Plane Strain (plane + strain)

Distribution by Scientific Domains

Terms modified by Plane Strain

  • plane strain condition

  • Selected Abstracts

    The evolution of the stress,strain fields near a fatigue crack tip and plasticity-induced crack closure revisited

    L. G. ZHAO
    ABSTRACT The evolution of the stress,strain fields near a stationary crack tip under cyclic loading at selected R -ratios has been studied in a detailed elastic,plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R -ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic,plastic finite element simulations of advancing fatigue cracks were carried out under plane-stress, plane-strain and generalized plane-strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane-strain and generalized plane-strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane-stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack-closure measurement, and indeed on the role of plasticity-induced crack closure in the reduction of the applied stress intensity factor range. [source]

    Numerical investigation on J -integral testing of heterogeneous fracture toughness testing specimens: Part I , weld metal cracks

    Y.-J. KIM
    ABSTRACT Based on extensive two-dimensional (2D) finite element (FE) analyses, the present work provides the plastic , factor solutions for fracture toughness J -integral testing of heterogeneous specimens with weldments. Solutions cover practically interesting ranges of strength mismatch and relative weld width, and are given for three typical geometries for toughness testing: a middle cracked tension (M(T)) specimen, single edge cracked bend (SE(B)) specimen and (C(T)) specimen. For mismatched M(T) specimens, both plane strain and plane stress conditions are considered, whereas for SE(B) and C(T) specimens, only the plane strain condition is considered. For all cases, only deep cracks are considered, and an idealized butt weld configuration is considered, where the weld metal strip has a rectangular cross section. Based on the present solutions for the strength mismatch effect on plastic , factors, a window is provided, within which the homogeneous J estimation procedure can be used for weldment toughness testing. The effect of the weld groove configuration on the plastic , factor is briefly discussed, concluding the need for further systematic analysis to provide guidance to practical toughness testing. [source]

    Numerical modelling of dynamic consolidation on granular soils

    S. López-Querol
    Abstract The application of Pastor,Zienkiewicz constitutive model for sands to dynamic consolidation problems is presented in this paper. This model is implemented in a coupled code formulated in terms of displacements for both solid and fluid phases (u,w formulation), which is firstly compared with u,pw formulation for some simple examples. Its range of validity, previously established for elastic problems and harmonic loading, is explored. Once the suitability of the u,w formulation has been ascertained for this kind of dynamic problems in soils, one- and two-dimensional (plane strain) dynamic consolidation numerical examples are provided, aiming to give some light into the physics of this ground improvement technique. A ,wave of dryness', observed at the soil surface during the impact in field cases, is numerically reproduced and justified. Some hints on the influence of the loading zone size are also given. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Inelastic constitutive properties and shear localization in Tennessee marble

    D. J. Holcomb
    Abstract The inelastic response of Tennessee marble is modelled by an elastic plastic constitutive relation that includes pressure dependence of yield, strain-softening and inelastic volume strain (dilatancy). Data from 12 axisymmetric compression tests at confining pressures from 0 to 100 MPa are used to determine the dependence of the yield function and plastic potential, which are different, on the first and second stress invariants and the accumulated inelastic shear strain. Because the data requires that the strain at peak stress depends on the mean stress, the locus of peak stresses is neither a yield surface nor a failure envelope, as is often assumed. Based on the constitutive model and Rudnicki and Rice criterion, localization is not predicted to occur in axisymmetric compression although faulting is observed in the tests. The discrepancy is likely due to the overly stiff response of a smooth yield surface model to abrupt changes in the pattern of straining. The constitutive model determined from the axisymmetric compression data describes well the variation of the in-plane stress observed in a plane strain experiment. The out-of-plane stress is not modelled well, apparently because the inelastic normal strain in this direction is overpredicted. In plane strain, localization is predicted to occur close to peak stress, in good agreement with the experiment. Observation of localization on the rising portion of the stress,strain curve in plane strain does not, however, indicate prepeak localization. Because of the rapid increase of mean stress in plane strain, the stress,strain curve can be rising while the shear stress versus shear strain curve at constant mean stress is falling (negative hardening modulus). Copyright © 2001 John Wiley & Sons, Ltd. [source]

