Plane Strain Finite Element Analysis Research Articles

Deformation in the wrinkle–crease transformation

We investigate deformation in the wrinkle–crease transformation to reveal the missing link between the wrinkling and creasing instabilities, which occur on the surface of elastomers under compression. Plane-strain finite element (FE) analysis is performed by combining a nonlinear perturbation approach to find two bifurcated solutions for the flat surface in a metastable state. The first solution is the stable deformation path for crease evolution, and the second solution is the previously unknown unstable deformation path from wrinkling to creasing. The two deformation paths are not independent, and they are connected at the critical strain for creasing εC. The resulting deformation at εC acts as a precursive deformation to cause creasing. Although the unstable path is initiated by the wrinkling instability as a bifurcation, the creasing instability (i.e., εC) is interpreted as the singular point at which the unstable path switches to the stable path. A chain reaction model is developed to describe the mechanism and deformation of the wrinkle–crease transformation, and it shows good agreement with the FE prediction within an inevitable limitation of FEs.

Correction of Plane Strain Analyses for Corrugated Metal Culverts Subjected to Patch Loads

Today, culverts are often analyzed and designed using plane strain finite element analyses in which a transverse slice of the structure is simulated and assumed equal to any other slice. Although this works well for soil loads, in reality live loads are discrete pressure loads from tires, and the out-of-plane effects can be significant, especially when cover depths are relatively low. While current design specifications define minimum cover that precludes significant localized pressure effects on culverts, many culverts are currently in service that were constructed under very shallow cover depths. In this study, analyses of corrugated metal culverts under truck load were carried out using two-dimensional (2D) (plane strain) and three-dimensional (3D) finite element analyses to assess the difference between structural responses predicted by these two approaches. Thirty-six culvert models with different shapes, spans, and cover depths were created using both 2D and 3D meshes. A significant difference was found between the results of these two analysis methods. Specifically, the thrust from the 3D models under shallow cover can be as much as three times the thrust results from the 2D model, which is unconservative from a safety standpoint. An innovative explanation was provided to explicate the differences. Finally, to address the issue, a reduction ratio method was developed to correct the 2D results to match the corresponding 3D results so that the relatively simple plane strain approach can be used.

Deterministic and probabilistic analysis of great-depth braced excavations: A 32 m excavation case study in Paris

The Fort d’Issy-Vanves-Clamart (FIVC) braced excavation in France is analyzed to provide insights into the geotechnical serviceability assessment of excavations at great depth within deterministic and probabilistic frameworks. The FIVC excavation is excavated at 32 m below the ground surface in Parisian sedimentary basin and a plane-strain finite element analysis is implemented to examine the wall deflections and ground surface settlements. A stochastic finite element method based on the polynomial chaos Kriging metamodel (MSFEM) is then proposed for the probabilistic analyses. Comparisons with field measurements and former studies are carried out. Several academic cases are then conducted to investigate the great-depth excavation stability regarding the maximum horizontal wall deflection and maximum ground surface settlement. The results indicate that the proposed MSFEM is effective for probabilistic analyses and can provide useful insights for the excavation design and construction. A sensitivity analysis for seven considered random parameters is then implemented. The soil friction angle at the excavation bottom layer is the most significant one for design. The soil-wall interaction effects on the excavation stability are also given.

Effectiveness of soil improvement for deep excavation in under-consolidated soil: A case study

The main objective of this article is to investigate the effectiveness of soil improvement methods, such as jet grouting and cement deep mixing, for a deep excavation in under-consolidated soil. A well-documented case history, located in Zhuhai, China, was used for analysis. The analyses were conducted using two-dimensional plane-strain finite element analysis. The studies included an examination of the effect of wall length on lateral wall deformation, the effect between the degree of consolidation and lateral wall deformation, and the influence of soil improvement on lateral deformation and settlement. The deformations induced by under consolidating states are greater than those caused by normally consolidated states. A similar trend was found with or without soil improvement. The greater the degree of consolidation is, the smaller the deflection of the wall. In this case, the retaining wall's length is well designed and stable, but the analysis results showed that the wall length can be shorter than the constructed length. Massive jet grouting was used behind the left wall to successfully reduce wall deflection and ground surface settlement. Finally, deep cement mixing has only a small effect on reducing wall deflection and ground surface settlement.

