Continuum Finite Element Analysis Research Articles

Multi-spring model for tubular rocking steel bridge piers subjected to earthquake loading

Recent decades have seen increased interest in using the controlled rocking concept in seismic resisting systems. Unlike conventional systems, where lateral deformation of a member is achieved through the formation of plastic hinges in critical regions, in the rocking systems this is achieved through a gap opening mechanism. Due to gravity load and/or post-tensioning forces, the rocking systems exhibit a self-centering behavior. Conducting a continuum finite element analysis to investigate the seismic response of such a system is quite expensive in terms of computational resources. On the other hand, a simplified macro model using two springs to simulate the gap opening/closing mechanism cannot accurately predict the dynamic response of the system. This study utilizes a multiple-spring model to simulate the nonlinear seismic response of circular tubular steel piers. An efficient optimization procedure based on a genetic algorithm is developed to calibrate the parameters of the springs. The results of continuum finite element analyses are compared with those obtained from the multi-spring model to verify the accuracy of the model. The proposed method is shown to be advantageous for accurately simulating the seismic response of a bridge model subjected to multi-directional ground motions, particularly the hysteretic force-displacement relationship, and dynamic response time history.

Near-fault ground motion effect on self-centering modular bracing panels considering soil-structure interaction

This study investigates the nonlinear seismic response behavior of self-centering modular steel bracing panel (SCMBP) systems subjected to near-fault ground motion records, considering the soil-structure interaction (SSI) effect. Analytical formulas for the load-displacement relationship of an SCMBP were validated through nonlinear 3D continuum finite element analysis while a simplified 2D wireframe model utilizing a constitutive spring model was verified by the 2D refined finite element model and subsequently adopted for time history analysis of the SCMBP structures with SSI effect. Based on the nonlinear time history analysis of a 6-story prototype building subjected to a suite of near-fault ground motions, the prototype structure is found to be able to re-center itself even under near-fault ground motion scaled to the design basis earthquake (DBE) level while frame members remain undamaged, except for fuse devices. Additionally, SSI reduces inter-story drift ratios under both far-field and near-fault ground motions. The findings provide insights into the promising performance of using SCMBP systems as a seismic strengthening system for sites with potential SSI effects and near-fault earthquake impact. The findings of this study can be insightful to other self-centering systems with flag-shaped story shear hysteresis.

Geometric tolerances of welded connections with inelastic panel zones

AbstractPrequalified beam‐to‐column connections in steel moment resisting frames usually concentrate inelastic deformations in the steel beam ends. As such, nonlinear geometric instabilities (i.e., local buckling) may occur in these regions at modest lateral drift demands, leading to potentially high residual deformations. Previous research has shown that welded connections featuring inelastic panel zones exhibit a stable hysteretic behaviour. In this case, residual deformations in steel beams are often not visually detectable after inelastic cyclic straining. This paper contrasts the residual deformations of steel beams as part of welded connections with elastic and inelastic panel zones through continuum finite element analyses. The employed finite element model is thoroughly validated with available test data. Besides the actual hysteretic response of the connections, the primary focus of the present work is on a number of geometric tolerance indicators, such as the web concavity, flange out‐of‐square and beam axial shortening. These are strongly correlated to the potential for reuse of structural steel members. The results suggest that connection designs featuring inelastic panel zones delay beam local buckling relative to their strong panel zone counterparts, achieving acceptable residual deformations even at lateral drift demands higher than 4% when considering the geometric tolerances of international standards.

