameters that define this mechanism are presented. The approach is extended to predict strain evolution under cyclic loading; this extension accounts for history effects associated with buckling, straightening, and re-buckling of the cross-section. The method is validated by comparing the predicted strain evolution to its counterpart as determined from CFE simulations. The results indicate that the proposed method is highly effective in predicting the evolution of local buckling induced strain, and shows minimal bias with respect to configurational parameters and loading history. As such, the method is a computationally efficient alternative to CFE simulations, which are currently the only means for estimating cyclic local buckling induced strains. Applications of the method are outlined along with a discussion of its limitations.

Discrete and Continuous Approaches for the Failure Analysis of Masonry Structures Subjected to Settlements

Numerical modelling of masonry structures is nowadays still an active research field, given a number of open issues related to preservation and restoration of historical constructions and the availability of computational tools that have become more and more refined. This work focuses on the analysis of settlement-induced failure patterns characterizing the in plane response of two-dimensional dry-joints masonry panels, which differ in terms of texture, geometry and settlement configuration. Brick-block masonry, interpreted as a jointed assembly of prismatic particles in dry contact, can be modelled as a discrete system of rigid blocks interacting through contact surfaces with no tensile strength and finite friction, modelled as zero thickness elasto-plastic Mohr-Coulomb interfaces. Different approaches and numerical models are adopted herein: Limit Analysis (LA), a discrete model DEM and a continuous Finite Element Model (FEM). Limit Analysis is able to provide fast and reliable results in terms of collapse multiplier and relative kinematics. In this work, a standard LA procedure is coded through Linearised Mathematical Programming to take into account sliding mechanisms through dilatant joints. Discrete models are particularly suitable to study historical masonry materials, where rigid bodies interacts between contact and friction. Here, a combined Finite/Discrete Element approach (FEM/DEM) is adopted. Finally, analyses are conducted through the Finite Element approach, resorting to a continuum anisotropic elastic-perfectly plastic constitutive model. Some selected case-studies have been investigated adopting the above mentioned models and numerical results have been interpreted to highlight the capability of the approaches to predict failure patterns for various geometrical features of the structure and settlement configurations.

Characterizing and Modeling the Precursors to Coarse Grain Formation during Beta-Annealing of Ti-6Al-4V

Coarse prior β grains exceeding 3 mm in diameter have been sporadically observed following β annealing of α+β forged titanium alloys. Recent work has shown that the occurrence of coarse grains may be due in part to the stabilization of a {001}&lt;110&gt; texture during hot working that was further enhanced in intensity at the expense of other texture components during the early stages of β annealing. With the majority of the material comprised of low misorientation subgrains of a single texture component, the nuclei for coarse grains was the minority fraction of grains that were highly misoriented, and therefore had boundaries with higher energy and mobility, compared to the average grain. In this work, Ti-6Al-4V bar was side-pressed to various reductions in the α+β phase field to further investigate the role of texture and the effects of strain, strain-path, and deformation heating on the propensity to form abnormally large grains during β-annealing. The experiments were interpreted in the context of a continuum finite element model and viscoplastic self-consistent crystal plasticity simulations. Based on the results from experiment and modeling, we make recommendations with respect to the α+β forging process to avoid the occurrence of excessively coarse β grains.