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Flow Rule (flow + rule)
Selected AbstractsMeasurement of the Debonding Resistance of Strongly Adherent Thick Coatings on Metals via In-plane Tensile Straining,ADVANCED ENGINEERING MATERIALS, Issue 5 2007S. Ryelandt When the ratio hc/hs of coating and substrate thicknesses is large enough, interfacial debonding can be induced to propagate from the root of a transverse crack under in-plane loading. An energy balance analysis accounting for the flow rule of the substrate allows translating the load for steady state debonding into an upper bound for the debonding toughness. The method is validated by FEM simulations using a cohesive zone model. [source] Damage analysis of laminated composites using a new coupled micro-meso approachFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 7 2010A. FARROKHABADI ABSTRACT In this study, the simplicity and strong physical meaning of micromechanics approach and capability of mesomechanics approach for damage analysis of structures with complex loadings are employed to develop a new micro-meso approach. For this purpose, a new micromechanics model is developed to predict the matrix cracking initiation and evolution in laminated composites. These damage initiation and evolution are replaced with the damage criteria and flow rule in the continuum damage approach, respectively. The results of this procedure are used in the FEM damage analyses of laminated composites to predict constitutive response of layered composites. It is shown that, the predicted stress distribution and strain energy in a lamina unit cell are in good agreement with the finite element results. Furthermore, it is shown that the predicted stress,strain behaviours are in good agreement with the available experimental results for various laminates with different lay-ups. [source] Incremental model for fatigue crack growth based on a displacement partitioning hypothesis of mode I elastic,plastic displacement fieldsFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 7 2007S. POMMIER ABSTRACT The mode I displacement field in the near crack tip region is assumed to be depicted by its partition into an elastic field and a plastic field. Then, each part of the displacement field is also assumed to be the product of a reference field, a function of space coordinates only, and of an intensity factor, function of the loading conditions. This assumption, classical in fracture mechanics, enables one to work at the global scale since fracture criteria can be formulated as a function of the stress intensity factors only. In the present case, the intensity factor of the plastic part of the displacement field measures crack tip plastic flow rate at the global scale. On the basis of these hypotheses, the energy balance equation and the second law of thermodynamics are written at the global scale, i.e. the scale of the K-dominance area. This enables one to establish a yield criterion and a plastic flow rule for the crack tip region. Then, assuming a relation between plastic flow in the crack tip region and fatigue crack growth allows an incremental model for fatigue crack growth to be built. A few examples are given to show the versatility of the model and its ability to reproduce memory effects associated with crack tip plasticity. [source] A destructuration theory and its application to SANICLAY modelINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2010Mahdi Taiebat Abstract Many natural clays have an undisturbed shear strength in excess of the remoulded strength. Destructuration modeling provides a means to account for such sensitivity in a constitutive model. This paper extends the SANICLAY model to include destructuration. Two distinct types of destructuration are considered: isotropic and frictional. The former is a concept already presented in relation to other models and in essence constitutes a mechanism of isotropic softening of the yield surface with destructuration. The latter refers to the reduction of the critical stress ratio reflecting the effect of destructuration on the friction angle, and is believed to be a novel proposition. Both the types depend on a measure of destructuration rate expressed in terms of combined plastic volumetric and deviatoric strain rates. The SANICLAY model itself is generalized from its previous form by additional dependence of the yield surface on the third isotropic stress invariant. Such a generalization allows to obtain as particular cases simplified model versions of lower complexity including one with a single surface and associative flow rule, by simply setting accordingly parameters of the generalized version. A detailed calibration procedure of the relatively few model constants is presented, and the performance of three versions of the model, in descending order of complexity, is validated by comparison of simulations to various data for oedometric consolidation followed by triaxial undrained compression and extension tests on two structured clays. Copyright © 2009 John Wiley & Sons, Ltd. [source] Non-coaxial elasto-plasticity model and bifurcation prediction of shear banding in sandsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2010Maosong Huang Abstract Numerous constitutive models built on coaxial theory and validated under