Effective Stress Concept Research Articles

New Strain-Energy-Based Coupled Elastoplastic Two-Parameter Damage and Healing Models for Earth-Moving Processes

Novel strain–energy-based coupled elastoplastic two-parameter damage and healing formulations for geomaterials are developed and implemented for a numerical simulation of two-dimensional earth-moving processes. A new class of elastoplastic damage–healing models is proposed within an initial-elastic strain–energy-based framework. The governing incremental damage and healing evolutions are coupled in volumetric and deviatoric parts and characterized through the effective stress concept. The plastic flow is established via an additive split of the stress tensor. Specifically, we introduce four characteristic energy norms of the tensile volumetric, tensile deviatoric, compressive volumetric, and compressive deviatoric strain tensors, respectively, for the corresponding volumetric and deviatoric damage and healing mechanisms. By adopting a micromechanics-motivated damage characterization (P+) and a healing characterization (P–) in the volumetric and deviatoric parts, the proposed two-parameter damage–healing models are implemented to demonstrate considerable versatility on numerical simulations of earth-moving processes. New computational algorithms are systematically developed based on the two-step operator splitting methodology. The volumetric and deviatoric elastic-damage–healing predictor and the effective plastic corrector are implemented within the Reproducing Kernel Particle Method (RKPM) meshfree codes. Numerical examples under earth excavation, transport, and compaction are presented to illustrate salient features of soils such as shear band and partial recovery of soil stiffness due to compaction by the new two-parameter damage–healing models.

Novel Strain Energy Based Coupled Elastoplastic Damage and Healing Models for Geomaterials – Part I: Formulations

Innovative strain energy based coupled elastoplastic hybrid isotropic and anisotropic damage and healing formulations for geomaterials are developed and implemented for numerical 2D earth-moving processes and cyclic loading simulations. A class of elastoplastic constitutive damage-healing models, based on a continuum thermodynamic framework, is proposed within an initial elastic strain energy based formulation. In particular, the governing incremental damage and healing evolutions are coupled and characterized through the effective stress concept in conjunction with the hypothesis of strain equivalence. The plastic flow is introduced by means of an additive split of the stress tensor. In this innovative formulation, we introduce two characteristic energy norms of the tensile and compressive strain tensors, respectively, for the damage and healing mechanisms. By incorporating a micromechanics-motivated brittle (tensile) damage characterization (P+) and a ductile (mixed tension–compression) damage-healing characterization ([Formula: see text]), the proposed hybrid isotropic and anisotropic models for soils are derived. Completely new computational algorithms are systematically developed in Part II of this sequel, based on the two-step operator splitting methodology. The elastic damage-healing predictor and the effective plastic return mapping corrector are implemented within the reproducing kernel particle method meshfree codes.

A thermo‐hydro‐mechanical model for unsaturated soils based on the effective stress concept

AbstractA simple thermo‐hydro‐mechanical (THM) constitutive model for unsaturated soils is described. The effective stress concept is extended to unsaturated soils with the introduction of a capillary stress. This capillary stress is based on a microstructural model and calculated from attraction forces due to water menisci. The effect of desaturation and the thermal softening phenomenon are modelled with a minimal number of material parameters and based on existing models. THM process is qualitatively and quantitatively modelled by using experimental data and previous work to show the application of the model, including a drying path under mechanical stress with transition between saturated and unsaturated states, a heating path under constant suction and a deviatoric path with imposed suction and temperature. The results show that the present model can simulate the THM behaviour in unsaturated soils in a satisfactory way. Copyright © 2010 John Wiley & Sons, Ltd.

Design Optimization of Components Based on Material Mechanics Fatigue Concepts

Abstract The paper deals with the fatigue design concepts for engineering components based on material properties and mechanics, i.e. the Short Crack Model (SCM), the Local Strain Approach (LSA), and the Effective Notch Stress Concept (ENSC) for welds. The calculation procedures are presented and their accuracy and robustness are demonstrated on the example of a cab bearing console providing complex geometry (geometry notch, weld with pronounced start and ends) and subjected to operating loading with variable stress amplitudes and mean stresses. Parametrical studies considering two ductile steels were performed. Comparison of calculated curves by means of the SCM and the LSA supported by the PSW T-parameter explores life factors of 3 to 6.7 emphasizing the crucial influence of load sequence effects on fatigue life and the usefulness of the SCM to consider them. The choice of the material influences the lifetime of the console significantly (life factors of ∼5 to ∼11 depending on the applied model). The weld design was assessed by the ENSC to be safe.