Digital‐Image‐Correlation for Simulating Cyclic Local Buckling in Steel Beams

AbstractNonlinear continuum finite element (CFE) analyses rely on accurate multiaxial constitutive law formulations along with reliable imperfection patterns for simulating nonlinear geometric instabilities in steel members under mechanical loading. Validations of these models usually rely on conventional measurements of macroscopic parameters (e.g., displacement and strain field). It is common to use global deformation characteristics (e.g., deduced moment versus chord rotation) for model validation purposes of steel members exhibiting inelastic cyclic local buckling. The reason is that measurements from conventional strain gauge readings are not deemed to be reliable well before the onset of local buckling. This is potentially problematic when the accurate prediction of local strain demands is essential. This paper discusses the experimental results from a steel beam instrumented with a digital image correlation (DIC) system and how optical measurements acquired from DIC can be used to benchmark a CFE model representation of this beam. It is shown that while different CFE model types simulate accurately the moment rotation relationship of the steel beam, local strain demand predictions could vary considerably between model types. The results suggest that DIC measurements can inform the selection of proper imperfection patterns to be used in CFE models for the reliable estimation of inelastic strain demands.

Continuum finite element analysis generalizes in vivo trabecular bone microstructural strength measures between two CT scanners with different image resolution

Fragility of trabecular bone (Tb) microstructure is increased in osteoporosis, which is associated with rapid bone loss and enhanced fracture-risk. Accurate assessment of Tb strength using in vivo imaging available in clinical settings will be significant for management of osteoporosis and understanding its pathogenesis. Emerging CT technology, featured with high image resolution, fast scan-speed, and wide clinical access, is a promising alternative for in vivo Tb imaging. However, variation in image resolution among different CT scanners pose a major hurdle in CT-based bone studies. This paper presents nonlinear continuum finite element (FE) methods for computation of Tb strength from in vivo CT imaging and evaluates their generalizability between two scanners with different image resolution. Continuum FE-based measures of Tb strength under different loading conditions were found to be highly reproducible (ICC ≥ 0.93) using ankle images of twenty healthy volunteers acquired on low- and high-resolution CT scanners 44.6 ± 2.7 days apart. FE stress propagation was mostly confined to Tb micro-network (2.3 ± 1.7 MPa) with nominal leakages over the marrow space (0.4 ± 0.5 MPa) complying with the fundamental principle of mechanics at in vivo imaging. In summary, nonlinear continuum FE-based Tb strength measures are reproducible among different CT scanners and suitable for multi-site longitudinal human studies.

Behavior of Sedimentary Rock Tunnel against Rigid Projectile Impact

The tunnels in present-day cities are experiencing varying degrees of loading conditions ranging from static to extreme loading. Therefore, the stability of underground tunnels needs to be analyzed and understood for safer and strengthened design. The present study was conducted to simulate the impact loading conditions due to a missile traveling at a velocity of 5 Mach for different rock tunnels. The nonlinear continuum finite element analysis has been carried out through Abaqus and Explicit. The four different types of sandstones considered in the present study include Kota, Jamrani, Singrauli, and Jhingurda sandstones. An elastoplastic Mohr–Coulomb constitutive material model has been considered to model the behavior of rock surrounding the tunnel opening. The tunnel has an opening of 7 m in diameter (d), and 50 m in height and breadth, with 50 m of longitudinal length. The deformation and stress in the rock and the damage to the concrete lining have been compared in different cases. The Concrete–Damage–Plasticity (CDP) model and the Johnson–Cook model were considered for modelling of the RC lining and steel reinforcement. It was concluded that Jhingurda sandstone has maximum deformations due to impacts caused by missiles.

Finite element analysis of trabecular bone microstructure using CT imaging and continuum mechanical modeling.

