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## Stress Invariants (stress + invariant)
## Selected Abstracts## A destructuration theory and its application to SANICLAY model INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2010Mahdi TaiebatAbstract 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] ## A return map algorithm for general isotropic elasto/visco-plastic materials in principal space INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004Luciano RosatiAbstract 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 computerized procedure for long-life fatigue assessment under complex multiaxial loading FATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 3 2001B. LiA computerized procedure is presented and evaluated for application examples of long-life fatigue analyses of metallic materials under complex multiaxial loading. The method is based on the stress invariants and uses the minimum circumscribed ellipse approach for evaluating the effective shear stress amplitude under complex multiaxial loading. The applicability of the procedure for handling non-proportional loading is examined through typical examples such as combined normal/shear stresses and combined bi-axial normal stresses with complex stress time histories. The effects of phase shift angles, frequency ratios and waveforms on fatigue endurance were re-analysed and compared with available experimental results from the literature. The comparison shows that the presented procedure based on stress invariants is a potential conservative engineering approach, very suitable for fast fatigue evaluation in the integrated computer aided fatigue design. [source] ## A discrete thermodynamic approach for anisotropic plastic,damage modeling of cohesive-frictional geomaterials INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2010Q. Z. ZhuAbstract A discrete plastic,damage model is developed for cohesive-frictional geomaterials subjected to compression-dominated stresses. Macroscopic plastic strains of material are physically generated by frictional sliding along weakness planes. The evolution of damage is related to the evolution of weakness planes physically in connection with the propagation of microcracks. A discrete approach is used to account for anisotropic plastic flow and damage evolution, by introducing two stress invariants and one plastic hardening variable for each family of sliding weakness planes. Plastic flow in each family is coupled with damage evolution. The proposed model is applied to typical geomaterials and comparisons between numerical predictions and experimental data are presented. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Modelling strain localization in granular materials using micropolar theory: mathematical formulations INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2006Mustafa I. AlsalehAbstract It has been known that classical continuum mechanics laws fail to describe strain localization in granular materials due to the mathematical ill-posedness and mesh dependency. Therefore, a non-local theory with internal length scales is needed to overcome such problems. The micropolar and high-order gradient theories can be considered as good examples to characterize the strain localization in granular materials. The fact that internal length scales are needed requires micromechanical models or laws; however, the classical constitutive models can be enhanced through the stress invariants to incorporate the Micropolar effects. In this paper, Lade's single hardening model is enhanced to account for the couple stress and Cosserat rotation and the internal length scales are incorporated accordingly. The enhanced Lade's model and its material properties are discussed in detail; then the finite element formulations in the Updated Lagrangian Frame (UL) are used. The finite element formulations were implemented into a user element subroutine for ABAQUS (UEL) and the solution method is discussed in the companion paper. The model was found to predict the strain localization in granular materials with low dependency on the finite element mesh size. The shear band was found to reflect on a certain angle when it hit a rigid boundary. Applications for the model on plane strain specimens tested in the laboratory are discussed in the companion paper. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Assessment of test data for selection of 3-D failure criterion for sand INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2006Poul V. LadeAbstract Data from three-dimensional experiments performed on sand in true triaxial equipment have been reviewed to sort out apparent disarray resulting from their interpretation. This has been done based on analyses made possible by recent developments and understanding of factors influencing sand behaviour: occurrence of shear banding, boundary conditions and/or specimen slenderness ratio, cross-anisotropy, and stability of experimental technique. These factors are reviewed and test data from the literature are evaluated. Experimental data are divided into three groups in which: (a) homogeneous behaviour controls the sand strength; (b) shear banding affects the shape of the three-dimensional failure surface in the midrange of values of b=(,2,,3)/(,1,,3), and (c) the data has been misinterpreted. Appropriate interpretation of three-dimensional strength data for sand exhibiting isotropic, homogeneous behaviour is represented by a smoothly rounded triangular failure surface expressible in terms of the first and third stress invariants. Shear banding effects will cause the failure surface to be ,indented' in the midrange of b -values in all sectors of the octahedral plane. Effects of cross-anisotropy will result in lower strengths in sector III than in sector I of the octahedral plane, and the failure surface will appear as rotated around the stress origin in principal stress space. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Inelastic constitutive properties and shear localization in Tennessee marble INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2001D. J. HolcombAbstract 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] |