Elasto-plastic Finite Element Research Articles

A plastic correction algorithm for full-field elasto-plastic finite element simulations: critical assessment of predictive capabilities and improvement by machine learning

AbstractThis paper introduces a new local plastic correction algorithm that is aimed at accelerating elasto-plastic finite element (FE) simulations for structural problems exhibiting localised plasticity (around e.g. notches, geometrical defects). The proposed method belongs to the category of generalised multi-axial Neuber-type methods, which process the results of an elastic prediction point-wise in order to calculate an approximation of the full elasto-plastic solution. The proposed algorithm relies on a rule of local proportionality, which, in the context of J2 plasticity, allows us to express the plastic correction problem in terms of the amplitude of the full mechanical tensors only. This lightweight correction problem can be solved for numerically using a fully implicit time integrator that shares similarities with the radial return algorithm. The numerical capabilities of the proposed algorithm are demonstrated for a notched structure and a specimen containing a distribution of spherical pores, subjected to monotonic and cyclic loading. As a second point of innovation, we show that the proposed local plastic correction algorithm can be further accelerated by employing a simple meta-modelling strategy, with virtually no added errors. At last, we develop and investigate the merits of a deep-learning-based corrective layer designed to reduce the approximation error of the plastic corrector. A convolutional architecture is used to analyse the neighbourhoods of material points and outputs a scalar correction to the point-wise Neuber-type predictions. This optional brick of the proposed plastic correction methodology relies on the availability of a set of full elasto-plastic finite element solutions to be used as a training data-set.

Axial capacity of cold-formed steel channel sections with slits

Cold-formed steel (CFS) studs often include slits in their webs to improve thermal performance. However, the inclusion of such slits reduces their axial capacity. The literature contains limited experimental studies on the axial capacity of these studs with slits, and no non-linear elasto-plastic finite element studies have been reported. This research aims to address this gap. Non-linear elasto-plastic finite element models were developed and validated against experimental test results. A parametric study consisting of 960 finite element analysis (FEA) models was then conducted, covering the effects of different channel dimensions, slit sizes, section thicknesses, and stud lengths. Ultimate axial capacities obtained from these analyses were compared to the current codified direct strength method (DSM) predictions as per the Australian/New Zealand Standard AS/NZS 4600. Finally, design recommendations in the form of strength reduction factors are proposed. Based on these recommendations, modified DSM design equations with a reliability index above 2.5 are presented.

Uncertainty quantification for damage detection in 3D-printed auxetic structures using ultrasonic guided waves and a probabilistic neural network

Auxetic structures hold significant potential for applications due to their outstanding properties. Ultrasonic waves and neural networks are the popular technologies used for structural health monitoring (SHM). To increase the reliability of the neural network output for SHM, comprehensive uncertainty quantification is needed for damage detection in unknown areas of auxetic structures. This paper presents the first comprehensive framework for health diagnosis and uncertainty quantification based on ultrasonic guided waves in two 3D-printed star hourglass honeycomb auxetic structures. The proposed framework integrates in-plane compression with simultaneous ultrasonic testing to receive ultrasonic signals across various deformation states. Additionally, fully elastic and elasto-plastic finite element simulations are conducted to analyze wave energy variations and mechanical responses in auxetic structure. Critical damage deformation is identified based on observed deformation patterns and variations in signal energy. The Hilbert transform is used to extract two damage-sensitive features, namely envelope and phase. These features serve as input data for the Flipout probabilistic convolutional neural network (FPCNN) model, which integrates pseudo-independent weight perturbations and a Gaussian probabilistic layer within the visual geometry group 13 architecture to predict structural deformations and associated uncertainties. The UQ framework effectively separates and quantifies the predictive variance of the FPCNN model into aleatoric and epistemic uncertainty. The framework’s effectiveness is demonstrated through the comprehensive approach, combining compression and ultrasonic tests, finite element simulation, and the FPCNN technique.