PurposeOsteoporosis is a bone disease associated with enhanced bone loss, microstructural degeneration, and fracture‐risk. Finite element (FE) modeling is used to estimate trabecular bone (Tb) modulus from high‐resolution three‐dimensional (3‐D) imaging modalities including micro‐computed tomography (CT), magnetic resonance imaging (MRI), and high‐resolution peripheral quantitative CT (HR‐pQCT). This paper validates an application of voxel‐based continuum finite element analysis (FEA) to predict Tb modulus from clinical CT imaging under a condition similar to in vivo imaging by comparing with measures derived by micro‐CT and experimental approaches.MethodVoxel‐based continuum FEA methods for CT imaging were implemented using linear and nonlinear models and applied on distal tibial scans under a condition similar to in vivo imaging. First, tibial axis in a CT scan was aligned with the coordinate z‐axis at 150 μm isotropic voxels. FEA was applied on an upright cylindrical volume of interests (VOI) with its axis coinciding with the tibial bone axis. Voxel volume, edge, and vertex elements and their connectivity were defined as per the isotropic image grid. A calibration phantom was used to calibrate CT numbers in Hounsfield unit to bone mineral density (BMD) values, which was then converted into calcium hydroxyapatite (CHA) density. Mechanical properties at each voxel volume element was defined using its ash‐density defined on CT‐derived CHA density. For FEA, the bottom surface of the cylindrical VOI was fixed and a constant displacement was applied along the z‐direction at each vertex element on the top surface to simulate a physical axial compressive loading condition. Finally, a Poisson's ratio of 0.3 was applied, and Tb modulus (MPa) was computed as the ratio of average von Mises stress (MPa) of volume elements on the top surface and the applied displacement. FEA parameters including mesh element size, substep number, and different tolerance values were optimized.ResultsCT‐derived Tb modulus values using continuum FEA showed high linear correlation with the micro‐CT‐derived reference values (r ∈ [0.87 0.90]) as well as experimentally measured values (r ∈ [0.80 0.87]). Linear correlation of computed modulus with their reference values using continuum FEA with linear modeling was comparable with that obtained by nonlinear modeling. Nonlinear continuum FEA‐based modulus values (mean of 1087.2 MPa) showed greater difference from their reference values (mean of 1498.9 MPa using micro‐CT‐based FEA) as compared with linear continuum methods. High repeat CT scan reproducibility (intra‐class correlation [ICC] = 0.98) was observed for computed modulus values using both linear and nonlinear continuum FEA. It was observed that high stress regions coincide with Tb microstructure as fuzzily characterized by BMD values. Distributions of von Mises stress over Tb microstructure and marrow regions were significantly different (p < 10–8).ConclusionVoxel‐based continuum FEA offers surrogate measures of Tb modulus from CT imaging under a condition similar to in vivo imaging that alleviates the need for segmentation of Tb and marrow regions, while accounting for bone distribution at the microstructural level. This relaxation of binary segmentation will extend the scope of FEA application to assess mechanical properties of bone microstructure at relatively low‐resolution imaging.

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.

Modeling of porosity and grain size effects on mechanical behavior of additively manufactured structures

Additive manufacturing (AM) methods such as Aerosol Jet (AJ) printing allow the fabrication of structures via sintering of micro and/or nanoparticles, leading to microstructures that consist of various combinations of pore and grain sizes. It has been reported that AJ printed and sintered silver micropillars show an unusual behavior of high stiffness and high strain-to-failure for structures with high porosity and vice versa (Saleh et al. 2018 [1]). This behavior, however, is accompanied by the stiffer structures having smaller grain sizes and softer structures having larger grain sizes. To explain the physics of this behavior where a trade-off between hardening caused by size effects (grain refinement and gradients) and softening caused by porosity is expected to play a critical role, a multi-scale modeling approach is proposed in this paper. The model formulation consists of a continuum dislocation dynamics (CDD) framework, coupled with continuum plasticity and finite element analysis. The dislocation dynamics formulation is introduced into a user material subroutine and coupled with a finite element commercial solver, in this case, LS-DYNA, to solve the model in three-dimensional scale with the same size as the AM micropillars. The results from the model capture the general trends observed in compression tests of AM micropillars. In particular, it is shown that the grain size and dislocation density have a disproportionately higher influence over the mechanical deformation of metallic structures when compared to the porosity. These results show that the behavior of AM structures in the plastic regime is dominated by grain size effects rather than porosity. Some limitations of the model and possible future refinements are discussed. The paper provides an important analytical framework to model the mechanical behavior of AM structures with internal porosity in the plastic regime.

