Plane Strain Finite Element Analysis Research Articles

Modelling of soil–structure interaction for a piled bridge abutment in plane strain FEM analyses

Abstract Full-height piled bridge abutments constructed on soft clay are prone to soil–structure interaction effects. A series of geotechnical centrifuge tests of this type of structure has been undertaken, and an accompanying series of plane strain finite element analyses are reported. Some aspects of the structure do not conform to a plane strain analysis (most notably the piles), and the methods used to incorporate this soil–structure interaction are described. Success of the methods is illustrated by good comparison with the centrifuge test results, and the numerical analyses revealed interaction effects which could not be specifically identified in the centrifuge tests.

J Estimation For Single-edge-notch Tension Specimens Subjected ToFixed-grip Loading

Two-dimensional plane strain finite element analyses have been used to develop J estimation equations for single-edge-notch specimens subjected to fixed-grip tensile loading from experimentally measured quantities, notably area under load vs. plastic load line displacement (Â LD ) and area under load vs. plastic crack mouth opening displacement (Â Moo )• It was found that J estimation from A^MOD is much more reliable than from A^LD since dependence on strain hardening coefficient is much reduced in the former case.

Finite element analysis of anterior tooth root stresses developed during endodontic treatment.

Vertical tooth root fractures are diagnostically challenging, frustrating, and an increasingly common cause of failure of tooth restoration. These vertical root fractures have been associated with many causes, including the endodontic process itself. To investigate these endodontic causes, various phases of crown replacement for an anterior tooth were modeled using nonlinear, plane strain finite element (FE) analysis. Stresses developed during obturation, post positioning, crown placement, and masticatory and occlusal loading of the restored tooth were estimated using this analysis method. The minimum (compressive) principal stress was greatest during obturation of cones 1 and 2, and during mastication of the restored tooth. Although these stresses were significant (-150 to -280 MPa), they did not exceed the compressive strength of dentin. The maximum (tensile) principal stresses, 160 to 300 MPa, were also observed during obturation of cones 1 and 2. These peak stresses exceed the dentin tensile strength.

The Effect of Strength Mis-Match on Mechanical Performance of Weld Joints

This paper presents numerical studies on strength mis-match effects in welded joints. Crack growth in a mis-matched single edge notched specimen under pure bending, with a crack lying at the center line of the weld metal, is simulated via a two-dimensional plane strain finite element analysis (FEA). The fracture process is modeled using a cohesive zone model (CZM). The work is focussed on the effects of yield strength mis-match as well as thickness of the weld metal on fracture resistance and load-deformation for both under- and overmatched specimens. Weld metal mis-match is achieved by keeping the same weld metal and changing the strength of the base metal.

Laboratory Determination of Smear Zone due to Vertical Drain Installation

This paper is mainly concerned with a laboratory study to investigate the effect of smear due to vertical drain installation. The extent of the smear zone around a vertical drain was studied utilizing a large-scale consolidometer apparatus. The test results reveal that a significant reduction in the horizontal permeability takes place toward the central drain, whereas the vertical permeability remains relatively unchanged. The radius of the smear zone was estimated to be a factor of four to five times the radius of the central drain (mandrel), and the measured ratio of horizontal to vertical permeability approached unity at the drain-soil interface. The laboratory measured settlements are subsequently compared with the predictions based on the theory of Hansbo and the finite element method. It is of relevance to note that the inclusion of the correct variation of permeability ratios of the smear zone in the plane strain finite element analysis improves the accuracy of settlement predictions.

A finite element analysis of fracture initiation in ductile/brittle periodically layered composites

A near-tip plane strain finite element analysis of a crack terminating at and normal to the interface in a laminate consisting of alternate brittle and ductile layers is conducted under mode-I loading. The studies are carried out for a system representing steel/alumina composite laminate. The Gurson constitutive model, which accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence, is employed within the framework of small deformation plasticity theory. Evolution of plastic zone and damage in the ductile layer is monitored with increasing load. High plastic strain localization and microvoid damage accumulation are found to occur along the brittle/ductile interface at the crack-tip. Fracture initiation in the ductile phase is predicted and the conditions for crack renucleation in the brittle layer ahead of the crack are established for the system under consideration. Ductile fracture initiation has been found to occur before plasticity spreads in multiple ductile layers. Effects of material mismatch and yield strength on the plastic zone evolution are briefly discussed.