Parametric optimization of corner radius in hexagonal honeycombs under in-plane compression

What is the optimum corner radius for a regular hexagonal honeycomb in the context of in-plane, quasistatic compression loading? Drawing inspiration from social insect hexagonal cell nests, where a non-zero corner radius appears to be a design feature, a 400-point design of experiments study is conducted using 2D plane strain Finite Element Analysis (FEA) to study the influence of cell size, beam thickness and corner radius on effective modulus and maximum corner stress in the honeycomb cells. An experimental study is conducted to examine these relationships beyond the bounds of the small deformation, linear elastic FEA analysis. The study finds that corner radii always increase the effective modulus of the honeycomb, even after accounting for the additional mass associated with the corner fillet. A key finding of this work is that while corner radii also reduces the maximum corner stress, there exists a clear optimum, beyond which stresses rise again as the corner radius increases in magnitude. This optimum corner radius is shown to be a function of the beam thickness (t) to beam length (l) ratio (t/l), with the optimum value increasing with increasing t/l. The experimental study shows that the presence of a corner radius shifts the failure mechanism from nodal fracture to plastic hinging for honeycombs with thick beams, and may have benefits for energy absorption applications. This work makes the case for the treatment of the corner radius as an independent design feature for optimization in the wider context of cellular materials, as well as has implications for the study of the geometry of insect nests.

VERIFICATION OF THE ELASTO-VISCOPLASTIC APPROACH ASSESSING THE LONG-TERM DEFORMATION OF THE QUASI-OVERCONSOLIDATED PLEISTOCENE CLAY DEPOSITS

A series of elasto-viscoplastic finite element analyses is performed to describe the long-term settlement measured at the reclaimed islands in Osaka Port. The compression modeling for the quasi-overconsolidated Pleistocene clays proposed by the authors has been incorporated to the procedure in which an elasto-viscoplastic deformation is assumed to occur even in the quasi-overconsolidated region (p 0 ≤p≥p c ), One-dimensional analysis is adopted for assessing the settlement of Sakishima and Yumeshima Reclaimed islands, whereas the plane-strain finite element analysis is carried out for investigating the deformation of the Pleistocene deposit beneath the sheet-pile composite revetment at Maishima Reclaimed Island. The proposed procedure is found to provide larger settlement for all cases compared to the conventional approach because of the consideration of viscoplastic deformation in the quasi-overconsolidated region. As for the case of the sheet-pile composite revetment, the effect of stress concentration due to ground improvement with SCP for the Holocene clay layer is remarkable on the underlying Pleistocene deposit. The measured settlement of the individual Pleistocene clay layers as well as the total settlement of the Pleistocene deposits are precisely described by the proposed procedure, whereas the conventional approach in which the instantaneous elastic deformation is assumed to occur in the quasi-overconsolidated region exhibits serious underestimation. From these results, the predictive accuracy of the proposed procedure is verified for assessing the long-term settlement at the reclaimed islands in Osaka Port.

A nonlinear plane strain finite element analysis for multilayer elastomeric bearings

The purpose of this paper is the prediction of the behaviour of multilayer elastomeric bearings by the finite element analysis. First, the finite element formulation of equilibrium equations of incompressible elasticity problem is presented. This approach is based on the modified potential energy taking into account the incompressibility. The linearized system obtained is solved by the Newton–Raphson iterative method with the total lagrangian formulation. A large plane strain element is developed for the analysis of elastomeric materials under large strain deformation. This element is then integrated into our software. After validating the plane strain element using examples with known exact solutions, an industrial case study made of laminated (metal-rubber) elastomeric component is examined. The stress distribution study is limited to the elastomeric layers, possible sources of crack appearance.

Simulations of crack extensions in arc-shaped tension specimens of uncharged and hydrogen-charged 21-6-9 austenitic stainless steels using cohesive zone modeling with varying cohesive parameters

Crack extensions in uncharged and hydrogen-charged side-grooved A(T) specimens of conventionally forged 21-6-9 austenitic stainless steels are simulated using the cohesive zone modeling approach. Two-dimensional plane strain finite element analyses with fixed cohesive parameters are first conducted to fit the experimental load-displacement curves. Similar analyses using varying cohesive parameters as functions of the crack extension are then conducted to fit the experimental load-crack extension and crack extension-displacement curves. The computational results with varying cohesive parameters can fit very well the experimental data. The computational results also indicate that the average cohesive energy for the hydrogen-charged A(T) specimen is lower than that for the uncharged A(T) specimen.