3D numerical simulation of injection into a porous natural gas storage

The increasing demand for the consumption of natural gas has attracted the interest to store natural gas in depleted reservoirs. Natural gas is injected into the depleted reservoir and then produced once needed to be supplied to the consumers through pipelines. Changes of reservoir fluid pressure due to injection/ depletion will result in the local changes of stress regime inside the reservoir as well as the surrounding rocks. These stress fluctuations will primarily lead to the deformations and changes of the loads exerted on the wellbore. This can potentially trigger hazardous events such as considerable land surface movements, wellbore instability and casing collapse, fault reactivation, and cap rock failure. Therefore a good knowledge of reservoir geomechanics is required when planning storage of natural gas in a depleted reservoir. In this paper the concept of effective stress and pore pressure will be reviewed. A 3D finite element (FE) numerical modelling technique is developed to investigate the changes in stresses and displacements either during the injection or the depletion in a complete isotropic elastic media. The numerical code is used to simulate the injection-induced stress and displacement fields at a field scale for a hypothetical model with an embedded porous formation. The effect of formation rock mechanical properties such as Young’s modulus is also investigated through a series of sensitivity analysis. The results are presented and interpreted and various conclusions are made.

New developments at the recent update of the IIW recommendations for fatigue of welded joints and components

AbstractThe International Institute of Welding (IIW) has published its first comprehensive recommendation on fatigue design of welded structures in 1996. The document appeared in English, French, German and Japanese. The idea was to describe the fatigue properties of welded joints and components independently from application groups with their specific preferences and interests. So, a comprehensive code was established, which covered all current methods of verification, such as component testing, nominal stress, structural stress, notch stress method as well as fracture mechanics assessment procedures. Detailed guidance for assessment of weld imperfections was also given. The outlined safety philosophy covers the different strategies and provides a detailed choice for the designer. The document had a considerable impact on code making bodies and thus it became an important source for the Eurocode. After more than one decade, a new update of the IIW recommendations has been published. The main areas of update are firstly a new consideration of high cycle fatigue in the grid of the Woehler S‐N curves, a standardized meshing for the structural hot‐spot stress concept, which allows now an economic and coarser meshing in finite element analysis, further on the extension of the effective notch stress concept to welded aluminium structures, followed by a numerical assessment of post weld treatments for improving the fatigue properties, and finally a new approach to cumulative damage in connection with multi‐axial stress. The update is a result of a worldwide collaboration of leading research institutions and it is expected that the new update will have the same impact on design and codes as the preceding document.

Modelling the effect of temperature on unsaturated soil behaviour

A simple thermohydromechanical (THM) constitutive model for unsaturated soils is described. The effective stress concept is extended to unsaturated soils with the introduction of a capillary stress. This capillary stress is based on a microstructural model and calculated from attraction forces due to water menisci. The effect of desaturation and the thermal softening phenomenon are modelled with a minimal number of material parameters and based on existing models. THM process is qualitatively and quantitatively modelled by using experimental data and previous work to show the application of the model, including a drying path under mechanical stress with transition between saturated and unsaturated states, a heating path under constant suction and a deviatoric path with imposed suction and temperature. The results show that the present model can simulate the THM behaviour in unsaturated soils in a satisfactory way.