J‐INTEGRAL SOLUTIONS FOR SHALLOW CRACK GEOMETRIES UNDER COMBINED TENSION AND BENDING

Abstract—This paper presents J‐integral solutions for geometries with shallow edge cracks (0.05 ≤a/W≤ 0.1) subjected to combined tension and bending. Tension and bending is applied simultaneously and sequentially. Curves of J versus structural strain are obtained from two‐dimensional plane strain finite element analyses using medium to low work hardening power laws to represent material behaviour. Empirical equations are derived from the finite element results to estimate the J‐integrals, using previously developed J‐estimation schemes for SENT and SENB specimens with only minor modifications. The predictions presented are invariably safe, but due to the complexity of the problems studied and the variability of the loadings considered, the degree of conservatism is found to be high in some cases.

A micromechanical analysis to predict the cord-rubber composite properties

Both three- and two-dimensional generalized plane strain finite element analyses based on a micromechanics approach were carried out to investigate the linear and nonlinear effective composite properties as well as the stress fields. A unit cell model of cord-rubber composite subjected to different loadings was studied to predict the effective composite properties. The numerical results of effective composite properties obtained from 2D and 3D finite element analyses were compared with experimental data and other finite element results available in the literature. The effects of rubber material nonlinearity and large deformation on the effective composite properties and interface stress distributions are presented and discussed.

Finite element simulation of mode I dynamic, ductile fracture initiation

In this work, two dimensional (plane strain) finite element analysis of a ductile three-point bend fracture specimen subjected to mode I quasistatic and dynamic (impact-like) loading is conducted. The Gurson constitutive model that accounts for the ductile failure mechanisms of micro-void nucleation, growth and coalescence is employed within the framework of a finite deformation plasticity theory. The interaction between the notch tip and a pre-nucleated hole ahead of it is modelled. Several dynamic analyses are performed considering rate-independent and rate-dependent material behaviour and with different impact speeds. The development of ductile failure is studied by monitoring the growth of the hole and the accumulation of the micro-void damage in the ligament between the hole and the notch tip. It is observed from the above analyses that though the effect of inertia on dynamic, ductile fracture initiation is moderate, strain rate sensitivity has a strong effect on many aspects of this phenomenon.

Local fracture mechanics analysis of stringer pull-off and delamination in a post-buckled compression panel

This paper describes some of the current global/local testing and analysis approaches to evaluating the design of composite structure. A case study for the local, fracture mechanics analysis of failure in a 4- stringer compression panel is described in detail. The analysis investigates the variation of strain energy release rate G with debond length using a 2-D plane strain finite element analysis (FEA) of one of the stringers. The boundary conditions on the local model were determined from a global shell element model of the panel. Delamination was also modelled in the cap of the stringer using FEA and a closed form solution. The values of G for these two damage modes were compared with the material's fracture toughness. Using this analysis, the load to initiate the stringer debond and to cause edge delamination of the cap may be determined.

Modelling the effect of vertical drains in two-dimensional finite element analyses of embankments on soft ground

A recently developed method for modelling the effect of vertical drains in plane strain finite element analyses of consolidation beneath embankments on soft ground is applied to three case histories. Analyses are reported for the consolidation of the soil served by a single drain (a unit cell) under conditions of no lateral strain. In all three cases a good match was obtained between the average degrees of consolidation in an axisymmetric unit cell and the equivalent plane strain unit cell. This suggests that the method could be used to facilitate full two-dimensional analyses of many embankments. The results of the analyses are also compared with the available field data. Key words : vertical drains, consolidation, finite elements, embankments.

