Deviatoric Plastic Strain Research Articles

Prediction of non-proportionality factors of multiaxial histories using the Moment Of Inertia method

This work studies further an approach originally proposed to evaluate equivalent stress and strain ranges in non-proportional (NP) load histories, called the Moment Of Inertia (MOI) method. The MOI method assumes that the path contour in the deviatoric stress or strain diagram is a homogeneous wire with unit mass. The center of mass of such wire gives then the mean component of the path, while the moments of inertia of the wire can be used to obtain the equivalent stress or strain ranges. The MOI method is an alternative to convex enclosure methods, such as Dang Van’s Minimum Ball or the Maximum Prismatic Hull methods, without the need for computationally-intensive search algorithms or adjustable parameters. The MOI method is extended here to calculate as well the non-proportionality factor Fnp of generic multiaxial load histories, formulated in an alternative sub-space of the deviatoric plastic strains. Experimental results for 14 different multiaxial histories prove the effectiveness of the MOI method to predict the observed non-proportionality factors. Hence, it can be a most useful tool for the computation of multiaxial fatigue damage in practical applications.

Progressive failure analysis of shallow foundations on soils with strain-softening behaviour

This paper presents a finite element approach to analyse the response of shallow foundations on soils with strain-softening behaviour. In these soils, a progressive failure can occur owing to a reduction of strength with increasing the plastic strains induced by loading. The present approach allows this failure process to be properly simulated by using a non-local elasto-viscoplastic constitutive model in conjunction with a Mohr–Coulomb yield function in which the shear strength parameters are reduced with the accumulated deviatoric plastic strain. Another significant advantage of the method is that it requires few material parameters as input data, with most of these parameters that can be readily obtained from conventional geotechnical tests. To assess the reliability of the proposed approach, some comparisons with experimental results from physical model tests are shown. A fairly good agreement is found between simulated and observed results. Finally, the progressive failure process that occurs in a dense sand layer owing to loading is analysed in details, and the main aspects concerning the associated failure mechanism are highlighted.

A three-dimensional sharp interface Cartesian grid method for solving high speed multi-material impact, penetration and fragmentation problems

This work presents a three-dimensional, Eulerian, sharp interface, Cartesian grid technique for simulating the response of elasto-plastic solid materials to hypervelocity impact, shocks and detonations. The mass, momentum and energy equations are solved along with evolution equations for deviatoric stress and plastic strain using a third-order finite difference scheme. Material deformation occurs with accompanying nonlinear stress wave propagation; in the Eulerian framework the boundaries of the deforming material are tracked in a sharp fashion using level-sets and the conditions on the immersed boundaries are applied by suitable modifications of a ghost fluid approach. The dilatational response of the material is modeled using the Mie-Gruneisen equation of state and the Johnson–Cook model is employed to characterize the material response due to rate-dependent plastic deformation. Details are provided on the treatment of the deviatoric stress ghost state so that physically correct boundary conditions can be applied at the material interfaces. An efficient parallel algorithm is used to handle computationally intensive three-dimensional problems. The results demonstrate the ability of the method to simulate high-speed impact, penetration and fragmentation phenomena in three dimensions.

The Anisotropy Characteristic of Rock Material Described by the Stress Softening Criterion in Civil Engineering

In this paper, firstly we utilize the elastic model, which provides the simplest representation of material behavior in civil engineering. This model is valid for homogeneous, isotropic, continuous materials that exhibit linear stress-strain behavior with no hysteresis on unloading. The elastic models include both isotropic and anisotropic elastic models. Then the Mohr-Coulomb model is used which can represent shear failure in soils and rocks in civil engineering and geotechnical engineering. After that, the strain- softening model is founded, which allows representation of nonlinear material softening and hardening behavior based on prescribed variations of the Mohr-Coulomb model properties (cohesion, friction, dilation, tensile strength) as functions of the deviatoric plastic strain. Finally, a case study is done for the stratified rock mass, the elastic modulus of the rock sample for different surrounding compressive are obtained, to exhibit the anisotropy characteristic of this type of rock material