Modelling of plastic deformation and damage in cement‐based material subjected to desiccation

AbstractThe present work is devoted to modelling of plastic deformation and damage in cement‐based materials subjected to desiccation and mechanical loading. Basic mechanical behaviours of cement‐based materials and influences of saturation degree on such behaviours are first recalled. Physical mechanisms of damage induced by desiccation process are analysed. An elastoplastic damage model is then proposed for the description of mechanical responses, taking into account the transition from brittle to ductile behaviours with the increase of confining pressure. The model is further extended to unsaturated conditions: a specific damage driving force and generalized effective stress concept for plastic flow are proposed. The procedure of determination of model's parameters is presented. The proposed model is applied to a standard mortar subjected to desiccation process. The main features of mechanical behaviours as well as the influence of saturation degree are correctly described by the proposed model. In particular, the kinetics of desiccation and related damage evolution are well reproduced. As an example of application, the responses of a concrete beam in three‐point bending test with different desiccation conditions is investigated. Again, the numerical simulations are in good agreement with the experimental data. Copyright © 2010 John Wiley & Sons, Ltd.

Coupled deformation–flow analysis for methane hydrate extraction

Methane hydrate is estimated to be present in substantial amounts below deep sea floors. Particular scientific and engineering interests that encourage studies of mechanical behaviour of methane hydrate soils include submarine geohazards, such as the initiation of marine landslides through hydrate dissociation, wellbore stability and estimation of future gas production from wells. To study these problems, a formulation of a multi-physics model of methane hydrate flow coupled to soil deformation is developed. By assuming deformable porous media (soil matrix) that accommodate non-movable but dissociable hydrate, a two-phase flow formulation of water and methane gas is suggested according to Darcy's law and capillary pressure law. A single-phase elastic–perfectly plastic constitutive model for hydrate soil sediments, based on the concept of effective stress, is developed to account for the effect of hydrate saturation on mechanical strength and stiffness. The formulation is incorporated into the explicit scheme of finite-difference code FLAC by solving three boundary value problems in parallel. The code is used to simulate the behaviour of horizontal unsupported and supported wells in hydrate-bearing sediments under different in situ stress conditions during methane hydrate extraction. Axial force, bending moment and well displacements were compared for supported and unsupported wells.

Bearing capacity factor, N γ , for unsaturated soils by ZEL method

Bearing capacity of foundations is often determined for saturated state of the soil, regarding its simple and conservative results. This assumption, however, results in very uneconomic and overconservative design for a wide range of climates in the world. In this paper, plasticity equations were employed and extended for unsaturated soils to establish a theoretical approach to investigate the bearing capacity of unsaturated soils. It is achieved by combining the concept of effective stress and plasticity equations in terms of effective stress in unsaturated soils. The advantage of Bishop’s (4) effective stress concept was employed to simplify the equations. The equations were then transformed onto the zero extension lines directions to generalize this method for both associative and non-associative problems by which both stress and velocity field can be determined for unsaturated soils. A computer code was also developed to solve the relatively complex plasticity equations for a wide range of soil friction angles and matric suctions to compute the corresponding bearing capacity factor, N γ , for strip foundations with smooth and rough base. This factor seems to be one of the major contributors in the bearing capacity of shallow foundations. The results have been presented in design charts and theoretical equations.

Influence of Ductile Damage Evolution on the Collapse Load of Frames

Abstract In this note we analyze the influence of four damage models on the collapse load of a structure. The models considered here have been developed using the hypothesis based on the concept of effective stress and the principle of strain equivalence and they were proposed by Lemaitre and Chaboche (1990, Mechanics of Solid Materials), Wang (1992, “Unified CDM Model and Local Criterion for Ductile Fracture—I. Unified CDM Model for Ductile Fracture,” Eng. Fract. Mech., 42, pp. 177–183), Chandrakanth and Pandey (1995, “An Isotropic Damage Model for Ductile Material,” Eng. Fract. Mech., 50, pp. 457–465), and Bonora (1997, “A Nonlinear CDM Model for Ductile Failure,” Eng. Fract. Mech., 58, pp. 11–28). The differences between them consist mainly in the form of the dissipative potential from which the kinetic law of damage is derived and also in the assumptions made about some parameters of the material.