Simplified Analysis of Long-Span Soil-Metal Structures

To analyze and design long-span soil-metal structures and other structures involving soil or reinforced soil, it is important to estimate accurately the soil properties. Triaxial tests are carried out on reinforced as well as unreinforced Lake Erie sand specimens. A hyperbolic stress-strain relation is proposed to represent the soil elastic properties. Expressions are deduced to evaluate the modulus of elasticity of the soil as well as the coefficient of soil reaction that is required for the proper design of soil-metal structures. The proposed expressions are valid for both reinforced and unreinforced soils. A simplified finite-element model is presented for the analysis of long-span unreinforced and reinforced soil-metal structures. Results from the simplified model are compared to those from a plane-strain finite-element analysis. The results are also verified using results obtained from tests carried out on reduced-scale models.

Stress and energy density fields near a blunted crack front in power hardening material

Using Jaumann and Dienes rates of Euler stress in elastic-plastic constitutive equations of finite deformation, plane strain finite element analysis for a compact tension specimen with a blunted crack front is made. The Euler stress, Kirchhoff stress and volume strain energy density near a blunted crack tip are computed. Constitutive relations with different deformation rates affect the the near crack tip solution in a region within an order of magnitude of the crack opening displacement. The results differed from the corresponding solution of deformation plasticity (or nonlinear elasticity) with increasing deformation. They are smaller in a local region of about 2 to 10 times of the crack opening distance. The volume energy density near the crack tip is computed, the stationary values of which determine the locations of extensive yielding and possible sites of crack initiation. It remained nearly constant with increasing deformation. Such a character tends to support the volume energy density criterion as a means for quantifying the ductile fracture behavior of metals.

ESTIMATING THE COEFFICIENT OF SUBGRADE REACTION FOR PLANE STRAIN CONDITIONS.

Keywords PARSONS BRINCKERHOFF, BABSON COLLEGE WELLESLEY SUBGRADE, REACTIONS, ESTIMATING, COEFFICIENTS, PLANE, STRAIN, CONDITIONS, METHODS, FINITE ELEMENTS, ANALYSIS, BEAMS, SLABS, LOADED, SURFACES, HOMOGENEOUS, ELASTIC, SOILS, LAYERS, DESIGN, CUT AND COVER, TUNNELS, MODIFIED, FOUNDATIONS, MODULUS, RATIOS, STIFFNESS, THICKNESS, LOADING, DESIGN, CHARTS, LINEAR, DIMENSIONS, LONG, MODELS, LOADS, VARIABLES, SPRING, MBEF... Show All

Performance of Embankment Stabilized with Vertical Drains on Soft Clay

The authors have carried out several two-dimensional plane strain analyses of the Muar test embankment in which the rate of settlement was overpredicted unless clogging of the vertical drains was assumed to have occurred. The modeling of drain clogging in the finite-element analysis is an interesting development, and the discussers would welcome clarification of the modeling method and how this differs from the use of a zone of reduced permeability adjacent to the drain. However, while accepting that clogging could have been a significant factor. the discussers suggest two further causes for the authors' overprediction of the rate of consolidation. namely, incorrect modeling of the vertical drains in the plane strain analysis and the use of a constant permeability during consolidation. The discussers have developed a matching procedure by which vertical drains installed in a regular grid can be modeled in a plane strain finite-element analysis (Hird et al. 1992) that has been validated for several case histories (e.g .. Russell 1992a). The method equates Hansbo's (1981) axisymmetric analytical solution for the consolidation of the soil surrounding a single vertical drain, termed a unit cell. with a similar solution for a plane strain unit cell. The method takes into account. if necessary. both well resistance and smear and can be summarized by two equations

An experimental and computational investigation of crack growth initiation in three-point bend fracture specimens

An experimental and computational study of HY-100 steel three-point bend fracture specimens was performed. Two specimens were considered in the experimental portion of the study, differing with respect to thickness and the presence of side grooves. Plane stress and plane strain finite element analyses of the specimens were conducted to assess the relative role of constraint on load vs crack opening displacement response and crack growth initiation. A critical value of the strain energy density associated with local material fracture was used to predict the onset of crack growth. The experimental responses were bounded by the predicted plane stress and plane strain load vs crack mouth opening responses. These results also provided an indication of the extent to which the side grooves in the thinner specimen provided more constraint than the thickness of the specimen without side grooves. A comparison with a previous investigation on an HY-100 compact fracture specimen suggests similarities concerning the interaction between material nonlinearity and specimen response nonlinearity.