    Limit analysis and convex programming: A decomposition approach of the kinematic mixed method

    Franck Pastor
    Abstract This paper proposes an original decomposition approach to the upper bound method of limit analysis. It is based on a mixed finite element approach and on a convex interior point solver using linear or quadratic discontinuous velocity fields. Presented in plane strain, this method appears to be rapidly convergent, as verified in the Tresca compressed bar problem in the linear velocity case. Then, using discontinuous quadratic velocity fields, the method is applied to the celebrated problem of the stability factor of a Tresca vertical slope: the upper bound is lowered to 3.7776,value to be compared with the best published lower bound 3.772,by succeeding in solving non-linear optimization problems with millions of variables and constraints. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Upper and lower bounds in limit analysis: Adaptive meshing strategies and discontinuous loading

    J. J. Muñoz
    Abstract Upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimization problems. The membership constraints for Von Mises and Mohr,Coulomb plasticity criteria are written as a set of quadratic constraints, which permits one to solve the optimization problem using specific algorithms for Second-Order Conic Program (SOCP). From the stress field at the lower bound and the velocities at the upper bound, we construct a novel error estimate based on elemental and edge contributions to the bound gap. These contributions are employed in an adaptive remeshing strategy that is able to reproduce fan-type mesh patterns around points with discontinuous surface loading. The solution of this type of problems is analysed in detail, and from this study some additional meshing strategies are also described. We particularise the resulting formulation and strategies to two-dimensional problems in plane strain and we demonstrate the effectiveness of the method with a set of numerical examples extracted from the literature. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    A contact algorithm for frictional crack propagation with the extended finite element method

    Fushen Liu
    Abstract We present an incremental quasi-static contact algorithm for path-dependent frictional crack propagation in the framework of the extended finite element (FE) method. The discrete formulation allows for the modeling of frictional contact independent of the FE mesh. Standard Coulomb plasticity model is introduced to model the frictional contact on the surface of discontinuity. The contact constraint is borrowed from non-linear contact mechanics and embedded within a localized element by penalty method. Newton,Raphson iteration with consistent linearization is used to advance the solution. We show the superior convergence performance of the proposed iterative method compared with a previously published algorithm called ,LATIN' for frictional crack propagation. Numerical examples include simulation of crack initiation and propagation in 2D plane strain with and without bulk plasticity. In the presence of bulk plasticity, the problem is also solved using an augmented Lagrangian procedure to demonstrate the efficacy and adequacy of the standard penalty solution. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Hybrid and enhanced finite element methods for problems of soil consolidation

    X. X. Zhou
    Abstract Hybrid and enhanced finite element methods with bi-linear interpolations for both the solid displacements and the pore fluid pressures are derived based on mixed variational principles for problems of elastic soil consolidation. Both plane strain and axisymmetric problems are studied. It is found that by choosing appropriate interpolation of enhanced strains in the enhanced method, and by choosing appropriate interpolations of strains, effective stresses and enhanced strains in the hybrid method, the oscillations of nodal pore pressures can be eliminated. Several numerical examples demonstrating the capability and performance of the enhanced and hybrid finite element methods are presented. It is also shown that for some situations, such as problems involving high Poisson's ratio and in other related problems where bending effects are evident, the performance of the enhanced and hybrid methods are superior to that of the conventional displacement-based method. The results from the hybrid method are better than those from the enhanced method for some situations, such as problems in which soil permeability is variable or discontinuous within elements. Since all the element parameters except the nodal displacements and nodal pore pressures are assumed in the element level and can be eliminated by static condensation, the implementations of the enhanced method and the hybrid method are basically the same as the conventional displacement-based finite element method. The present enhanced method and hybrid method can be easily extended to non-linear consolidation problems. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    Fast and accurate 4-node quadrilateral