Elastoplastic finite element simulation of domino fault formation associated with tilting of highly structured ground

Ground deformation on the Earth’s surface layer is strongly affected by the nonlinearity of geomaterials. However, the formation process of such deformation has yet to be described in a unified manner based on mechanics. The present study focuses on the normal faults in a submarine ground with highly developed soil skeleton structures and attempts to reproduce the process of normal fault formation associated with the tilting of a horizontally deposited submarine ground using an elastoplastic finite element simulation. The simulation was conducted using the soil–water coupled finite deformation analysis code GEOASIA, which incorporates an elastoplastic constitutive equation of the soil skeleton based on the modified Cam-clay model and the soil skeleton structure concept. The key findings are as follows:1) Normal faults are formed from the ground surface to depth as shear bands, where shear strain is localized while exhibiting softening behavior with plastic volume compression.2) Multiple normal faults are almost equally spaced and parallel to each other, with the inter-fault blocks rotating backward. The morphology of normal faults formed by the tilting of the ground shows domino-style characteristics.3) The degree of the soil skeleton structure influences the formation of normal faults.This study demonstrates that elastoplastic geomechanics can explain the formation process of ground deformation, which has usually been interpreted from the perspectives of geomorphology and geology.

A wavelet-based denoising method for pipeline dent assessments

Strain-based assessments of dents in buried steel oil and gas pipelines are commonly carried out in practice. Dent signals obtained from the caliper inspection tool contain noises that can have a large impact on the accuracy of the estimated strain. This paper proposes a novel wavelet-based denoising method for dent signals based on the overcomplete expansion with the corresponding dictionary constructed using the stationary and hyperbolic wavelet transforms. The proposed method is validated based on noise-free and noisy dent signals generated from elasto-plastic finite element analyses of a pipe segment subjected to an indenter and shown to be more effective than the commonly used wavelet transform-based hard- and soft-thresholding methods in terms of the root mean square error and the accuracy of the effective dent strain estimated from the denoised signal. The proposed method is further employed to denoise 42 real dent signals from in-service pipelines to illustrate its effectiveness and potential practical application to facilitate strain-based dent assessments.

Effect of unit cell rotation on mechanical performance of selective laser melted Gyroid structures for bone tissue engineering

Gyroid lattice structures, inspired by the natural interconnectivity of human bone, show promise in bone tissue engineering (BTE). This study explores the mechanical properties, and failure mechanisms of selective laser melted (SLM) Gyroid Ti6Al4V lattice structures with varying unit cell rotation angles (RA) of 0∘ (G0), 30∘ (G30), and 60∘ (G60) around the x-axis. The study assesses their mechanical and energy absorption properties through quasi-static compression testing and elastoplastic finite element (FE) analysis. Despite similar relative densities for all designed lattices, the RA variation significantly impacts mechanical performance. G30 exhibits superior load-bearing capacity, with higher modulus of elasticity, yield strength, ultimate strength, and plateau stress. It also has the highest energy absorption capacity, while G60 shows the highest surface area (SA) and surface area-to-volume ratio (SA/VR). These findings highlight the potential of Gyroid lattices for bone replacements due to their tunable mechanical and biological responses.

A multiobjective optimization framework based on FEA, ANN, and NSGA-II to optimize the process parameters of tube-to-tubesheet joint

This study presents a multiobjective optimization framework that integrates Artificial Neural Network (ANN) and Non-dominated Sorting Genetic Algorithm-II (NSGA-II) for the optimization of rolling process parameters of tube-to-tubesheet joint (TTT-joint). During the rolling process, both beneficial contact pressure and detrimental tensile residual stress are generated within the joint. The primary objective of this framework is to minimize the tensile residual stress while maximizing the contact pressure in the TTT-joint. To achieve this, a backpropagation ANN model is trained to rapidly estimate the residual stress and contact pressure for various sets of rolling process parameters. For training purposes, a series of nonlinear elastoplastic finite element (FE) simulations are performed to generate the input database for the neural network. A detailed parametric study is performed based on the axisymmetric FE model of the TTT-joint. The trained neural network is then incorporated into the NSGA-II optimization algorithm to find the fitness function and optimized process parameters. The contact pressure and residual stress predicted by the proposed ANN-NSGA-II framework are validated by finite element analysis (FEA) using the optimized parameters. The present analysis established that the proposed methodology can be applied in practical engineering problems to obtain the process parameters that yield the maximum contact pressure and minimum tensile residual stress in the TTT-joint.