Critical state finite element models of contractional fault-related folding: Part 2. Mechanical analysis

Finite element modeling of contractional fault-related folding with critical state mechanics concepts reveals fundamentally different behaviors at two levels, depending on (1) mechanical stratigraphy and (2) initial fault geometry. Deviatoric plastic strain rate and strain patterns show that ‘strong’ layers, like normally consolidated sandstone or overconsolidated shale, develop strain localization in form of narrow plastic shear bands. ‘Soft’ layers like normally consolidated shale fail to develop localizations and respond by diffuse, distributed plastic strain. Inter-layered overburdens display both deformation modes. Models with listric thrust fault seeds develop basement-cored anticlines in the hangingwall that are characterized by locally tensile stress regimes within overall compressive regional stress fields. The anticline crests of these models show evidence for strain softening. By contrast, anticlines emerging in detached fault-related fold models are subject to locally compressive stress regimes, consistent with the applied far-field shortening. These anticline crests strain-harden during deformation. Stresses resulting from the finite element models deviate from stress estimates based on integrated densities. The discrepancy is small for basement-involved models but significant for detached style models, suggesting that stress predictions based on integrated densities may be inaccurate for contractional systems. First-order predictions of plastic deformation suggest that footwall synclines in basement-involved fold styles may host reservoirs with relatively poor quality owing to horizontal and vertical compaction. Anticlines found in detached deformation styles are bounded by compactive domains whereas the crestal regions are less affected by volumetric plastic deformation thus producing relatively better reservoir quality.

Anisotropic bounding-surface plasticity model for the cyclic shakedown and degradation of saturated clay

The cyclic behaviours of embedded offshore structures under different cyclic loading levels are related to the cyclic shakedown and degradation of the surrounding soils. In the present study, a damage-dependent bounding-surface model based on a newly proposed hardening rule was developed to predict the cyclic shakedown and degradation of saturated clay and the effect of the initial anisotropic stress state. By extending the Masing’s rule to the bounding-surface plasticity theory, the stress reversal point is taken as the generalised homological centre of the bounding surface. With movement of the generalised homological centre, at lower stress amplitudes, the cyclic process ends at a steady state, and cyclic shakedown is reached. At higher stress amplitudes, a damage parameter related to the accumulated deviatoric plastic strain is incorporated into the form of the bounding surface, which is hence able to contract to model degradations in stiffness and strength. To take into account the effects of initial anisotropic conditions on the cyclic behaviour of soils, an initial anisotropic tensor is introduced in the bounding surface. The developed model is validated through undrained isotropic and anisotropic cyclic triaxial tests in normally consolidated and overconsolidated saturated clay under both one-way and two-way loadings. Both cyclic shakedown and degradation are well reproduced by the model, as is the anisotropy effect induced by the initial anisotropic consolidation process.

Assessment of liquefaction potential based on modified disturbed state concept

In this paper, the application of the disturbed state concept model for the assessment of liquefaction potential is examined through experimental and analytical investigation. In order to achieve a more realistic description of the dynamic responses of saturated sands, the disturbed state concept model was modified based on the dynamic effective stress path and excess pore pressure development. Static and cyclic undrained triaxial tests were performed for sands with different relative densities and confining stresses. Based on test results, a classification of liquefaction phases was proposed, in terms of the dynamic effective stress path and the excess pore pressure development. This was adopted into the modified disturbed state concept model. The liquefaction assessment method is also proposed, using the disturbed state concept model based on the deviatoric plastic strain trajectory. Factors of safety, calculated from the equivalent cyclic stress concept, were compared with the proposed method using the original and modified disturbed state concept models. This was proposed by using examples with different soil and earthquake conditions.

A two‐mechanism elastoplastic model for shakedown of unbound granular materials and DEM simulations

SUMMARYAn elastoplastic model has been developed for the finite elements modelling of repeated load triaxial tests. This model is based on the shakedown theory established by Zarka for metallic structures. To the previous works, which were based on the Drucker–Prager yield surface and the plastic potential of Von Mises, a compression cap has been added to each one. The model straightforwardly determines the purely elastic state or the elastic shakedown state or the plastic shakedown state and calculates the deviatoric and the volumetric plastic strains. The calibration of the elastoplastic model has been carried out with DEM simulations and an unbound granular material for roads under repeated load triaxial tests using finite element method. The calculations underline the capabilities of the model to take into account, with a unique formalism, the accumulation of the deviatoric and volumetric plastic strains along the loading cycles. Copyright © 2011 John Wiley & Sons, Ltd.

