Plane Strain Loading Conditions Research Articles

Constitutive models for porous materials with evolving microstructure

A constitutive model is developed for the effective behavior of nonlinear porous materials which is capable of accounting, approximately, for the evolution of the material's microstructure under large quasi-static deformations. The model is formulated in terms of an effective potential function for the porous material, which depends on appropriate variables characterizing the state of the microstructure, together with evolution equations for these state variables. For the special case of triaxial loading of an initially isotropic porous material, the appropriate state variables are the porosity and the aspect ratios of the typical void; they serve respectively to characterize the evolution of the size and shape of the pores. The implications of the model are studied in the context of two specific examples: axisymmetric and plane strain loading conditions. It is found that the porosity acts as a hardening mechanism when the material is subjected to boundary conditions resulting in overall hydrostatic compression, and as a softening mechanism for overall hydrostatic tension. On the other hand, the change in shape of the voids is found to have a more subtle influence on the overall behavior of the porous material. Thus the change in shape of the voids has a direct effect which may range from strong softening during void collapse to slight hardening during void elongation, but it also has an indirect effect through its concomitant effect on the evolution of the porosity, which may actually be quite significant. Because of the complex interplay between these hardening-softening mechanisms, the new model is found to yield significantly different predictions, in particular for the onset of localization, than the well-known model of Gurson, which neglects the change in shape of the voids, especially, for low-triaxiality loading conditions. The model, in its present form, is not meant to be used for high-triaxialities for which the Gurson and other associated models are considered to be quite accurate.

Reinforced granular fill-soft soil system: Membrane effect

A new model for a reinforced shallow foundation bed is proposed by incorporating the ‘rough membrane’ element for a single layer reinforcement. Mechanics of the rough membrane element with the assumption of horizontal shear stress transfer at the soil/reinforcement interfaces are explained and formulated. The model is generalized by incorporating nonlinear responses of the soft soil and of the granular fill under plane strain loading conditions. The membrane effect is quantified in terms of the improvement in the load-settlement responses of the composite foundation system over the unreinforced one. Parametric results indicate that reinforcement while in tension spreads the load over a larger area, leading to a reduction in the settlement beneath the footing.

Stresses due to flow past a circular cylinder

An analysis has been presented to calculate the stresses and deformations in the cylinder for both the axisymmetric and axiasymmetric cases of flow past a stationary circular cylinder by adopting a numerical technique. The cylinder has been considered to be a thick cylinder under plane strain loading conditions. The pressure distribution on the cylinder surface has been approximated by Fourier series. The solution has been obtained by using Airy's stress function approach. It has been observed that the values for maximum and minimum stresses and deformations are quite remote from those of the values for a cylinder having uniform pressure.

Settlement response of a reinforced shallow earth bed

Presently, reinforcement in the form of extensible (e.g. geosynthetics) or apparently inextensible (e.g. metallic strips) inclusions are applied widely for strengthening shallow foundation beds. The effective use of reinforcement requires the understanding of its performance in combination with the strength characteristics of the soil to be reinforced. This paper is concerned with the development of a simple mathematical model to account for the membrane effect of a reinforcement layer on the load-settlement response of a reinforced granular fill-soft soil foundation system. The nonlinear loading pressure-settlement response of the granular fill and soft soil, respectively, for plane strain loading condition are incorporated into the formulation. Parametric studies for a uniformly loaded strip footing show that membrane action of reinforcement causes reduction in the settlement below the footing which is over and above the effect of granular fill.

The influence of specimen geometry on the Portevin-Le Chatelier effect in an AlMg alloy

The nature of stress-strain discontinuities and surface deformation markings, in an aluminiummagnesium alloy known to exhibit serrated flow associated with dynamic strain ageing (DSA), has been investigated as a function of specimen geometry during tensile deformation. It is demonstrated that specimen shape and size can significantly influence both the type of deformation bands observed as well as the characteristics of the flow serrations when Portevin-Le Chatelier (PLC) bands are produced. The observations are discussed in terms of criteria that determine the transition from plane stress to plane strain loading conditions and the implications for interpretation of data used to identify specific categories of serrated flow are considered.

The influence of nucleation criterion on shear localization in rate-sensitive porous plastic solids

The influence of the void nucleation criterion on localization in strain rate-sensitive porous plastic solids is analyzed under plane strain and axisymmetric tensile loading conditions using an infinite band model. The void nucleation process is described in terms of a void nucleation stress that depends linearly on the hydrostatic tension with a coefficient that is less than unity. Although the nucleation strain depends monotonically on the void nucleation stress coefficient, the dependence of the localization strain on this quantity is not necessarily monotonic. With the void nucleation stress coefficient fixed, there can also be a nonmonotonic dependence of the critical strain for localization on imposed strain rate.