The influence of welding-induced 3D residual stress and distortion on the ultimate strength of multi-stiffened thin plate structures under cyclic load

Stiffened thin plates made of high-strength steel are widely employed in ship hull structures. Their strength capacity is highly sensitive to the welding imperfections and potential extreme cyclic loading from harsh sea state. In this work, a thermal elasto-plastic finite element analysis is conducted to simulate the 3D distribution of welding-induced residual stress and distortion of stiffened thin plate structures with triple spans and triple bays varying the plate thickness and heat input. Experimental results provided by other scholars are used to validate the welding simulation. Afterwards, the ultimate strength and collapse behaviour of the welded structures under different load patterns are dealt with, including monotonic compression load, cyclic compression-tension load and cyclic compression load. Observation from numerical results indicates that, in general, the compressive strength is reduced in each considered cycle by the residual stress as the amplitude of cyclic compression-tension load approximates to the ultimate compressive strain. When this parameter is much greater than the ultimate compressive strain or the stiffened plate is subjected to cyclic compression load, the reduction in ultimate strength is significant in the first cycle, whereas the reduction is ignorable in the later cycles. Besides, if the buckling mode of initial deflection with antisymmetric configuration is superposed to the symmetric out-of-plane welding distortion, impact of the residual stress will be diminished as the asymmetry becomes notable.

Ultimate Bearing Capacity of Weak Foundations under Coal Pillars

In many underground coal mines, a seam is underlain by weak floor material, and the load-carrying capacity of a pillar may be limited not by its own strength but by the bearing capacity of the floor. It has been proposed that bearing capacity may be estimated by formulae such as those of Terzaghi for structural footings on soil, but that approach is generally not valid because, for the slip surfaces assumed in the derivations of the formulae, the rock rises out of the floor beneath adjacent pillars. In the limiting equilibrium analysis proposed here, the distance to the side of a pillar to which a slip surface extends can be constrained according to the roadway or bord width. Examples are shown of the computation of bearing capacities of both homogeneous and multilayer dry and fully saturated floors, and results compared with those of elastoplastic finite element analysis. An approximate comparison with bearing capacities according to Terzaghi's formula for a strip footing is also presented for the hypothetical cases of wider roadways for which the assumed slip surfaces do not extend under adjacent pillars. For the cases considered, there is satisfactory agreement with Terzaghi’s analysis and good agreement with the results of finite element analysis. However, only one finite element analysis was carried out, and it remains to be seen whether such agreement is consistently achieved for ranges of floor strength parameters and horizontal stress.

3D slope stability analysis considering strength anisotropy by a micro-structure tensor enhanced elasto-plastic finite element method

This article presents a micro-structure tensor enhanced elasto-plastic finite element (FE) method to address strength anisotropy in three-dimensional (3D) soil slope stability analysis. The gravity increase method (GIM) is employed to analyze the stability of 3D anisotropic soil slopes. The accuracy of the proposed method is first verified against the data in the literature. We then simulate the 3D soil slope with a straight slope surface and the convex and concave slope surfaces with a 90° turning corner to study the 3D effect on slope stability and the failure mechanism under anisotropy conditions. Based on our numerical results, the end effect significantly impacts the failure mechanism and safety factor. Anisotropy degree notably affects the safety factor, with higher degrees leading to deeper landslides. For concave slopes, they can be approximated by straight slopes with suitable boundary conditions to assess their stability. Furthermore, a case study of the Saint-Alban test embankment A in Quebec, Canada, is provided to demonstrate the applicability of the proposed FE model.