Nonlinear dynamic analysis of Qom Monorail Bridge considering Soil-Pile-Bridge-Train Interaction

Railway tracks experience has shown that considering the effects of Soil-Structure Interaction (SSI) especially for soft soil sites is necessary. These effects can also be important for monorail bridges on soft soil beds. The main aim of this study is to investigate the effects of Soil-Pile-Bridge-Train Interaction (SPBTI) on the Qom Monorail Bridge (QMB) responses. In spite of many studies on the effects of monorail train-bridge (fixed-base structure) interaction, very little information is available in the literature on the effects of monorail trains on SPB systems. In this paper, an advanced three-dimensional (3D) continuum finite element analysis of QMB subjected to train moving loads was developed. The SPBT models have been validated using three case studies (two bridge-monorail train studies and a soil-pile-structure study) available in the literature. The maximum displacements of the guideway beam at the different train speeds were obtained for various SPBT system conditions. The effects of the stiffness and thickness of the soil, the bridge span length, and the amplitude, length, and geometry of the train loading on the critical speed of the SPBT system are discussed in detail. Finally, the results have been synthesized into simple design charts to select the appropriate straddle-type monorail train and determine its critical speed for a particular soil-bridge condition. In addition, a new simple method for simulating the behavior of the finger-bands (as one of the excitation source of vertical bridge vibrations) in commercial software was presented. The results show that the position of a monorail train bogies plays an important role in determining critical speed so that with uniformity the spacing between the bogies decreases the critical speed in the vertical direction.

Development and validation of p‐y modeling approach for seismic response predictions of highway bridges

SummaryThis study aims to realistically simulate the seismic responses of typical highway bridges in California with considerations of soil–structure interaction effects. The p‐y modeling approaches are developed and validated for embankments and pile foundations of bridges. The p‐y approach models the lateral and vertical foundation flexibility with distributed p‐y springs and associated t‐z and q‐z springs. Building upon the existing p‐y models for pile foundations, the study develops the nonlinear p‐y springs for embankments based on nonlinear 2D and 3D continuum finite element analysis under passive loading condition along both longitudinal and transverse directions. Closed‐form expressions are developed for two key parameters, the ultimate resistant force pult and the displacement y50, where 0.5pult is reached, of embankment p‐y models as functions of abutment geometry (wall width and height, embankment fill height, etc.) and soil material properties (wall‐soil friction angle, soil friction angle, and cohesion). In order to account for the kinematic and site responses, depth‐varying ground motions are derived and applied at the free‐end of p‐y springs, which reflects the amplified embankment crest motion. The modeling approach is applied to simulate the seismic responses of the Painter Street Bridge and validated through comparisons with the recorded responses during the 1992 Petrolia earthquake. It is demonstrated that the flexibility and motion amplification at end abutments are the most crucial modeling aspects. The developed p‐y models and the modeling approach can effectively predict the seismic responses of highway bridges. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Effect of strain hardening and volume fraction of crystalline phase on strength and ductility of bulk metallic glass composites

Continuum finite element analyses are performed to ascertain the role played by the volume fraction (Vf) and strain hardening behavior of crystalline reinforcements on the strength and ductility of bulk metallic glass matrix composites (BMGCs). Results show that a highly strain hardening elongated dendrite with Vf ~45% would make the BMGC ductile without any penalty on the strength. These results provide design guidelines for strong yet ductile BMGCs.

Notch sensitivity in nanoscale metallic glass specimens: Insights from continuum simulations

Recent experiments have shown that nano-sized metallic glass (MG) specimens subjected to tensile loading exhibit increased ductility and work hardening. Failure occurs by necking as opposed to shear banding which is seen in bulk samples. Also, the necking is generally observed at shallow notches present on the specimen surface. In this work, continuum finite element analysis of tensile loading of nano-sized notched MG specimens is conducted using a thermodynamically consistent non-local plasticity model to clearly understand the deformation behavior from a mechanics perspective. It is found that plastic zone size in front of the notch attains a saturation level at the stage when a dominant shear band forms extending across the specimen. This size scales with an intrinsic material length associated with the interaction stress between flow defects. A transition in deformation behavior from quasi-brittle to ductile becomes possible when this critical plastic zone size is larger than the uncracked ligament length. These observations corroborate with atomistic simulations and experimental results.