Quantitative Dependence of the Effective Modulus of Particle Reinforced Composites on Partially Debonding Damage

BACKGROUND Interfacial deboding may be one of the main damage modes, and largely influence the mechanical performance of the composites. Developing a simple method for accurately predicting the effect of this damage is in keen demand in the domains of both science and engineering. To realize this objective, quantitative characterization of the relationship between the effective material properties and the damage degree should be a prerequisite. Zhao et al. [1] proposed a fictitious inclusion method, and used the volume of the inclusion directly beneath the interfacial cracks as a measure of damage degree. However, the final prediction by this definition made a large difference against the corresponding FE results. Liu et al. [2] adopted the ratio between the projected damaged area in a certain direction and the original interface area to determine the damage variables. Wada [3-4] conducted a systematic analysis of damage variables ranging from 0 to 1, and picked out optimum damage variables for each debonding angle. The change of load carrying capacity of the damaged particles was also studied by FEM. Zheng et al. [5] made use of FEM to examine the influence of debonding angle on the stiffness of the composite. Cho et al. [6] proposed a novel FE model to study the load carrying capacity of a broken particle, and this method can be equally applied to study the influence of partially debonding. So far, the accuracy of these damage variables has never been clearly addressed yet. Since most of FEM analysis were based on a unit cell model, so a big obstacle in the process of verifying these damage variables is the absence of appropriate equivalent medium model. Fortunately, Jiang et al. [7-8] developed a micromechanics model for composites with regularly distributed particles, and thus the validity of the damage variables can be fully examined. A micromechanics method is employed for particle reinforced composite (PRC) with partially debonding damage, and to establish quantitative dependence of the effective modulus on the damage. FEM is also used to study the stress field and implore the inherent damage mechanism. METHODS Particles with elastic stiffness Cp are randomly located in the matrix with stiffness Cm. The terms for particle, matrix and PRC are represented by symbols with the subscripts ‘p’, ‘m’ and an upper bar, respectively. Additionally, tensors and vectors are denoted by bold face letters. Based on Kachanov’s concept of effective stress [9], Chow and Wang [10] proposed a damage effect tensor M(di) to account for the reduction of elastic stiffness of materials at three principal directions, here d1 , d2 and d3 are the damage variables at three principal axes. Defining the effective compliance tensor Dp as T pp =⋅ ⋅

Décomposition de Kelvin et concept de contraintes effectives multiples pour les matériaux anisotropes

The effective stress concept, now classical in continuum damage mechanics, is generalized to the case of an initial anisotropy. In order to be used for both damage–elasticity and damage–(visco-)plasticity coupling, the effective stress should not depend on the elastic properties. Kelvin decomposition of the elasticity tensor allows to define such a stress for isotropic and cubic symmetries. For other material symmetries, the concept of multiple effective stresses is proposed. To cite this article: R. Desmorat, C. R. Mecanique 337 (2009).

Investigation of the Damage-Dependent Response of Mooring Ropes

The focus of this paper is on the development of an analytical damage model for predicting the deterioration of the mechanical properties of polyester (PET) ropes subjected to static tension loading. Experimental data on small PET ropes are used to estimate the evolution of damage using the effective stress concept and the principle of strain equivalence. The proposed damage model relies on an empirically based cumulative scalar damage function, which is founded on the assumption that the strain range experienced by rope elements is the main source of damage under static tension loading conditions. In this particular study, the evolution of the damage function is represented by both power law and polynomial forms. Based on experimental observations, softening behavior is developed by rope elements after reaching their maximum load-carrying capacities. This softening behavior is captured by the damage function through an asymptotic expansion technique (perturbation method). Comparisons between predicted rope responses and experimental data are provided to illustrate the use of the proposed damage model to estimate PET rope response.