Ejector pin-related high-cycle fatigue fracture of the critical die corner during automatic multistage cold forging of an automotive wheel nut

An experimental and numerical study on the ejector pin's mechanics during automatic multistage cold forging (AMSCF) of an automobile wheel nut is conducted. The traditional, decoupled die structural analysis method (DDSM) of analyzing die structures as one of the post-processing functions is criticized, which uses the tractions exerting on the die parts predicted from the forging simulation under the rigid die assumption. To cope with the matter of the DDSM, a multibody treatment scheme (MBTS) is proposed to simulate the AMSCF process, emphasizing the ejector pin's mechanics, using an implicit elastoplastic finite element method. The experiments qualitatively validate the finite element predictions. It is shown that the asymmetric sheared material in AMSCF greatly influences the ejector pin's mechanics, which is characterized by its lateral and longitudinal displacements because of its structural flexibility. It is emphasized that the detailed understanding of the ejector pin's mechanics may not only give a helpful connection towards smart manufacturing because of its mechanical flexibility and sensitivity to the excitations and responses, but it also reveals the reason for the die's high-cycle fatigue (HCF) fracture of the critical die corner (CDC) near at the end of the ejector pin.

Effects of anisotropy and infill pattern on compression properties of 3D printed CFRP: mechanical analysis and elasto-plastic finite element modelling

PurposeFinite element (FE) analysis can be used for both design and verification of components. In the case of 3D-printed materials, a proper characterization of properties, accounting for anisotropy and raster angles, can help develop efficient material models. This study aims to use compression tests to characterize short carbon-reinforced PA12 made by fused filament fabrication (FFF) and to model its behaviour by the FE method.Design/methodology/approachIn this work, the authors focus on compression tests, using post-processed specimens to overcome external defects introduced by the FFF process. The material’s elastoplastic mechanical behaviour is modelled by an elastic stiffness matrix, Hill’s anisotropic yield criterion and Voce’s isotropic hardening law, considering the stacking sequence of raster angles. A FE analysis is conducted to reproduce the material’s compressive behaviour through the LS-DYNA software.FindingsThe proposed model can capture stress values at different deformation levels and peculiar aspects of deformed shapes until the onset of damage mechanisms. Deformation and damage mechanisms are strictly correlated to orientation and raster angle.Originality/valueThe paper aims to contribute to the understanding of 3D-printed material’s behaviour through compression tests on bulk 3D-printed material. The methodology proposed, enriched with an anisotropic damage criterion, could be effectively used for design and verification purposes in the field of 3D-printed components through FE analysis.

Finite element analyses of burst capacities of corroded pipelines containing pinhole-in-corrosion defects

This study carries out extensive parametric three-dimensional elasto-plastic finite element analysis to evaluate the burst capacity of oil and gas pipelines containing pinhole-in-corrosion (PIC) defects. The analysis results reveal that the burst capacity of the PIC defect is insensitive to the pinhole diameter but largely affected by the depth of the pinhole and length of the general corrosion. A pinhole located at the centre of the general corrosion is found to have a larger impact on the burst capacity than the same pinhole located near the edge of the general corrosion. The observed size and location effects on the burst capacity are attributed to the bulging deformation of a corroded pipeline under internal pressure. The findings of this study provide the basis for developing a practical, accurate engineering burst capacity model for PIC defects.

Assessment of Thermal Osteonecrosis during Bone Drilling Using a Three-Dimensional Finite Element Model.