Variation of cutting forces in machining of f.c.c. single crystals

In this study, micro-machining of f.c.c. single-crystal materials was investigated based on a hybrid modelling approach combining smoothed particle hydrodynamics and continuum finite element analysis. The numerical modelling was implemented in the commercial software ABAQUS/Explicit by employing a user-defined subroutine VUMAT for a crystal plasticity formulation to gain insight into the underlying mechanisms that drive a plastic response of materials in high deformation processes. The numerical studies demonstrate that cutting force variations in different cutting directions are similar for different f.c.c. crystals even though the magnitudes of the cutting forces are different.

A novel approach for time-dependent axial soil resistance in the analysis of subsea pipelines

A novel approach for modelling axial pipe–soil interaction, consisting of bespoke finite elements, is proposed. The purpose is to have a model that represents a two-dimensional slice of soil perpendicular to the pipe which is computationally cheap enough to be incorporated in global analysis of subsea pipelines, whilst capable of capturing detailed time-dependent soil response, which involves partial drainage and cyclic plasticity. This is achieved by handling the circumferential dimension analytically, reducing the behaviour of the two-dimensional soil slice to a one-dimensional case. Coupled consolidation analysis along a vertical sequence of one-dimensional elements beneath each pipeline node, tailored to represent the axial–vertical (or -radial) plane across the seabed semi-space, is supplemented by an analytical solution for the circumferential drainage. The paper presents the model development, its implementation through symbolic programming and validation against previously published continuum finite element analysis results.

Experimental Validation of Finite Element Analysis of Human Vertebral Collapse Under Large Compressive Strains

Osteoporosis-related vertebral fractures represent a major health problem in elderly populations. Such fractures can often only be diagnosed after a substantial deformation history of the vertebral body. Therefore, it remains a challenge for clinicians to distinguish between stable and progressive potentially harmful fractures. Accordingly, novel criteria for selection of the appropriate conservative or surgical treatment are urgently needed. Computer tomography-based finite element analysis is an increasingly accepted method to predict the quasi-static vertebral strength and to follow up this small strain property longitudinally in time. A recent development in constitutive modeling allows us to simulate strain localization and densification in trabecular bone under large compressive strains without mesh dependence. The aim of this work was to validate this recently developed constitutive model of trabecular bone for the prediction of strain localization and densification in the human vertebral body subjected to large compressive deformation. A custom-made stepwise loading device mounted in a high resolution peripheral computer tomography system was used to describe the progressive collapse of 13 human vertebrae under axial compression. Continuum finite element analyses of the 13 compression tests were realized and the zones of high volumetric strain were compared with the experiments. A fair qualitative correspondence of the strain localization zone between the experiment and finite element analysis was achieved in 9 out of 13 tests and significant correlations of the volumetric strains were obtained throughout the range of applied axial compression. Interestingly, the stepwise propagating localization zones in trabecular bone converged to the buckling locations in the cortical shell. While the adopted continuum finite element approach still suffers from several limitations, these encouraging preliminary results towards the prediction of extended vertebral collapse may help in assessing fracture stability in future work.

FE/SPH modelling of orthogonal micro-machining of f.c.c. single crystal

With an increased use of mechanical micro-machining in manufacture of small-sized components with complex geometries, the need to understand mechanics of machining at micro-scale is recognized. Numerical modelling is a powerful tool which can be used to gain insight into the underlying mechanisms that drive a plastic response of materials in high-deformation processes. Excessive element distortion in a finite-element simulation is a fundamental problem in numerical modelling of machining processes. In this study, we present a hybrid modelling approach for micro-machining of crystalline metals with the use of smoothed particle hydrodynamics and continuum finite element analysis to overcome this problem. The model is implemented in a commercial software ABAQUS/Explicit using a user-defined subroutine (VUMAT). The model is used to elucidate the effect of crystallographic anisotropy on a response of face centred cubic (f.c.c.) metals to machining. Based on our study, cutting in the (100) plane is least sensitive to the cutting direction with (101) plane being the most sensitive. The maximum cutting force is observed to be on the (101) plane with the cutting tool oriented in the 0°.

