Home About us Contact
|
Home About us Contact | ||
|
|
||
Gradient Theory (gradient + theory)
Selected AbstractsModelling strain localization in granular materials using micropolar theory: mathematical formulationsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2006Mustafa I. Alsaleh Abstract 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] A visco-plastic constitutive model for granular soils modified according to non-local and gradient approachesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2002C. di Prisco Abstract An already available non-associated elastic,viscoplastic constitutive model with anisotropic strain hardening is modified in order to describe both the constitutive parameter dependency on relative density and the spatio-temporal evolution of strain localization. To achieve this latter goal, two distinct but similar approaches are introduced: one inspired by the gradient theory and one by the non-local theory. A one-dimensional case concerning a simple shear test for a non-homogeneous infinitely long dense sand specimen is numerically discussed and a finite difference scheme is employed for this purpose. The results obtained by following the two different approaches are critically analysed and compared. Copyright © 2001 John Wiley & Sons, Ltd. [source] Non-uniform plastic deformation of micron scale objectsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2003Christian F. Niordson Abstract Significant increases in apparent flow strength are observed when non-uniform plastic deformation of metals occurs at the scale ranging from roughly one to ten microns. Several basic plane strain problems are analysed numerically in this paper based on a new formulation of strain gradient plasticity. The problems are the tangential and normal loading of a finite rectangular block of material bonded to rigid platens and having traction-free ends, and the normal loading of a half-space by a flat, rigid punch. The solutions illustrate fundamental features of plasticity at the micron scale that are not captured by conventional plasticity theory. These include the role of material length parameters in establishing the size dependence of strength and the elevation of resistance to plastic flow resulting from constraint on plastic flow at boundaries. Details of the finite element method employed in the numerical analysis of the higher order gradient theory will be discussed and related to prior formulations having some of the same features. Copyright © 2003 John Wiley & Sons, Ltd. [source] Thermodynamic Modeling of Polymer Solution InterfaceMACROMOLECULAR THEORY AND SIMULATIONS, Issue 2 2009Majid Ghiass Abstract A new method is presented to characterize the interfacial concentration field and interfacial tension between equilibrium polymer solution phases, using readily accessible equilibrium concentration data. The new method is tested and validated using experimental data from different polystyrene solutions and it consists of i) calculation of a universal expression for the concentration gradient coefficient based on the Cahn-Hilliard model and the Wolf interfacial tension master equation, and ii) development of a highly accurate algebraic function (Kappa distribution) that, for a given equilibrium polymer concentration set, yields the essentially exact interfacial profile predicted by the classical gradient theory for polymer solutions. [source] Compactness in Ginzburg-Landau energy by kinetic averagingCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 9 2001Pierre-Emmanuel Jabin We consider a Ginzburg-Landau energy for two dimensional divergence free fields appearing in the gradient theory of phase transition for instance. We prove that, as the relaxation parameter vanishes, families of such fields with finite energy are compact in Lp (,). Our proof is based on a kinetic interpretation of the entropies which were introduced by Desimone, Kohn, Müller and Otto. The so-called kinetic averaging lemmas allow to generalize their compactness results. Also the method yields a kinetic equation for the limit where the right-hand side is an unknown kinetic defect bounded measure from which we deduce some Sobolev regularity. This measure also satisfies some cancellation properties depending on its local regularity, which seem to indicate several level of singularities in the limit. © 2001 John Wiley & Sons, Inc. [source] | ||||||||||