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Internal Variables (internal + variable)
Selected AbstractsRheological characteristics of solid,fluid transition in dry granular dense flows: A thermodynamically consistent constitutive model with a pressure-ratio order parameterINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2010Chung Fang Abstract Dry granular flows are characterized as quasi-static, dense and collisional states by the interactions among the grains, which is indexed macroscopically by an internal variable, called the order parameter defined as the square root of the static pressure to the total pressure. The solid,fluid state transition is regarded as a second-order phase transition process, and is described by a kinematic evolution of the order parameter. The thermodynamic analysis, based on the Müller,Liu entropy principle, is employed to deduce the equilibrium responses of the constitutive equations, while the dynamic responses are postulated on the basis of a quasi-linear and the second-order Ginzburg,Landau phase transition theories. The obtained model is applied to study the rheological characteristics of a dry granular dense flow between two infinite parallel plates, of which the results are compared with those from DEM simulations to estimate the model validity. The present study provides a general framework for the theoretical justifications on the thermodynamic consistencies of order-parameter-based constitutive models, and can be extended to flows in quasi-static or collisional states. Copyright © 2009 John Wiley & Sons, Ltd. [source] Architectural Methodology Based on Intentional Configuration of BehaviorsCOMPUTATIONAL INTELLIGENCE, Issue 1 2001François Michaud Intelligence has been an object of study for a long time. Different architectures try to capture and reproduce these aspects into artificial systems (or agents), but there is still no agreement on how to integrate them into a general framework. With this objective in mind, we propose an architectural methodology based on the idea of intentional configuration of behaviors. Behavior-producing modules are used as basic control components that are selected and modified dynamically according to the intentions of the agent. These intentions are influenced by the situation perceived, knowledge about the world, and internal variables that monitor the state of the agent. The architectural methodology preserves the emergence of functionality associated with the behavior-based paradigm in the more abstract levels involved in configuring the behaviors. Validation of this architecture is done using a simulated world for mobile robots, in which the agent must deal with various goals such as managing its energy and its well-being, finding targets, and acquiring knowledge about its environment. Fuzzy logic, a topologic map learning algorithm, and activation variables with a propagation mechanism are used to implement the architecture for this agent. [source] A critical plane fatigue model with coupled meso-plasticity and damageFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 1 2008N. HUYEN ABSTRACT The work proposed in this paper is a possible way of modelling some local observations at the surface of mild steel specimens submitted to uniaxial and multiaxial loads. It is clearly seen that local plasticity, controlled by local microstructural heterogeneities, plays a fundamental role in microcrack nucleation and damage orientation is closely related to the applied loading mode. The framework of irreversible thermodynamics with internal variables for time-independent, isothermal and small deformations has been used to build a critical plane damage model by assuming the existence of a link between mesoplasticity and mesodamage. Non-associated plasticity and damage rules allow the evolution of some plastic slip before any damage nucleation, as seen during the observations. A key feature of this proposal is the capacity to reflect nonlinear damage accumulation under variable amplitude loading. [source] Numerical modelling method for wave propagation in a linear viscoelastic medium with singular memoryGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2004Jian-Fei Lu SUMMARY A numerical modelling method for wave propagation in a linear viscoelastic medium with singular memory is developed in this paper. For a demonstration of the method, the Cole,Cole model of viscoelastic relaxation is adopted here. A formulation of the Cole,Cole model based on internal variables satisfying fractional relaxation equations is applied. In order to avoid integrating and storing of the entire history of the variables, a new method for solving fractional differential equations of arbitrary order based on a set of secondary internal variables is developed. Using the new method, the velocity,stress equations and the fractional relaxation equations are reduced to a system of first-order ordinary differential equations for the velocities, stresses, primary internal variables as well as the secondary internal variables. The horizontal spatial derivatives involved in the governing equations are calculated by the Fourier pseudo-spectral (PS) method, while the vertical ones are calculated by the Chebychev PS method. The physical boundary conditions and the non-reflecting conditions for the Chebychev PS method are also discussed. The global solution of the first-order system of ordinary