Numerical Modeling of Buried HDPE Pipelines Subjected to Normal Faulting: A Case Study

A systematic study is presented herein on the seismic response of buried pipelines subjected to ground fault rupture in the form of normal faulting. In this study, advanced computational simulations are conducted in parallel with physical testing using a geotechnical centrifuge. For the numerical simulations, the pipeline was modeled using isotropic 3-D shell elements and the soil was modeled using either 1-D spring elements or 3-D solid (continuum) elements. The results from continuum finite-element analyses are compared with those from a Winkler-type model (in which the pipe is supported by a series of discrete springs) and with results from centrifuge tests. In addition, via appropriate modeling of the soil-pipe interaction, the q-z relation of the soil medium is elucidated for normal faulting events. The numerical analysis results demonstrate the potential for continuum modeling of events that induce pipe-soil interaction and results in improved understanding of pipe-soil interaction under normal faulting.

二维裂隙密度及其渗透率的逾渗关系研究

在低渗透介质储存中，裂隙是石油运移的主要通道。因而裂隙介质的渗透率是石油勘探的一个重要参数。应用连续逾渗模型分析，把低渗透储存的裂隙网络合理简化，能够对深层复杂介质的渗透规律进行研究。使用排除体积对裂隙密度进行无量纲化，从而使裂隙的宏观性与裂隙的形状无关。使用Monte Carlo方法模拟得到不同裂隙密度时的裂隙网络图，然后基于连续逾渗模型，采用有限元方法利用COMSOL Multiphysics求解器解，数值模拟得到裂隙的渗透率与无量纲化密度成乘幂关系。该模拟结果可能为裂隙网络渗透率的定量评价提供一个简单而又实用的方法。这一规则的发现也增强了逾渗理论在油气田勘探中的应用。 Fracture networks strongly influence oil migration in reservoirs, especially in low-permeability reservoirs. So the parameter of fracture permeability plays an important role during the exploration of oil and gas fields. Simplifying the fracture network of reservoirs, and continuum percolation theory are successfully applied for studying the fracture permeability in deep and complex media. By using excluded area to dimensionless the fracture density, macroscopic properties of fracture networks become independent of fracture shape. Using Monte Carlo simulation, the facture net-work with different fracture density is obtained, and then based on continuum percolation theory and finite element analysis software, called COMSOL Multiphysics, we get the relationship between dimensionless density and macro-scopic permeability, which is scaling law. The simulated results may offer a simple and practical method to evaluate frac-ture permeability quantitatively and enhance the applications of percolation theory in the exploration of oil and gas fields.

Cavitation in materials with distributed weak zones: Implications on the origin of brittle fracture in metallic glasses

Several experimental studies have shown that fracture surfaces in brittle metallic glasses (MGs) generally exhibit nanoscale corrugations which may be attributed to the nucleation and coalescence of nanovoids during crack propagation. Recent atomistic simulations suggest that this phenomenon is due to large spatial fluctuations in material properties in a brittle MG, which leads to void nucleation in regions of low atomic density and then catastrophic fracture through void coalescence. To explain this behavior, we propose a model of a heterogeneous solid containing a distribution of weak zones to represent a brittle MG. Plane strain continuum finite element analysis of cavitation in such an elastic-plastic solid is performed with the weak zones idealized as periodically distributed regions having lower yield strength than the background material. It is found that the presence of weak zones can significantly reduce the critical hydrostatic stress for the onset of cavitation which is controlled uniquely by the local yield properties of these zones. Also, the presence of weak zones diminishes the sensitivity of the cavitation stress to the volume fraction of a preexisting void. These results provide plausible explanations for the observations reported in recent atomistic simulations of brittle MGs. An analytical solution for a composite, incompressible elastic-plastic solid with a weak inner core is used to investigate the effect of volume fraction and yield strength of the core on the nature of cavitation bifurcation. It is shown that snap-cavitation may occur, giving rise to sudden formation of voids with finite size, which does not happen in a homogeneous plastic solid.