Constraint and size effects in confined layer plasticity

Plane strain finite element analyses are used to model the experiments of Mu et al. (2014, 2016) for a thin metal layer confined between elastic solids. The thin metal layer undergoes elastic–plastic deformations, here modeled by strain gradient plasticity, while the rest of the solid deforms only elastically. Plane strain is assumed and finite strains are accounted for. The microscopic boundary condition at the band interface is initially taken to be zero plastic strain increment, but plastic straining at the interface is allowed when the plastic strain gradient at the interface has exceeded a critical value. When the narrow metal band is inclined 45° relative to the direction of compression of the solid, simple shear develops in the band and predictions are rather similar to those of a one-dimensional analysis for an infinite band. For a band at 90° the elastic parts give significant constraint on plastic flow, the stress fields are non-uniform along the band and the average nominal compressive stress shows strong sensitivity to the layer thickness and to the width of the specimen. Remarkably good qualitative, and in some cases quantitative, agreement is found with the experimental observations of Mu et al. (2014, 2016). Considering also other band angles, both the average nominal shear and compressive stress show variations with the angle.

Deep excavation in under-consolidated clayey deposit

In this study, a deep excavation in an under-consolidated deposit in Zhuhai, China, was reported and investigated via plane strain finite element analysis (FEA). First, the project was simulated via FEA (under-consolidated deposit), and a reasonable agreement between the lateral displacement of the measured and simulated retaining wall was obtained. Another FEA was then conducted under the assumption that the deposit was in a normally consolidated state. The numerical results indicate that the under-consolidated case resulted in a 25% increase in maximum lateral displacement of the contiguous pile-formed retaining wall, a 32% increase in bending moment in the wall, and approximately twice the maximum surface settlement behind the wall, when compared with those of the normally consolidated case. The main reasons for this are as follows: (1) the under-consolidated deposit was weaker, and (2) the ongoing consolidation of the under-consolidated deposit induced green-field settlement (approximately 4 mm) during the project period, thereby enhancing the bending deformation of the wall. Therefore, when designing deep excavation in an under-consolidated deposit, not only its weaker strength but also the negative effect of green-field settlement during the project period should be considered.

Structural Behavior of Pipelines Buried in Expansive Soils under Rainfall Infiltration (Part I: Transverse Behavior)

Landslides, fault movements as well as shrink/swell soil displacements can exert important additional loadings on soil buried structures such as pipelines. These loadings may damage the buried structures whenever they reach the strength limits of the structure material. This paper presents a two-dimensional plane-strain finite element analysis of an 800 mm diameter water supply pipeline buried within the expansive clay of the Ain-Tine area (Mila, Algeria), considering the unsaturated behavior of the soil under a rainfall infiltration of 4 mm/day intensity and which lasts for different time durations (8, 15 and 30 days). The simulations were carried out using the commercial software module SIGMA/W and considering different initial soil suction conditions P1, P2, P3 and P4. The soil surface heave and the radial induced forces on the pipeline ring (i.e., Axial , Shear forces and bending moments ) results indicated that following the changes of suction the rainfall infiltration can cause considerable additional loads on the buried pipeline. Moreover, these loads are proportionally related to the initial soil suction conditions as well as to the rainfall infiltration time duration. The study highlighted that the unsaturated behavior of expansive soils because of their volume instability are very sensitive to climatic conditions and can exert adverse effects on pipelines buried within such soils. As a result, consistent pipeline design should seriously consider the study of the effect of the climatic conditions on the overall stability of the pipeline structure.

An elastoplastic finite element study of cylindrical plane-strain contact for steel/steel and Inconel 617/Incoloy 800H undergoing unidirectional sliding

The current work employs a two-dimensional plane strain finite element analysis to investigate the unidirectional sliding contact between a deformable half-cylinder and a deformable flat block. The unidirectional sliding is governed by a displacement-controlled action where the materials of the two contacting bodies are first set to identical steels at 20 ℃ and then to Inconel 617 and Incoloy 800H at 800 ℃. First, a normal interference (indentation) is applied, which is followed by unidirectional sliding. The von Mises stress distribution, plastic strain distribution, junction growth, normal force, tangential force, effective coefficient of friction, and scars on the surface of the block are obtained during the sliding motion. The leading edge of the contacting area and the bulk material under the leading edge experience large von Mises stresses. The large plastic strain is found on the surface of the block, and forms a “pocket” shape under the surface. The junction growth is also investigated, showing the direction of the growth is in the same direction of the tangential force that the weaker material experiences. The forces and the effective coefficient of friction are found to stabilize after a certain sliding distance, and the effective coefficient of friction converges to the coefficient of friction used in the model. Pileup is found on the surface of the block after a sufficient unidirectional sliding distance.