differential equations is advanced in time by the Euler predictor,corrector methods. For the demonstration of our method, some numerical results are presented. [source] Numerical local analysis of relevant internal variables for constitutive modelling of granular materialsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2010Yuhanis Yunus Abstract DEM simulations on spherical materials have been performed to study the behaviour of model granular materials not only under monotonous stress path such as triaxial compression or extension, but also under two-way cycling loading paths. Three reference states have been considered to characterize the behaviour of the granular material: the characteristic state, transitory state between volumetric contraction and dilation, the state of maximum resistance and the critical state. These states are regarded with respect to void ratio and anisotropy of fabric which are the two internal variables retained for the description of the internal state of the material. The characteristic state and the state at maximum resistance are clearly dependent on both levels of density and anisotropy at the beginning of a loading path. Bilinear models involving the two internal variables were designed for the characteristic state, the maximum dilatancy and the extent of the dilatancy domain for axisymetric loadings. They show that in each case the effect of density and anisotropy are different in compression and extension. The influence of anisotropy and density seems to be of the same order of magnitude. Copyright © 2009 John Wiley & Sons, Ltd. [source] A constitutive model for bonded geomaterials subject to mechanical and/or chemical degradationINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2003R. Nova Abstract The mechanical behaviour of bonded geomaterials is described by means of an elastoplastic strain-hardening model. The internal variables, taking into account the ,history' of the material, depend on the plastic strains experienced and on a conveniently defined scalar measure of damage induced by weathering and/or chemical degradation. For the sake of simplicity, it is assumed that only internal variables are affected by mechanical and chemical history of the material. Despite this simplifying assumption, it can be shown that many interesting phenomena exhibited by weathered bonded geomaterials can be successfully described. For instance, (i) the transition from brittle to ductile behaviour with increasing pressure of a calcarenite with collapsing internal structure, (ii) the complex behaviour of chalk and other calcareous materials in oedometric tests, (iii) the chemically induced variation of the stress and strain state of such kind of materials, are all phenomena that can be qualitatively reproduced. Several comparisons with experimental data show that the model can capture the observed behaviour also quantitatively. Copyright © 2003 John Wiley & Sons, Ltd. [source] Micromechanical modelling of monotonic drained and undrained shear behaviour of granular media using three-dimensional DEMINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2002Thallak. Abstract In this paper, numerical simulation results of isotropic compression and triaxial static shear tests under drained and undrained stress paths on polydisperse assembly of loose and dense spheres are presented. An examination of the micromechanical behaviour of loose and dense assemblies under drained and undrained conditions, considering the particulate nature of granular materials, has been carried out to explain micromechanically the granular material behaviour at the grain scale level. The numerical simulations have been carried out using a discrete element model (DEM) which considers a 1000 sphere particle polydisperse assembly with periodic space representing an infinite three-dimensional space. In this paper, we present how DEM simulations can contribute to developments in constitutive modelling of granular materials through micromechanical approach using information on microstructure evolution. A series of numerical tests are performed using DEM on 3-D assemblages of spheres to study the evolution of the internal variables such as average co-ordination number and induced anisotropy during deformation along with the macroscopic behaviour of the assemblage in drained and undrained shear tests. In a qualitative sense, the macroscopic stress,strain results and stress path evolution in these simulations using 3-D assemblies demonstrate that DEM simulations are capable of reproducing realistic compression and shear behaviour of granular materials. Copyright © 2002 John Wiley & Sons, Ltd. [source] An augmented Lagrange multiplier approach to continuum multislip single crystal thermo,elasto,viscoplasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2005C. C. Celigoj Abstract The material and structural behaviour of single crystals is going to be investigated. On the constitutive level the concept of ,generalized standard materials (gsm)' is used to set up the equations for finite deformation multislip single crystal thermo,elasto,viscoplasticity within a continuum slip theory. The only two scalar quantities needed are a thermodynamic potential and a dissipation potential. The resulting evolution equations for the internal (viscoplastic) variables are discretized in time and solved via a backward Euler scheme, using an ,augmented Lagrange