Directional plasticity of clay showing instability

A graphical approach is used to sketch the field of small plastic strains (ϵ < 0.1 %) of Pisa clay along different axi-symmetric stress paths associated to a partial confining stress reduction. Within the classic framework of elasto-plasticity, volumetric and deviatoric plastic strains contours are determined from data obtained from triaxial tests, assuming a cross-anisotropic hypo-elastic formulation calibrated on a wide set of tests and with non linear evolution of the elastic moduli calibrated along a quasi-1D swelling stress path. The evolutions of the plastic strains and of the plastic strain vectors are shown along the stress path directly explored with tests and along virtual paths interpolated from the actual data along intermediate directions at various strain levels.

Stability analysis of slopes in soils with strain-softening behaviour

This paper presents a numerical approach to analyse the stability of slopes in soils with strain-softening behaviour. In these materials, a progressive failure can occur owing to a reduction of strength with increasing strain. Such a phenomenon can be analysed using methods that are able to simulate the formation and development of the shear zones in which strain localises. From a computational point of view, this presents many difficulties because the numerical procedures currently used are often affected by a lack of convergence, and the solution may depend strongly on the mesh adopted. In order to overcome these numerical drawbacks, in the present study use is made of a non-local elasto-viscoplastic constitutive model within the framework of the finite element method. The Mohr–Coulomb yield function is adopted, and the strain-softening behaviour of the soil is simulated by reducing the strength parameters with the increasing deviatoric plastic strain. To assess the reliability of the proposed approach, some comparisons with the results obtained using other constitutive models for soils with strain-softening behaviour are presented. Finally, a slope subjected to a prescribed process of weathering is considered, and the effects of this process on the slope stability are discussed.

Numerical aspects of non-coaxial model implementations

Abstract This paper ascertains the reasons for the numerical problems when the yield vertex non-coaxial model is implemented in the finite element analysis to predict the behaviour of complicated geotechnical engineering problems. The numerical problem, reflected in the failure of convergence in the non-linear solutions in ABAQUS, is likely to happen when a smaller non-coaxial plastic modulus is used. It is found that a large non-coaxial influence at the start of elastoplastic loading, which causes the predominance of non-coaxial plastic strain rate over the coaxial plastic strain rate in stress–strain responses, is the reason for the numerical problem. The original yield vertex non-coaxial model is modified to overcome the numerical problem. Instead of a constant non-coaxial plastic modulus in the original yield vertex non-coaxial model, the non-coaxial modulus is made a function of cumulative deviatoric plastic strain. It shows that the modified non-coaxial model retains the functions of the original non-coaxial model. Meanwhile, it overcomes the non-convergence problem when a smaller non-coaxial plastic modulus, representing a larger non-coaxial influence, is used.

Development in modeling cyclic loading of sands based on kinematic hardening

AbstractIn this paper, there is presented an elastoplastic constitutive model to predict sandy soils behavior under monotonic and cyclic loadings. This model is based on an existing model (Cambou‐Jafari‐Sidoroff) that takes into account deviatoric and isotropic mechanisms of plasticity. The flow rule used in the deviatoric mechanism is non‐associated and a mixed hardening law controls the evolution of the yield surface. In this research the critical state surface and history surface, which separates the virgin and cyclic states in stress space, are defined. Kinematic hardening modulus and stress–dilatancy law for monotonic and cyclic loadings are effectively modified. With taking hardening modulus as a function of deviatoric and volumetric plastic strain and with defining the history surface and stress reversal, the model has the ability to predict the sandy soils' behavior. All of the model parameters have clear physical meanings and can be determined from usual laboratory tests. In order to validate the model, the results of homogeneous tests on Hostun and Toyoura sands are used. The results of validation show a good capability of the proposed model. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Path-independent integrals to identify localized plastic events in two dimensions