axi-symmetric condition often describe the stress,stain relationships and predict the inceptions of shear banding in sands inaccurately under true triaxial condition. By adopting an elaborated Mohr,Coulomb yield function and using non-coaxial non-associated flow rule, a 3D non-coaxial elasto-plasticity model is proposed and validated by a series of true triaxial tests on loose sands. The bifurcation analysis of true triaxial tests on dense sands predicts the influence of the intermediate principal stress ratio on the onset of shear band accurately. The failure of soils is shown to be related to the formation of shear band under most intermediate principal stress ratio conditions except for those which are close to the axi-symmetric compression condition. Copyright © 2009 John Wiley & Sons, Ltd. [source] Nonlinear SEM numerical analyses of dry dense sand specimens under rapid and dynamic loadingINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2007C. di Prisco Abstract The paper mainly concerns the mechanical response of 2D dry dense sand specimens under shock loading. The problem is numerically analysed by means of a SEM dynamic code, within which an already conceived non-local viscoplastic constitutive model characterized by a non-associated flow rule and by an anisotropic strain hardening has been implemented. In particular the strain localization and time dependency of the material mechanical response are taken into consideration. Both rapid/static loading and dynamic histories are numerically simulated. In the first case, the time dependency of the material mechanical response can be captured by neglecting inertial effects, while in the second one the two factors are superimposed and the propagation of the stress waves within the specimen is discussed. The interest of these analyses derives from the fact that the diffusion phenomenon takes place within a specimen already localized. Copyright © 2006 John Wiley & Sons, Ltd. [source] Liquefaction and cyclic mobility model for saturated granular mediaINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2006S. López-Querol Abstract A new constitutive law for the behaviour of undrained sand subjected to dynamic loading is presented. The proposed model works for small and large strain ranges and incorporates contractive and dilative properties of the sand into the unified numerical scheme. These features allow to correctly predict liquefaction and cyclic mobility phenomena for different initial relative densities of the soil. The model has been calibrated as an element test, by using cyclic simple shear data reported in the literature. For the contractive sand behaviour a well-known endochronic densification model has been used, whereas a plastic model with a new non-associative flow rule is applied when the sand tends to dilate. Both dilatancy and flow rule are based on a new state parameter, associated to the stiffness degradation of the material as the shaking goes on. Also, the function that represents the rearrangement memory of the soil takes a zero value when the material dilates, in order to easily model the change in the internal structure. Proceeding along this kind of approach, liquefaction and cyclic mobility are modelled with the same constitutive law, within the framework of a bi-dimensional FEM coupled algorithm developed in the paper. For calibration purposes, the behaviour of the soil in a cyclic simple shear test has been simulated, in order to estimate the influence of permeability, frequency of loading, and homogeneity of the shear stress field on the laboratory data. Copyright © 2006 John Wiley & Sons, Ltd. [source] A unified bounding surface plasticity model for unsaturated soilsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2006A.R. Russell Abstract A unified constitutive model for unsaturated soils is presented in a critical state framework using the concepts of effective stress and bounding surface plasticity theory. Consideration is given to the effects of unsaturation and particle crushing in the definition of the critical state. A simple isotropic elastic rule is adopted. A loading surface and a bounding surface of the same shape are defined using simple and versatile functions. The bounding surface and elastic rules lead to the existence of a limiting isotropic compression line, towards which the stress trajectories of all isotropic compression load paths approach. A non-associated flow rule of the same general form is assumed for all soil types. Isotropic hardening/softening occurs due to changes in plastic volumetric strains as well as suction for some unsaturated soils, enabling the phenomenon of volumetric collapse upon wetting to be accounted for. The model is used to simulate the stress,strain behaviour observed in unsaturated speswhite kaolin subjected to three triaxial test load paths. The fit between simulation and experiment is improved compared to that of other constitutive models developed using conventional Cam-Clay-based plasticity theory and calibrated using the same set of data. Also, the model is used to simulate to a high degree of accuracy the stress,strain behaviour observed in unsaturated Kurnell sand subjected to two triaxial test load paths and the oedometric compression load path. For oedometric compression theoretical