multiplier method' for satisfying the multiple constraints, thus circumventing the cumbersome and less robust ,active set strategies'. As a computational reference frame serves the Eulerian setting. The structural behaviour (non-linear coupled thermomechanics) is solved in a staggered algorithm: in an isothermal mechanical phase via q1(displacements)/p0(pressure)/j0(jacobian)-finite elements and in an isogeometric thermal phase via q1(temperatures)-finite elements, followed by an isogeometric and isothermal update phase of the internal variables. Numerical results of the simple isothermal shear test of a single face-centred cubic (fcc) crystal and of the thermomechanical behaviour of a geometrically imperfect strip consisting of initially equally oriented (0/45/30 in Euler angles) fcc-crystals under tension and plane strain conditions are given. Copyright © 2005 John Wiley & Sons, Ltd. [source] Numerical analysis of Augmented Lagrangian algorithms in complementary elastoplasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004L. Contrafatto The main subject of the paper is the investigation of Augmented Lagrangian algorithms and update formulas in the solution of elastoplastic problems. A stress rate formulation for elastoplastic models with internal variables and its finite increment form is employed to state the mechanical problem. In this formulation the Augmented Lagrangian is used to enforce the constraint of plastic admissibility directly on the stresses and thermodynamic forces. This is not a limitation of the Augmented Lagrangian approach, and the same framework can be built on more classical displacement formulations as well. The meaning and the derivation of various first and second order Lagrangian multipliers update formulas and iterative schemes is shown. A new diagonal iteration algorithm and the introduction of a scale factor for the Augmented Lagrangian term are proposed. Numerical examples compare the efficiency of several forms of Augmented Lagrangian algorithms and illustrate the influence of the scale factor and of the penalty parameter. Copyright © 2004 John Wiley & Sons, Ltd. [source] Analysis of microstructure development in shearbands by energy relaxation of incremental stress potentials: Large-strain theory for standard dissipative solidsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003Christian Miehe Abstract We propose a fundamentally new approach to the treatment of shearband localizations in strain softening elastic,plastic solids at finite strains based on energy minimization principles associated with microstructure developments. The point of departure is a general internal variable formulation that determines the finite inelastic response as a standard dissipative medium. Consistent with this type of inelasticity we consider an incremental variational formulation of the local constitutive response where a quasi-hyperelastic stress potential is obtained from a local constitutive minimization problem with respect to the internal variables. The existence of this variational formulation allows the definition of the material stability of an inelastic solid based on weak convexity conditions of the incremental stress potential in analogy to treatments of finite elasticity. Furthermore, localization phenomena are interpreted as microstructure developments on multiple scales associated with non-convex incremental stress potentials in analogy to elastic phase decomposition problems. These microstructures can be resolved by the relaxation of non-convex energy functionals based on a convexification of the stress potential. The relaxed problem provides a well-posed formulation for a mesh-objective analysis of localizations as close as possible to the non-convex original problem. Based on an approximated rank-one convexification of the incremental stress potential we develop a computational two-scale procedure for a mesh-objective treatment of localization problems at finite strains. It constitutes a local minimization problem for a relaxed incremental stress potential with just one scalar variable representing the intensity of the microshearing of a rank-one laminate aligned to the shear band. This problem is sufficiently robust with regard to applications to large-scale inhomogeneous deformation processes of elastic,plastic solids. The performance of the proposed energy relaxation method is demonstrated for a representative set of numerical simulations of straight and curved shear bands which report on the mesh independence of the results. Copyright © 2003 John Wiley & Sons, Ltd. [source] An arbitrary Lagrangian,Eulerian finite element method for finite strain plasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2003Francisco Armero Abstract This paper presents a new arbitrary Lagrangian,Eulerian (ALE) finite element formulation for finite strain plasticity in non-linear solid mechanics. We consider the models of finite strain plasticity defined by the multiplicative decomposition of the deformation gradient in an elastic and a plastic part (F = FeFp), with the stresses given by a hyperelastic relation. In contrast with more classical ALE approaches based on plastic models of the hypoelastic type, the ALE formulation presented herein considers the direct interpolation of the motion of the material with respect to the reference mesh together with the motion of the spatial mesh with respect to this same reference