Bone drilling is a common procedure used to create pilot holes for inserting screws to secure implants for fracture fixation. However, this process can increase bone temperature and the excessive heat can lead to cell death and thermal osteonecrosis, potentially causing early fixation failure or complications. We applied a three-dimensional dynamic elastoplastic finite element model to evaluate the propagation and distribution of heat during bone drilling and assess the thermally affected zone (TAZ) that may lead to thermal necrosis. This model investigates the parameters influencing bone temperature during bone drilling, including drill diameter, rotational speed, feed force, and predrilled hole. The results indicate that our FE model is sufficiently accurate in predicting the temperature rise effect during bone drilling. The maximum temperature decreases exponentially with radial distance. When the feed forces are 40 and 60 N, the maximum temperature does not exceed 45 °C. However, with feed forces of 10 and 20 N, both the maximum temperatures exceed 45 °C within a radial distance of 0.2 mm, indicating a high-risk zone for potential thermal osteonecrosis. With the two-stage drilling procedure, where a 2.5 mm pilot hole is predrilled, the maximum temperature can be reduced by 14 °C. This suggests that higher feed force and rotational speed and/or using a two-stage drilling process could mitigate bone temperature elevation and reduce the risk of thermal osteonecrosis during bone drilling.

A Study on the Effects of Welding Deformation According to Weld Sequence in Overlay-Welded Structures

In this study, thermal elasto-plastic finite element analysis was conducted to derive the optimal welding sequence to minimize overlay welding deformation on the water wall panels of an SRF (solid refuse fuel) boiler. The water wall panels of an SRF boiler are exposed to high temperatures and corrosive environments, making overlay welding essential. However, because the length of the water wall panels and tubes exceeds 7 m, significant deformation occurs after overlay welding. Additionally, due to the large size of the water wall panels, full-size thermal elasto-plastic analysis requires huge computational costs. Therefore, in this study, the effects of welding sequence on overlay welding deformation were first investigated for a reduced model to derive the optimal welding sequence. Subsequently, an analysis model for the full-size pipe panels was established to compare and analyze the conventional welding sequence with the optimal welding sequence, thereby verifying the validity of the study. According to the welding sequence derived from the reduced model, welding deformation in the full-size model was significantly reduced compared to the conventional sequence. This reduction in deformation was discussed by analyzing the deformation behavior of the structure at each stage of the overlay welding process.

Numerical simulation of the uplift bearing behavior of pile foundations for transmission towers in expansive soil area

Piles are commonly used as foundations for power transmission towers located in expansive soil areas. The strength of expansive soil is highly sensitive to the changing water content, which complicates the pile–soil interaction. In this study, a 3D elastoplastic finite element analysis of a typical pile foundation for a transmission tower in an expansive soil area was conducted to understand the effect of water content in expansive soil on the uplift bearing capacity of the pile foundation. The results that the failure mode of the pile foundation is almost unaffected by the water content. Shear failure was observed at the pile–soil interface, and, when the pile was pulled out, it lost its uplift bearing capacity. With the increasing water content of the soil, the ultimate uplift bearing capacity of the pile foundation exhibited a significant decreasing trend, whereas the displacement of soil around the pile became remarkable. The distribution of pile axial force and lateral frictional resistance during the uplift process was also evaluated. The pile axial force decreased gradually and at a higher rate with increasing depth. Once the pile reached the ultimate uplift bearing state, the pile lateral friction increased almost linearly with depth.

Artificial neural networks-based J-integral prediction for cracked bodies under elasto-plastic deformation state –cyclic loading

The study builds upon a prior modeling framework designed for monotonic loading to compute the cyclic J-integral encompassing a crack tip experiencing elastic–plastic deformation due to cyclic loads. The proposed modeling approach extends the authors' earlier time-efficient method for computing the J-integral by combining artificial neural networks (ANNs) with finite element (FE) analyses. The ANN-FE integration allows efficient and accurate prediction of elastic–plastic stresses, strains and displacement fields for a crack body under cyclic loadings from the linear elastic FE solution. In the context of cyclic loading, stress, strain, and displacement fields near the crack tip of stainless steel (SS304) are determined by FE analyses under both elastic and elasto-plastic states for various crack sizes and R-ratios. ANNs models are developed to establish the nonlinear relationship between these two states. Consequently, the proposed approach enables the prediction of the elasto-plastic cyclic J-integral through the equivalent domain integral method, based on the elastic FE solution bypassing the need of a complicated elasto-plastic FE solution under cyclic loadings. The results show that this approach can effectively predict elasto-plastic cyclic J-integral while avoiding the complex computation of elastic–plastic deformation fields around the crack tip during cyclic loadings.