PROCESS MODELING OF CARBON-EPOXY COMPOSITES: RESIDUAL STRESS DEVELOPMENT DURING CURE AND ANALYSIS OF FREE EDGE EFFECTS

Last decades, increased attention is paid to the deep understanding of the process induced residual stresses (locked-in) and their effect on shape distortion and fracture. Residual stresses evaluation is particularly important in multilayered composites with anisotropic thermo-mechanical properties, where the ply orientations and stacking sequences highly influence the appearing of manufacturing stresses. In the present study, the effect of free edge on residual stresses inherited during manufacturing of thermoset multilayered composites was investigated. In order to understand the stress-strain state in samples after free edge cut a simplified 2D plane strain finite element analysis was performed. Many phenomena, such as sensitivity of the results to the size of the numerical grid, stress redistribution and size of the area affected by free edge was analyzed. In the current research, the behavior of AS4/8552-1 carbon-epoxy composite during manufacturing cycle was studied by means of finite element modeling in ABAQUS. To describe the behavior of the composite material during the manufacturing process − including processes of formation, polymerization, development of residual strains and stresses was done by developed user subroutine-UMAT, describing the visco-elastic material behavior of the material. The program was implemented in ABAQUS and validated on the basis of literature data. The results of the study can be applied for prediction of residual stresses in composite structure by means of virtual simulation and further understanding the nature of fracture of composites.

A Preliminary Two-Dimensional Palpation Mechanics for Detecting a Hard Inclusion by Indentation of a Soft Matrix Under Large Strain

A rigid inclusion is embedded at a finite depth in a soft layer resting on a rigid substrate. A spherical indenter presses vertically onto the surface, deforming the matrix and displacing the inclusion. A subsurface inclusion initially near the indentation axis moves primarily downward, until an unstable lateral jump occurs to minimize the energy stored in the elastic medium. Such an instability is unique to soft materials undergoing large deformation. A two-dimensional plane-strain finite element analysis is used to simulate the 3D phenomenon.

Numerical Modelling and Experimental Monitoring of a Full-Scale Diaphragm Wall

Ground movements due to deep excavation may cause damage or loss of functionality to nearby building, especially in urban areas: embedded diaphragm walls between the new and the existing buildings can be effective in reducing these movements. The paper reports the results of an experimental and numerical study carried on a full-scale anchored piles diaphragm used to supporting deep excavation in urban area devoted to the new Library of the University of Enna “Kore”, Enna (Italy). Two piles, located in the central part of the diaphragm wall, have been instrumented with conventional inclinometer cases and embedded piezoelectric accelerometers. The experimental measurements recorded during the construction and in operation are reported and discussed in detail. Plane strain finite element analyses using the code PLAXIS 2D are presented in which the diaphragm was modelled to evaluate the geotechnical system behavior. It has been observed that this model allows for a satisfactory simulation of the displacement of the wall during the construction phases under a static loading scenario. The results in terms of horizontal displacements obtained by numerical modelling are in good agreement with those derived by measurements. Furthermore, on the basis of measured data, an empirical method has been used to evaluate the surface settlements, whose values guarantee a good safety threshold to the nearby building.

Simulations of fracture tests of uncharged and hydrogen-charged additively manufactured 304 stainless steel specimens using cohesive zone modeling

Fracture tests of uncharged and hydrogen-charged single edge bend specimens of additively manufactured 304 stainless steels are simulated using the cohesive zone modeling (CZM) approach. Two-dimensional plane strain finite element analyses without cohesive elements are conducted to identify the values of cohesive energy. Similar analyses using CZM with the trapezoidal traction-separation laws are then conducted. The best-fit cohesive parameters show the values of cohesive strength for the uncharged specimens are higher than those for the hydrogen-charged ones whereas the value of cohesive energy for the uncharged specimens can be either slightly lower or higher than that for the hydrogen-charged ones.