simulations indicate that the suction was not sufficiently large to cause samples to separate from the confining ring. Copyright © 2005 John Wiley & Sons, Ltd. [source] An elastoplastic model based on the shakedown concept for flexible pavements unbound granular materialsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2005Taha Habiballah Abstract Nowadays, the problem of rutting of flexible pavements linked to permanent deformations occurring in the unbound layers is taken into account only by mechanistic empirical formulas. Finite element modelling of realistic boundary value problems with incremental rheological models will lead to unrealistic calculation time for large cycle numbers. The objective of the authors is to present a simplified model which can be used to model the flexible pavements rutting with the finite elements framework. This method is based on the shakedown theory developed by Zarka which is usually associated to materials like steels. It has been adapted for granular materials by introducing a yield surface taking into account the mean stress influence on the mechanical behaviour and a dependency of the hardening modulus with the stress state. The Drucker,Prager yield surface has been used with a non-associated flow rule. Comparisons with repeated load triaxial tests carried out on a subgrade soil have been done. These comparisons underline the capabilities of the model to take into account the cyclic behaviour of unbound materials for roads. Finally, a discussion, dealing with the use of the simplified method within a finite element modelling of a full-scale experiment, is presented. Copyright © 2005 John Wiley & Sons, Ltd. [source] Explicit solutions for the instantaneous undrained contraction of hollow cylinders and spheres in porous elastoplastic mediumINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2002A. Giraud Abstract In this article we present closed-form solutions for the undrained variations in stress, pore pressure, deformation and displacement inside hollow cylinders and hollow spheres subjected to uniform mechanical pressure instantaneously applied to their external and internal boundary surfaces. The material is assumed to be a saturated porous medium obeying a Mohr,Coulomb model failure criterion, exhibiting dilatant plastic deformation according to a non-associated flow rule which accounts for isotropically strain hardening or softening. The instantaneous response of a porous medium submitted to an instantaneous loading is undrained, i.e. without any fluid mass exchange. The short-term equilibrium problem to be solved is now formally identical to a problem of elastoplasticity where the constitutive equations involve the undrained elastic moduli and particular equivalent plastic parameters. The response of the model is presented (i) for extension and compression undrained triaxial tests, and (ii) for unloading problems of hollow cylinders and spheres through the use of appropriately developed closed-form solutions. Numerical results are presented for a plastic clay stone with strain hardening and an argilite with strain softening. The effects of plastic dilation, of the strain softening law and also of geometry of the cavity on the behaviour of the porous medium have been underlined. Analytical solutions provide valuable benchmarks enabling various numerical methods in undrained conditions with a finite boundary to be verified. Copyright © 2002 John Wiley & Sons, Ltd. [source] Application of thermodynamics to the global modelling of shallow foundations on frictional materialINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2001Y. Le Pape Abstract Soil,shallow foundation interaction has been theoretically analysed within the framework of thermomechanics. The design of a global interaction model has been achieved with an original treatment of the Clausius,Duhem inequality. The role of the gravity volume forces is emphasized. The paper is focused on a strip footing based on dense sand and subjected to time-independent plastic processes. The theoretical approach has confirmed that an associated global flow rule cannot be expected to hold true. The analysis of the sources of dissipation has led to the development of a soil,footing interface model and a complete interaction model accounting for the interface constraints and the intrinsic frictional properties of the soil. Finally, the abilities of the complete model are checked by comparisons with experimental results found in the literature. Copyright © 2001 John Wiley & Sons, Ltd. [source] The use of an SQP algorithm in slope stability analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2005Jian Chen Abstract In the upper bound approach to limit analysis of slope stability based on the rigid finite element method, the search for the minimum factor of safety can be formulated as a non-linear programming problem with equality constraints only based on a yield criterion, a flow rule, boundary conditions, and an energy-work balance equation. Because of the non-linear property of the resulting optimization problems, a non-linear mathematical programming algorithm has to be employed. In this paper, the relations between the numbers of nodes, elements, interfaces, and subsequent unknowns and constraints in the approach have been derived. It