Simulation of crack closure effect on cracked beam vibrations

Vibrations of beams containing cracks are usually investigated by using open or breathing crack models. Neither one of these approaches considers the plasticity induced crack closure (PICC) phenomena which occurs in fatigue crack growth. In this study, PICC is integrated into the vibration analysis of a cracked beam. First, fatigue crack growth at a notch is simulated with elastoplastic finite element analysis. Residual deformations, stresses and the contact pressures on crack faces are obtained. In the second phase, the model which includes these quantities is used for forced vibration analysis under harmonic loading by using implicit finite element method. For comparison, analyses are also running without PICC. Simulation results indicate that PICC has a significant effect on vibrations of cracked beams. For low load amplitude levels, cracked beam behaves like an intact beam. Nonlinear behavior appears only at rather high amplitude levels. It is concluded that PICC could suppress the crack breathing behavior and this could make it difficult to detect a fatigue crack in a beam from its nonlinear vibration response.

Basal stability analysis of braced excavations with flexible embedded walls in undrained clay

An upper bound mechanism for the basal stability analysis in non-homogeneous undrained clay is presented. The current streamline-based velocity field formulas are extended into broader forms, allowing for the deformation compatibility between the wall and the soil. The proposed mechanism, comprising three shear zones, integrates consideration of the plastic bending moment of the embedded wall. The present study is validated by comparisons with solutions from the finite element limit analysis and elastoplastic finite element analysis. Results demonstrate that the proposed mechanism yields lower upper bounds compared to existing analytical methods, with predicted failure surfaces aligning well with elastoplastic finite element analysis and finite element limit analysis outcomes. Furthermore, a novel dimensionless number is proposed to quantify the relative strength of the plastic bending moment to soil undrained strength. Investigation into the influence of wall plastic bending moment, soil non-homogeneity, and wall penetration depth reveals beneficial effects. Following the analysis of case studies, it becomes evident that the proposed mechanism offers more dependable predictions compared to the existing circular upper bound mechanism.

Optimizing Interfaces in Laser-Brazed Ceramic-Stainless Steel Joints for Hydrothermal Sensors through Finite-Element Modeling

The development of reliable joining techniques for ceramics and metals is crucial for energy applications, such as fuel cells, nuclear reactors, and high-temperature sensors, most especially for the sealing of hydrothermal sensors to study multiphase flows. However, during one-step active laser brazing it is a serious problem that a high thermal stress concentration can occur at the joint interfaces or on the ceramic side of the joint due to mismatches between the CTEs (coefficients of thermal expansion) and/or elastic constants. The uncontrolled thermal residual stress can lead to cracks and defects in the brazement. In the present work, an elastoplastic finite element method/numerical model was formulated to study the thermal residual stresses developed in the brazement between ceramics and austenitic stainless steel during cooling in active laser brazing. Calculations and comparison experiments were conducted to validate the simulated stress distribution in un-patterned ceramics. Stress analyses were conducted for planar and cylindrical specimen geometries (lab joints) relevant for miniaturized energy sensors. Laser interface patterning was employed to create micro-scale features on ceramic interfaces that reduce thermal stress concentrations. The optimization of the interface designing parameters including hatch size, structure width, pattern depth and metal/ceramic thickness ratio was performed using the Taguchi method with orthogonal arrays. The study suggests that laser interface structuring can modify thermal residual stresses in ceramic-to-metal brazements, thereby increasing the reliability of active brazing joints.