Analysis of Elastomeric O-Ring Seals in Compression Using the Finite Element Method

The need for a methodology to determine the stiffness characteristics of elastomeric seals with complex geometry has prompted an investigation using a commercially available finite element code. Axial and radial compression of O-rings, as well as the influence of restraining grooves and friction, are investigated. Axisymmetric analyses are performed, and their results are compared with those obtained by other researchers who assumed plane strain conditions. The differences in the results of the axisymmetric and plane strain loading conditions increase with the level of compression, except for one loading case. The method of reduced integration is shown to effectively handle the problem of high localized hydrostatic stresses, which are especially enhanced in confined geometries, and to provide accurate results. Stiffness characteristics of O-ring seals having a range of geometric and material properties are given in a nondimensional form. This form allows for general modeling of the O-ring stiffness as a f...

Effect of Deformation-Induced Heating on the Cold Drawing of Polymeric Films

The destabilizing effect of deformation-induced heating on the cold drawing of polymeric films is investigated under adiabatic and plane-strain loading conditions. An approximate method, previously devised to study the steady-state cold drawing of polymers with viscoplastic properties, is further modified to incorporate the softening effects due to temperature. Parametric studies are carried out showing the interaction of material properties with the kinematics of the process.

Evaluation of a Modified Monotonic Neuber Relation

It has been proposed in the literature that the Neuber relation be modified to read Kε/Kt×(Kσ/Kt)m=1 in order to improve its predictive capability when plane strain loading conditions exist. Kε, Kσ, and Kt are respectively the strain, stress, and elastic concentration factors. The exponent m is proposed to be 1 for plane stress and 0 for plane strain. This paper reports the results of biaxial notch root strain measurements on three sets of double-notched aluminum specimens that have different thicknesses and root radiuses. Elastoplastic strains are measured over gage lengths as short as 150 micrometers with a laser-based in-plane interferometric technique. The measured strains are used to compute Kε directly and Kσ using the uniaxial stress-strain curve. The exponent m can then be determined for each amount of constraint. The amount of constraint is defined as the negative ratio of lateral to longitudinal strain at the notch root and determined from elastic finite element analyses. As this ratio decreases for the three cases, the values of m are found to be 0.65, 0.48, and 0.36. The modified Neuber relation is an improvement, but discrepancies still exist when plastic yielding begins at the notch root.

A continuum damage model for simulation of the progressive failure of brittle rocks

A constitutive model is developed in which a set of continuous field variables, called damage vectors are used to describe the anisotropic response of a brittle solid due to the growth of cracks under general applied loads. The model is tested numerically by studying the response of infinitely extended solids under a number of general plane strain loading conditions.

A finite element study of the near crack tip deformation of a ductile material under mixed mode loading

In ductile fracture, voids near a crack tip play an important role. From this point of view, a large deformation finite element analysis has been made to study the deformation, stress and strain, and void ratio near the crack tip under mixed mode plane strain loading conditions, employing Gurson's constitutive equation which has taken into account the effects of void nucleation and growth. The results show that: (i) one corner of the crack tip sharpens while the other corner blunts, (ii) the stress and strain distributions except for the near crack tip region, can be superimposed by normalizing distance from the crack tip by a crack tip deformation length, i.e., a steady-state solution under a mixed mode condition has been obtained, (iii) the field near a crack tip can be divided into four characteristic fields ( K field, HRR field, blunted crack tip field, and damaged region), and (iv) the strain and void volume fraction become concentrated in the sharpened part of a crack tip with increasing Mode II component.

Behaviour of a brittle sandstone in plane-strain loading conditions : Stavropoulos, V G Proc 23rd Symposium on Rock Mechanics, Berkeley, 25–27 August 1982, P351–358. Publ New York: AIME, 1982

Behaviour of a brittle sandstone in plane-strain loading conditions : Stavropoulos, V G Proc 23rd Symposium on Rock Mechanics, Berkeley, 25–27 August 1982, P351–358. Publ New York: AIME, 1982

Further development of generalized constitutive relations for metal deformation

A set of constitutive equations is presented to describe the history dependent plastic deformation behavior of anisotropic metals under multiaxial loading conditions. The primary variables that characterize the material behavior with increasing deformation are the effective flow strength,k; the residual or back stress vectorαi; and the anisotropy matrix,Mtj. The strain rate is given in terms of an equivalent plastic strain rate, the gradient of a plastic potential, which incorporates key material variables and the stress state. All the material parameters have been determined for a recrystallized Zircaloy-2 from 25 to 450 °C and a solution treated 304 stainless steel from 25 to 650 °C based on experiments that included monotonic, load reversal, and load relaxation tests. The analytical model has been used to simulate the deformation behavior of both metals under a variety of testing conditions, including cyclic and plane strain loading conditions. The general form of the constitutive relation is shown to be consistent with experimental data obtained for various material orientations under different loading conditions.