can be shown that in the large-scale problems, the unknowns are subject to a highly sparse set of equality constraints. Because of the existence of non-linear equalities in the approach, this paper applies first time a special sequential quadratic programming (SQP) algorithm, feasible SQP (FSQP), to obtain solutions for such non-linear optimization problems. In FSQP algorithm, the non-linear equality constraints are turned into inequality constraints and the objective function is replaced by an exact penalty function which penalizes non-linear equality constraint violations only. Three numerical examples are presented to illustrate the potentialities and efficiencies of the FSQP algorithm in the slope stability analysis. Copyright © 2004 John Wiley & Sons, Ltd. [source] The least-squares meshfree method for elasto-plasticity and its application to metal forming analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2005Kie-Chan Kwon Abstract A new meshfree method for the analysis of elasto-plastic deformation is presented. The method is based on the proposed first-order least-squares formulation for elasto-plasticity and the moving least-squares approximation. The least-squares formulation for classical elasto-plasticity and its extension to an incrementally objective formulation for finite deformation are proposed. In the formulation, equilibrium equation and flow rule are enforced in least-squares sense, i.e. their squared residuals are minimized, and hardening law and loading/unloading condition are enforced pointwise at each integration point. The closest point projection method for the integration of rate-form constitutive equation is inherently involved in the formulation, and thus the radial-return mapping algorithm is not performed explicitly. The proposed formulation is a mixed-type method since the residuals are represented in a form of first-order differential system using displacement and stress components as nodal unknowns. Also the penalty schemes for the enforcement of boundary and frictional contact conditions are devised and the reshaping of nodal supports is introduced to avoid the difficulties due to the severe local deformation near contact interface. The proposed method does not employ structure of extrinsic cells for any purpose. Through some numerical examples of metal forming processes, the validity and effectiveness of the method are discussed. Copyright © 2005 John Wiley & Sons, Ltd. [source] Numerical Investigations on the Plastic Memory Effect of PTFE CompoundsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Thomas Kletschkowski Dipl.-Ing. To describe the nonlinear material behaviour of thermoplastic materials via the example of Polytetrafluorethylene (PTFE), a viscoplastic material model of overstress type is proposed. The approach is motivated by a rheological model, consisting of a rate-independent elastoplastic element with an endochronic flow rule and a nonlinear elastic element in parallel connection with a nonlinear Maxwell model. For the generalization to three dimensions, the theory of finite viscoplasticity based on material isomorphisms is applied. To describe the non-isothermal plastic memory effect, thermally induced plastic strains and a scalar back stress (inside the equilibrium branch) are taken into account. [source] Ground response curves for rock masses exhibiting strain-softening behaviourINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2003E. Alonso Abstract A literature review has shown that there exist adequate techniques to obtain ground reaction curves for tunnels excavated in elastic-brittle and perfectly plastic materials. However, for strain-softening materials it seems that the problem has not been sufficiently analysed. In this paper, a one-dimensional numerical solution to obtain the ground reaction curve (GRC) for circular tunnels excavated in strain-softening materials is presented. The problem is formulated in a very general form and leads to a system of ordinary differential equations. By adequately defining a fictitious ,time' variable and re-scaling some variables the problem is converted into an initial value one, which can be solved numerically by a Runge,Kutta,Fehlberg method, which is implemented in MATLAB environment. The method has been developed for various common particular behaviour models including Tresca, Mohr,Coulomb and Hoek,Brown failure criteria, in all cases with non-associative flow rules and two-segment piecewise linear functions related to a principal strain-dependent plastic parameter to model the transition between peak and residual failure criteria. Some particular examples for the different failure criteria have been run, which agree well with closed-form solutions,if existing,or with FDM-based code results. Parametric studies and specific charts are created to highlight the influence of different parameters. The proposed methodology intends to be a wider and general numerical basis where standard and newly featured behaviour modes focusing on obtaining GRC for tunnels excavated in strain-softening materials can be implemented. This way of solving such problems has proved to be more efficient and less time consuming than using FEM- or FDM-based numerical 2D codes. Copyright © 2003 John Wiley & Sons, Ltd. [source] | |||||||||||||