We use a power expansion representation of plane-elasticity complex potentials due to Kolossov and Muskhelishvili to compute the elastic fields induced by a localized plastic deformation event. Far from its center, the dominant contributions correspond to first-order singularities of quadrupolar and dipolar symmetry which can be associated, respectively, with pure deviatoric and pure volumetric plastic strain of an equivalent circular inclusion. By construction of holomorphic functions from the displacement field and its derivatives, it is possible to define path-independent Cauchy integrals which capture the amplitudes of these singularities. Analytical expressions and numerical tests on simple finite-element data are presented. The development of such numerical tools is of direct interest for the identification of local structural reorganizations, which are believed to be the key mechanisms for plasticity of amorphous materials.

A new numerical procedure for elasto-plastic analysis of a circular opening excavated in a strain-softening rock mass

A simple numerical procedure for calculating the distribution of stresses and radial displacements around a circular tunnel excavated in a strain-softening Mohr–Coulomb or generalized Hoek–Brown rock mass is proposed. The problem is considered as axisymmetric, i.e. the initial stress state is assumed to be hydrostatic and the rock mass is said to be isotropic. By invoking the finite difference approximation of the equilibrium and compatibility equations, the increments of stresses and strains for each ring, starting from the outmost one for which boundary conditions are known a priori, are calculated in a successive manner. In the proposed approach, the potential plastic zone is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium equation. For the strain-softening behavior, it is assumed that all the strength parameters are a linear function of deviatoric plastic strain. Several illustrative examples are given to demonstrate the performance of the proposed method. For the brittle–plastic case, the results show a very good agreement with the closed-form solution. For strain-softening cases, the predictions by the proposed method are also in good agreement with the known rigorous numerical solutions. It is shown that the approximate solution converges to the exact solution when the increment of stress for each ring becomes smaller. The influence of the strength parameter ‘a’, appearing in the generalized Hoek–Brown criterion, on the elasto-plastic solutions is examined through the establishment of ground reaction curves and the discussion for the locations of the plastic radii.

Extended yield condition of soils with tensile yield strength and rotational hardening

An extended yield condition of soils applicable to the range of negative pressure is proposed. A closed surface is formulated in a simple mathematical form not limited to the range of positive pressure. A hardening function of plastic volumetric strain is adopted, based on the linear relation of both logarithms of volume and pressure extended to the negative range of pressure for the isotropic consolidation. Isotropic softening, due to the deviatoric plastic strain rate, and anisotropic hardening, due to rotation of yield surface (rotational hardening) are also incorporated into the extended yield condition.

An experimental investigation into the mechanical behaviour of a structured stiff clay

In recent years, fundamental research has been carried out into the properties of some natural stiff clays and the corresponding reconstituted materials, highlighting the role of microstructural features in the observed differences. In this paper the results of an experimental investigation into the mechanical behaviour of an Italian stiff clay of marine origin are presented. Medium-pressure and high-pressure stress-controlled triaxial cells were used in which natural samples underwent isotropic and anisotropic compression and swelling before drained or undrained shearing. Comparison of soil behaviour observed after different compression histories up to different values of maximum effective stress allowed the following aspects to be discussed: the effects of the initially structured state on the medium to large strain response and shear strength characteristics of the soil; the relevance of volumetric and deviatoric plastic strain to the structure degradation; the role and implications of the imposed non-isotropic stress histories; the permanent differences between reconstituted samples and fully destructured natural samples; and the uniqueness of the critical state condition.

