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Yield Function (yield + function)
Selected AbstractsNon-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] Implicit integration of a mixed isotropic,kinematic hardening plasticity model for structured claysINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2008Angelo Amorosi Abstract In recent years, a number of constitutive models have been proposed to describe mathematically the mechanical response of natural clays. Some of these models are characterized by complex formulations, often leading to non-trivial problems in their numerical integration in finite elements codes. The paper describes a fully implicit stress-point algorithm for the numerical integration of a single-surface mixed isotropic,kinematic hardening plasticity model for structured clays. The formulation of the model stems from a compromise between its capability of reproducing the larger number of features characterizing the behaviour of structured clays and the possibility of developing a robust integration algorithm for its implementation in a finite elements code. The model is characterized by an ellipsoid-shaped yield function, inside which a stress-dependent reversible stiffness is accounted for by a non-linear hyperelastic formulation. The isotropic part of the hardening law extends the standard Cam-Clay one to include plastic strain-driven softening due to bond degradation, while the kinematic hardening part controls the evolution of the position of the yield surface in the stress space. The proposed algorithm allows the consistent linearization of the constitutive equations guaranteeing the quadratic rate of asymptotic convergence in the global-level Newton,Raphson iterative procedure. The accuracy and the convergence properties of the proposed algorithm are evaluated with reference to the numerical simulations of single element tests and the analysis of a typical geotechnical boundary value problem. Copyright © 2007 John Wiley & Sons, Ltd. [source] Effect of suction on the mechanical behaviour of iron ore rockINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 8 2005Dragan Grgic Abstract The effect of suction on the behaviour of iron ore has been studied from both physical and mechanical points of view. The porosity and the suction phenomena have been analysed using different experimental techniques. Uniaxial compressive tests on partially saturated samples have shown that the suction is responsible for strength and cohesion improvement. Considering the theory of partially saturated porous soils of Coussy and Dangla (Mécanique des sols non saturés (2002 edn). Hermès Science: 2002; 390), we have proposed a constitutive law for partially saturated iron ore. The real increase in the apparent cohesion due to the capillary attraction forces is overestimated if the yield function is written in terms of effective stresses. The effect of the capillary cohesion has been modelled with a function in the expression of the apparent cohesion of the yield function. The effect of suction on the mechanical behaviour has been represented in the effective stresses space and in the total stresses space like the Alonso model (Géotechnique 1990; 40:405,430). Copyright © 2005 John Wiley & Sons, Ltd. [source] A critical state model for sands dependent on stress and densityINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2004Y.P. Yao Abstract An elastoplastic model for sands is presented in this paper, which can describe stress,strain behaviour dependent on mean effective stress level and void ratio. The main features of the proposed model are: (a) a new state parameter, which is dependent on the initial void ratio and initial mean stress, is proposed and applied to the yield function in order to predict the plastic deformation for very loose sands; and (b) another new state parameter, which is used to determine the peak strength and describe the critical state behaviour of sands during shearing, is proposed in order to predict simply negative/positive dilatancy and the hardening/softening behaviour of medium or dense sands. In addition, the proposed model can also predict the stress,strain behaviour of sands under three-dimensional stress conditions by using a transformed stress tensor instead of ordinary stress tensor. Copyright © 2004 John Wiley & Sons, Ltd. [source] Inelastic constitutive properties and shear localization in Tennessee marbleINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2001D. 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] Lower bound limit analysis of cohesive-frictional materials using second-order cone programmingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2006A. Makrodimopoulos Abstract The formulation of limit analysis by means of the finite element method leads to an optimization problem with a large number of variables and constraints. Here we present a method for obtaining strict lower bound solutions using second-order cone programming (SOCP), for which efficient primal-dual interior-point algorithms have recently been developed. Following a review of previous work, we provide a brief introduction to SOCP and describe how lower bound limit analysis can be formulated in this way. Some methods for exploiting the data structure of the problem are also described, including an efficient strategy for detecting and removing linearly dependent constraints at the assembly stage. The benefits of employing SOCP are then illustrated with numerical examples. Through the use of an effective algorithm/software, very large optimization problems with up to 700 000 variables are solved in minutes on a desktop machine. The numerical examples concern plane strain conditions and the Mohr,Coulomb criterion, however we show that SOCP can also be applied to any other problem of lower bound limit analysis involving a yield function with a conic quadratic form (notable examples being the Drucker,Prager criterion in 2D or 3D, and Nielsen's criterion for plates). Copyright © 2005 John Wiley & Sons, Ltd. [source] A return map algorithm for general isotropic elasto/visco-plastic materials in principal spaceINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004Luciano Rosati Abstract We describe a methodology for solving the constitutive problem and evaluating the consistent tangent operator for isotropic elasto/visco-plastic