Performance of a foundation pit supported by bored piles and steel struts: A case study

Retaining structures with bored piles and temporary inclined steel struts are suitable for the reinforcement of underground projects located in urban areas of high-density development as they are convenient for use in earth excavations and their use leads to considerable savings in time and cost. However, few data are available on foundation pits supported by bored piles and inclined steel struts. This paper presents a case study to investigate the behavior of a large-scale foundation pit supported by bored piles and inclined steel struts, in which the movement of the foundation pit and the displacement of the retaining structure are reported. The measured results along the length of the foundation pit were found to be smaller than those along the width (with a difference of approximately 13.5–30.0%), including the vertical and lateral displacement of the foundation pit, as well as the lateral displacement of the bored piles. The lateral displacement at the top of the bored piles, δh, was 0.2–0.5% of the excavation depth, He. The lateral displacement of the bored piles decreased with the decreasing distance from the corner (with a difference of approximately 50%), which demonstrated the corner effect on the movement of the bored piles. Based on the measured results of this field case, it was found that the maximum settlement and the lateral displacement were located at the cross section through the center of the west side of the foundation pit. In order to predict the distribution of settlement at the surface and the basal heave at this section, plane-strain finite element analyses were conducted to estimate the location where the maximum settlement occurred at the surface of the foundation pit. The difference between the numerical results and the measurements was found to be in the range of 2.6–33.0%, which validates the numerical model with some reasonable accuracy. The numerical results show that the maximum surface settlement occurred at a distance of 0.6 He away from the top of the foundation, whereas the settlement at the bottom of the foundation was almost uniform at the final construction stage (e.g., 25 mm).

Fracture toughness testing using non-standard bend specimens – Part I: Constraint effects and development of test procedure

This work addresses the development of a fracture toughness test procedure using standard and non-standard SE(B) specimens, including non-standard 4-point bend configurations. In the present study, extensive plane-strain finite element analyses are conducted on non-standard bend geometries with varying specimen span over width ratio (S/W) and loaded under 3-point and 4-point bending. The potential influence of specimen geometry and loading on fracture behavior in terms of J-Q descriptions to quantify constraint effects is characterized first. Next, a large new set of plastic η-factors applicable to these non-standard bend geometries which serve to estimate the experimentally measured toughness values in terms of load-displacement records, including the J-integral and the crack tip opening displacement (CTOD), is provided. To facilitate contact with other test protocols, a new set of rotational factors, rp, to determine the CTOD based on the plastic hinge model is also described. The extensive numerical analyses conducted here provide a large set of fracture toughness test parameters, which not only validate the existing relationships available in current standards, but also provide support to standardization efforts for fracture toughness testing using non-standard bend geometries.

MARS inverse analysis of soil and wall properties for braced excavations in clays

A major concern in deep excavation project in soft clay deposits is the potential for adjacent buildings to be damaged as a result of the associated excessive ground movements. In order to accurately determine the wall deflections using a numerical procedure such as the finite element method, it is critical to use the correct soil parameters such as the stiffness/strength properties. This can be carried out by performing an inverse analysis using the measured wall deflections. This paper firstly presents the results of extensive plane strain finite element analyses of braced diaphragm walls to examine the influence of various parameters such as the excavation geometry, soil properties and wall stiffness on the wall deflections. Based on these results, a multivariate adaptive regression splines (MARS) model was developed for inverse parameter identification of the soil relative stiffness ratio. A second MARS model was also developed for inverse parameter estimation of the wall system stiffness, to enable designers to determine the appropriate wall size during the preliminary design phase. Soil relative stiffness ratios and system stiffness values derived via these two different MARS models were found to compare favourably with a number of field and published records.

A multivariate adaptive regression splines model for estimation of maximum wall deflections induced by braced excavation

With rapid economic growth, numerous deep excavation projects for high-rise buildings and subway transportation networks have been constructed in the past two decades. Deep excavations particularly in thick deposits of soft clay may cause excessive ground movements and thus result in potential damage to adjacent buildings and supporting utilities. Extensive plane strain finite element analyses considering small strain effect have been carried out to examine the wall deflections for excavations in soft clay deposits supported by diaphragm walls and bracings. The excavation geometrical parameters, soil strength and stiffness properties, soil unit weight, the strut stiffness and wall stiffness were varied to study the wall deflection behaviour. Based on these results, a multivariate adaptive regression splines model was developed for estimating the maximum wall deflection. Parametric analyses were also performed to investigate the influence of the various design variables on wall deflections.