Modelling inelastic hinges using CDM for nonlinear analysis of reinforced concrete frame structures

A new formulation based on lumped plasticity and inelastic hinges is presented in this paper for nonlinear analysis of Reinforced Concrete (RC) frame structures. Inelastic hinge behaviour is described using the principles of Continuum Damage Mechanics (CDM). Member formulation contains provisions to model stiffness degradation due to cracking of concrete and yielding of reinforcing steel. Depending on its nature, cracking is classified as concentrated or distributed. Concentrated cracking is accounted through a damage variable and its growth is defined based on strain energy principles. Presence of distributed flexural cracks in a member is taken care of by modelling it as non-prismatic. Plasticity theory supported by effective stress concept of CDM is applied to describe the post-yield response. Nonlinear quasi-static analysis is carried out on a RC column and a wide two-storey RC frame to verify the formulation. The column is subjected to constant axial load and monotonic lateral load while the frame is subjected to only lateral load. Computed results are compared with those due to experiments or other numerical methods to validate the performance of the formulation and also to highlight the contribution of distributed cracking on global response.

Poroplastic damage modeling of unsaturated cement-based materials

An elastoplastic damage model is proposed for cement-based material is unsaturated condition. A generalized effective stress concept is used for poroplastic coupling. Damage by microcracks is coupled with plastic deformation. The proposed model is applied to a mortar in triaxial compression tests with different degrees of saturation. The mechanical response of a concrete beam in different saturation conditions is also analyzed using the proposed model. The model’s predictions are in close agreement with experimental data.

Micromorphic continuum. Part II: Finite deformation plasticity coupled with damage

It is demonstrated how a micromorphic plasticity theory may be formulated on the basis of multiplicative decompositions of the macro- and microdeformation gradient tensor, respectively. The theory exhibits non-linear isotropic and non-linear kinematic hardening. The yield function is expressed in terms of Mandel stress and double stress tensors, appropriately defined for micromorphic continua. Flow rules are derived from the postulate of Il’iushin and represent generalized normality conditions. Evolution equations for isotropic and kinematic hardening are introduced as sufficient conditions for the validity of the second law of thermodynamics in every admissible process. Finally, it is sketched how isotropic damage effects may be incorporated in the theory. This is done for the concept of effective stress combined with the hypothesis of strain equivalence.

A CDM-based study of fatigue–creep interaction behavior

Under stress control mode, the damage evolution during fatigue, creep and their interaction behavior actually is a ductility exhaustion process in response to cyclic and static creep. Based on the ductility dissipation theory and effective stress concept of continuum damage mechanism (CDM), a new fatigue–creep interaction damage model has been developed in this paper, where the change of the inelastic strain energy density is used to define the damage variable. To assess this damage model, high temperature fatigue–creep interaction experiments have been carried out for 1.25Cr0.5Mo steel under stress control mode employing a trapezium waveform. The damage evolution laws of 1.25Cr0.5Mo steel under various combinatorial conditions with different maximum stresses and stress amplitudes are derived. Results indicate that the damage parameter and damage model presented in this paper are applicable to describe the damage evolution for fatigue–creep interaction.

A mixed damage model for unsaturated porous media

The aim of this study is to present a framework for the modeling of damage in continuous unsaturated porous geomaterials. The damage variable is a second-order tensor. The model is formulated in net stress and suction independent state variables. Correspondingly, the strain tensor is split into two independent thermodynamic strain components. The proposed framework mixes micro-mechanical and phenomenological approaches. On the one hand, the effective stress concept of Continuum Damage Mechanics is used in order to compute the damaged rigidities. On the other hand, the concept of equivalent mechanical state is introduced in order to get a simple phenomenological formulation of the behavior laws. Cracking effects are also taken into account in the fluid transfer laws. To cite this article: C. Arson, B. Gatmiri, C. R. Mecanique 337 (2009).

Drying response and effective stress in a double porosity aggregated soil

Shrinkage and water retention characteristics of a double porosity compacted soil are studied. Results from a series of suction controlled oedometric drying tests at different net stresses are presented. Water retention curves exhibit a bimodal response which is a characteristic of the double porosity structure of the soil. Validity of the expression proposed by Khalili et al. [Khalili, N., Witt, R., Laloui, L., Vulliet, L., Koliji, A., 2005. Effective stress in double porous media with two immiscible fluids. Geophys. Res. Lett. 32 (15): Art. No. 15309.] for the determination of the effective stress in double porosity media is investigated. It is shown that quantitative predictions of volume change in unsaturated aggregated soils can be made using the effective stress concept.