    Magnus Fredriksson
    Abstract An accurate and variationally consistent 4-node quadrilateral element is introduced where high coarse mesh accuracy and low mesh distortion sensitivity are characteristic qualities, even when incompressibility is approached for plane strain. One-point quadrature integration procedure is adopted and a new improved stabilization technique is developed. Orthogonality conditions are utilized so that the patch test is satisfied for arbitrary quadrilaterals. Several numerical examples including a convergence rate study are presented which confirm the excellent performance of this element. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Crack,Tip Toughness of a Soft Lead Zirconate Titanate

    Alain B. Kounga Njiwa
    Crack,opening displacement (COD) measurements were performed on a commercial lead zirconate titanate (PZT). The intrinsic fracture toughness (or crack,tip toughness) of this material was determined using a new evaluation procedure, which takes into account the near,tip CODs and complete crack profile CODs. The crack,tip toughness KI0 was determined from an extrapolation of COD data obtained at various loading stages, thus avoiding the complications caused by subcritical crack growth in PZT. Results for plane strain and plane stress condition are presented. [source]

    An adaptive displacement/pressure finite element scheme for treating incompressibility effects in elasto-plastic materials

    Franz, Theo SuttmeierArticle first published online: 13 AUG 200
    Abstract In this article, a mixed finite element formulation is described for coping with (nearly) incompressible behavior in elasto-plastic problems. In addition to the displacements, an auxiliary variable, playing the role of a pressure, is introduced resulting in Stokes-like problems. The discretization is done by a stabilized conforming Q1/Q1 -element, and the corresponding algebraic systems are solved by an adaptive multigrid scheme using a smoother of block Gauss,Seidel type. The adaptive algorithm is based on the general concept of using duality arguments to obtain weighted a posteriori error bounds. This procedure is carried out here for the described discretization of elasto-plastic problems. Efficiency and reliability of the proposed adaptive method is demonstrated at (plane strain) model problems. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:369,382, 2001 [source]

    Modelling interactions between fold,thrust belt deformation, foreland flexure and surface mass transport

    BASIN RESEARCH, Issue 2 2006
    Guy D. H. Simpson
    ABSTRACT Interactions between fold and thrust belt deformation, foreland flexure and surface mass transport are investigated using a newly developed mathematical model incorporating fully dynamic coupling between mechanics and surface processes. The mechanical model is two dimensional (plane strain) and includes an elasto-visco-plastic rheology. The evolving model is flexurally compensated using an elastic beam formulation. Erosion and deposition at the surface are treated in a simple manner using a linear diffusion equation. The model is solved with the finite element method using a Lagrangian scheme with marker particles. Because the model is particle based, it enables straightforward tracking of stratigraphy and exhumation paths and it can sustain very large strain. It is thus ideally suited to study deformation, erosion and sedimentation in fold,thrust belts and foreland basins. The model is used to investigate how fold,thrust deformation and foreland basin development is influenced by the non-dimensional parameter , which can be interpreted as the ratio of the deformation time scale to the time scale for surface processes. Large values of imply that the rate of surface mass transport is significantly greater than the rate of deformation. When , the rates of surface processes are so slow that one observes a classic propagating fold,thrust belt with well-developed wedge top basins and a largely underfilled foreland flexural depression. Increasing causes (1) deposition to shift progressively from the wedge top into the foredeep, which deepens and may eventually become filled, (2) widespread exhumation of the fold,thrust belt, (3) reduced rates of frontal thrust propagation and possible attainment of a steady-state orogen width and (4) change in the style and dynamics of deformation. Together, these effects indicate that erosion and sedimentation, rather than passively responding to tectonics, play an active and dynamic role in the development of fold,thrust belts and foreland basins. Results demonstrate that regional differences in the relative rates of surface processes (e.g. because of different climatic settings) may lead to fold,thrust belts and foreland basins with markedly different characteristics. Results also imply that variations in the efficiency of surface processes through time (e.g., because of climate change or the emergence of orogens above sea level) may cause major temporal changes in orogen and basin dynamics. [source]