To cut or not to cut: a thermomechanical stress analysis of polyimide thin-film on ceramic structures

When thin-film polyimide-on-ceramic multilayered structures are subjected to thermal loads during manufacturing processes, stresses can be produced at the interface of the film and ceramic due to a mismatch in the coefficients of thermal expansion of the materials. These stresses, which may cause delamination and peeling of the films, are typically largest near the free edge of the structure. This has raised the question of whether cross-sectioning these structures to examine the interior for such defects as interfacial de-adhesion or delamination may change the stress distribution and actually generate flaws, thereby defeating the purpose of the cross-sectioning. In this paper, thermally induced stresses are evaluated for laminated thin-film Kapton on alumina structures, taking into account creep deformation and stress relaxation of the Kapton layer. After experimentation temperature and stress-dependent creep-strain constitutive models were developed; the properties of nonlinear temperature-dependent elastic-plastic and the coefficient of thermal expansion were also described. Stress analysis was performed, using plane-strain finite element analysis. It was found that sufficient stress relaxation can occur to arrest interface peeling and delamination at the free edge.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Large stable crack growth in fracture mechanics specimens

According to the J concept, information is reported about the crack resistance behaviour up to 8 mm crack growth of side-grooved CT-25 as well as CCT-25 specimens made from German standard steel StE 460. Numerical simulations controlled by J R curves make the calculation of J from the stresses and strains of specimen models during large crack growth feasible. These data allow a comparison to standards and rules describing the evaluation of J from experiments. Using stress, strain and displacement fields from a plane-strain finite-element analysis, the extended J concept is discussed concerning larger ductile crack growth. Additionally, the distribution of other fracture mechanics parameters such as the crack tip opening displacement (CTOD) and the crack tip opening angle (CTOA) are presented for larger crack growth.

Modelling the plane strain compression test to obtain constitutive equations of aluminium alloys

Hot plane strain compression tests on 1050, 1198, 3003 and 3004 aluminium alloys have been conducted. Based on these experiments and on a set of internal type constitutive equations for hot working, the values of the parameters in the constitutive functions are determined. The constitutive equations proposed here, with the constitutive functions and material parameters associated, accurately reproduce the basic tests. The procedure used to fit the material parameters is improved, in comparison with classical slip line analysis, by using a finite element modelling of the plane strain compression test. It is demonstrated that accurate plane strain or three-dimensional large strain finite element analysis can be used to correct the friction and lateral spread effects. Furthermore, it is demonstrated from comparison with the experimental observations that microstructural parameters can be accurately determined from numerical modelling. The constitutive equations and finite element procedure proposed here can be useful for obtaining an improved analysis of hot rolling of aluminium alloys.

Elastic-plastic fracture analysis of finite bodies—II. Conditions of fracture initiation

The normal and triaxial stresses on uncracked ligament for different specimens were analyzed by large deformation plane strain finite element analysis (FEM) at their fracture loads, and the critical characteristic parameters ( J, Q, k) of the stress field established in Part I [Fashang Ma and Zhen-Bang Kuang, Engng Fracture Mech. 48, 727–737 (1994)] were determined by fitting. Using several continuum damage mechanics (CDM) models and the present stress field, the conditions of the initiation of elastic-plastic fracture growth for different specimens were discussed in detail, and it was verified by experimental data that the critical conditions suggested in this paper are independent of specimen geometry and of the ratios of crack depth a to specimen width w when an appropriate microscopic model for fracture initiation is adopted. When characteristic parameters of the stress field k = 1 and Q = 0, the present conditions will reduce to the well-known elastic-plastic single parameter fracture criteria.