A new methodology to delineate the compactive yield cap of two porous sandstones under undrained condition

We have developed an experimental methodology to investigate the compactive yield behavior of porous sandstones under undrained condition and to distinguish it from the conventional method we refer to it as “modified undrained”. In a conventional undrained test a sample is deformed while the confining pressure and pore volume are fixed. Our novel method is designed to simulate undrained experiments by maintaining a constant pore fluid volume during triaxial loading. However, unlike in typical undrained experiments where pore pressure is allowed to vary, the modified method maintains a constant pore pressure, and instead relies on the simultaneous manipulation of the confining pressure and axial stress to maintain a constant pore fluid pressure. We apply this method to two sandstones precompacted inelastically to a range of porosities. The stress paths from a modified undrained test map out isoporosity stress contours that would coincide with the yield caps, if the elastic strain is negligible. Conventional triaxial experiments under drained condition, in which strain hardening was observed, provide constraints on the yield caps for different values of plastic volumetric strains. While at high mean stresses the yield caps for plastic strains <3% correlate with the isoporosity contours, we observed that at high deviatoric stresses and plastic strains the yield caps diverged from the isoporosity contours. This point of divergence was concomitant with an upsurge of acoustic emissions, implying that the stress path for an undrained experiment has pushed into a stress regime beyond the current yield cap thus triggering inelastic damage.

Numerical analysis of a landslide in soils with strain-softening behaviour

The results of an analysis concerning a landslide of great dimensions, which occurred at Senise (Southern Italy) on 26 July 1986, are presented. The landslide was of a translational type, and the failure developed within a thin clayey silt layer interbedded by a slightly cemented sand formation. Both these soils experienced a pronounced strain-softening behaviour during laboratory tests. From the analyses performed using the traditional limit equilibrium approach, it has been found that the average operational resistance along the sliding surface was less than that of the peak and greater than the residual resistance deduced from the laboratory tests. As a consequence, it has been postulated that a progressive failure had occurred. Such a failure process can be appropriately studied using methods that are capable of simulating the formation and development of shear zones, where strain is localised. From a computational point of view this presents many difficulties, because the numerical procedures currently used are very often affected by a lack of convergence, and the solution may depend strongly on the mesh adopted. In order to overcome these numerical drawbacks, in the present study use is made of both an elasto-viscoplastic constitutive model and a nonlocal elasto-viscoplastic model implemented in a finite element code. The Mohr–Coulomb plastic law is adopted, and the strain-softening behaviour of the soil is simulated by reducing the strength parameters with the accumulated deviatoric plastic strains. The results of the analysis show that a progressive failure occurred owing to deep excavations carried out at the toe of the slope. In addition, the soil mass involved in the sliding and the location of the failure surface deduced from the numerical simulation are found to be very similar to those observed.

Effect of deviatoric plastic strain on the mechanical behaviour of composite powder compacts with large amount of hard phase

The effect of increasing amounts of deviatoric plastic strain on the mechanical behaviour of powder composite compacts is investigated. The study focuses on a highly charged composite of soft Aluminium particles with hard Nickel based super-alloy particles. Three mechanical tests, imposing different stress states, are carried out at various temperatures on powder compacts that have been submitted to increasing amount of deviatoric plastic strain. These tests are used to gather information on the alterations that such deviatoric strains cause on the powder compact mechanical response. It is shown that the ductility and the yield stress of the powder compacts increase with increasing amounts of cumulated plastic strain. The particulate nature of the compact fades, but some aspects of the mechanical behaviour (macroscopic rate dependence in particular) are still characteristic of the original particulate material even after significant amount of accumulated deviatoric strain. Microstructural observations are carried out to provide a reasonable scenario for the mechanisms responsible of the alterations that deviatoric strains bring.

압축력을 받는 콘크리트에 대한 세 직교 응력 성분을 이용한 소성 모델

A plasticity model was developed to predict the behavioral characteristics of concrete in multiaxial compression. To extend the applicability of the proposed model to concrete in various stress states, a new approach for failure criteria was attempted. A stress was decomposed into one volumetric and two deviatoric components orthogonal to each other. Three failure criteria wire provided independently for each stress component. To satisfy the three failure criteria, the plasticity model using multiple failure criteria was Implemented. Each failure surface was defined by equivalent volumetric or deviatoric plastic strain. To present dilatancy due to compressive damage a non-associative flow nile was proposed. The proposed model was implemented to finite element analysis, and it was verified by comparisons with various existing test results. The comparisons show that the proposed model predicted well most of the experiments by using three independent failure criteria.