models whose yield function incorporates the third stress invariant . The developments presented are based upon original results, proved in the paper, concerning the derivatives of eigenvalues and eigenprojectors of symmetric second-order tensors with respect to the tensor itself and upon an original algebra of fourth-order tensors obtained as second derivatives of isotropic scalar functions of a symmetric tensor argument . The analysis, initially referred to the small-strain case, is then extended to a formulation for the large deformation regime; for both cases we provide a derivation of the consistent tangent tensor which shows the analogy between the two formulations and the close relationship with the tangent tensors of the Lagrangian description of large-strain elastoplasticity. Copyright © 2004 John Wiley & Sons, Ltd. [source] A new path-following constraint for strain-softening finite element simulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004E. Lorentz Abstract The application of strain-softening constitutive relations to model the failure modes of real-life structures is faced to numerical difficulties related to instabilities that appear as sharp snap-backs of the structural response. A path-following method has to complement the solution algorithm to achieve convergence despite these critical points. Because of the sharpness of the snap-backs, it is believed essential that the path-following constraint distinguish between a purely elastic unloading and a dissipative path. For that purpose, a new constraint based on the maximal value of the elastic predictor for the yield function is proposed. As it is highly non linear, a specific solution algorithm is required. The robustness of this constraint is illustrated by three applications: the study of crack propagations by means of a cohesive zone model, the failure of a structure submitted to nonlocal damage and the simulation of a nonlocal strain-softening plastic specimen. Copyright © 2004 John Wiley & Sons, Ltd. [source] A basic thin shell triangle with only translational DOFs for large strain plasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2001Fernando G. Flores Abstract A simple finite element triangle for thin shell analysis is presented. It has only nine translational degrees of freedom and is based on a total Lagrangian formulation. Large strain plasticity is considered using a logarithmic strain,stress pair. A plane stress isotropic behaviour with an additive decomposition of elastic and plastic strains is assumed. A hyperelastic law is considered for the elastic part while for the plastic part a von Mises yield function with non-linear isotropic hardening is adopted. The element is an extension of a previous similar rotation-free triangle element based upon an updated Lagrangian formulation with hypoelastic constitutive law. The element termed BST (for basic shell triangle) has been implemented in an explicit (hydro-) code adequate to simulate sheet-stamping processes and in an implicit static/dynamic code. Several examples are shown to assess the performance of the present formulation. Copyright © 2001 John Wiley & Sons, Ltd. [source] Land under pressure: soil conservation concerns and opportunities for EthiopiaLAND DEGRADATION AND DEVELOPMENT, Issue 1 2003B. G. J. S. Sonneveld Abstract This paper evaluates the future impact of soil degradation on national food security and land occupation in Ethiopia. It applies a spatial optimization model that maximizes national agricultural revenues under alternative scenarios of soil conservation, land accessibility and technology. The constraints in the model determine whether people remain on their original site, migrate within their ethnically defined areas or are allowed a transregional migration. Key to this model is the combination of a water erosion model with a spatial yield function that gives an estimate of the agricultural yield in its geographical dependence of natural resources and population distribution. A comparison of simulated land productivity values with historical patterns shows that results are interpretable and yield more accurate outcomes than postulating straightforward reductions in yield or land area for each geographic entity. The results of the optimization model show that in absence of soil erosion control, the future agricultural production stagnates and results in distressing food shortages, while rural incomes drop dramatically below the poverty line. Soil conservation and migration support a slow growth, but do not suffice to meet the expected food demand. In a transregional migration scenario, the highly degraded areas are exchanged for less affected sites, whereas cultivation on already substantially degraded soils largely continues when resettlement is confined to the original ethnic,administrative entity. A shift to modern technology offers better prospects and moderates the migration, but soil conservation remains indispensable, especially in the long term. Finally, an accelerated growth of non-agricultural sectors further alleviates poverty in the countryside, contributing to higher income levels of the total population and, simultaneously, relieving the pressure on the land through rural,urban migration. Copyright © 2002 John Wiley & Sons, Ltd. [source] Micromechanical modeling of fiber reinforced composites based on elastoplasticity and its application for 3D braided glass/Kevlar compositesPOLYMER COMPOSITES, Issue 6 2007Ji Hoon Kim Micromechanical modeling to calculate the mechanical properties of fiber reinforced composites is proposed. To describe the mechanical behavior of the yarn and the matrix, which are the main constituents of fiber reinforced composites, the elastoplastic constitutive law was adopted. In particular, anisotropic elastoplasticity based on Hill's orthotropic yield function and anisotropic kinematic hardening was utilized for the yarn, while the isotropic elastoplastic constitutive law was applied for the matrix. The effective properties of the unit cell in fiber reinforced composites were then calculated based on the finite element method. For verification, the method was successfully applied for 3D braided glass/Kevlar fiber reinforced composites in both linear elastic and nonlinear inelastic ranges. POLYM. COMPOS., 28:722,732, 2007. © 2007 Society of Plastics Engineers [source] | ||||||||||