mesh. This aspect is shown to be crucial for a simple treatment of the advection of the plastic internal variables and dynamic variables. In fact, this advection is carried out exactly through a particle tracking in the reference mesh, a calculation that can be accomplished very efficiently with the use of the connectivity graph of the fixed reference mesh. A staggered scheme defined by three steps (the smoothing, the advection and the Lagrangian steps) leads to an efficient method for the solution of the resulting equations. We present several representative numerical simulations that illustrate the performance of the newly proposed methods. Both quasi-static and dynamic conditions are considered in these model examples. Copyright © 2003 John Wiley & Sons, Ltd. [source] Strain-driven homogenization of inelastic microstructures and composites based on an incremental variational formulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002Christian Miehe Abstract The paper investigates computational procedures for the treatment of a homogenized macro-continuum with locally attached micro-structures of inelastic constituents undergoing small strains. The point of departure is a general internal variable formulation that determines the inelastic response of the constituents of a typical micro-structure as a generalized standard medium in terms of an energy storage and a dissipation function. Consistent with this type of inelasticity we develop a new incremental variational formulation of the local constitutive response where a quasi-hyperelastic micro-stress potential is obtained from a local minimization problem with respect to the internal variables. It is shown that this local minimization problem determines the internal state of the material for finite increments of time. We specify the local variational formulation for a setting of smooth single-surface inelasticity and discuss its numerical solution based on a time discretization of the internal variables. The existence of the quasi-hyperelastic stress potential allows the extension of homogenization approaches of elasticity to the incremental setting of inelasticity. Focusing on macro-strain-driven micro-structures, we develop a new incremental variational formulation of the global homogenization problem where a quasi-hyperelastic macro-stress potential is obtained from a global minimization problem with respect to the fine-scale displacement fluctuation field. It is shown that this global minimization problem determines the state of the micro-structure for finite increments of time. We consider three different settings of the global variational problem for prescribed linear displacements, periodic fluctuations and constant stresses on the boundary of the micro-structure and discuss their numerical solutions based on a spatial discretization of the fine-scale displacement fluctuation field. The performance of the proposed methods is demonstrated for the model problem of von Mises-type elasto-visco-plasticity of the constituents and applied to a comparative study of micro-to-macro transitions of inelastic composites. Copyright © 2002 John Wiley & Sons, Ltd. [source] A new update procedure for internal variables in an ALE-description of rolling contactPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005M. Ziefle In FEM analysis of rolling contact problems Arbitrary Lagrangian-Eulerian (ALE) methods are the state of the art. These methods allow mesh refinements concentrated to the contact region and offer a time independent formulation of stationary elastic rolling. The relative-kinematic description of rolling leads to a relative motion between the finite element mesh and the material points. Thus in the case of inelastic material behavior history dependent constitutive equations contain convective terms. The handling of these convective terms is performed by a so called fractional step method. A material step is followed by a convection step. In the first step the nonlinear solid contact problem is resolved by neglecting the convective terms. In the following step the internal variables are transported on the streamlines of the material particles by solving the advection equation via a time-discontinuous Galerkin method. This update procedure is demonstrated on a typical FEM-tire model. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Homogenization in the Theory of ViscoplasticityPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Sergiy Nesenenko We study the homogenization of the quasistatic initial boundary value problem with internal variables which models the deformation behavior of viscoplastic bodies with a periodic microstructure. This problem is represented through a system of linear partial differential equations coupled with a nonlinear system of differential equations or inclusions. Recently it was shown by Alber [2] that the formally derived homogenized initial boundary value problem has a solution. From this solution we construct an asymptotic solution for the original problem and prove that the difference of the exact solution and the asymptotic solution tends to zero if the lengthscale of the microstructure goes to zero. The work is based on monotonicity properties of the differential equations or inclusions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Weakly nonlocal irreversible thermodynamicsANNALEN DER PHYSIK, Issue 3 2003P. Ván Abstract Weakly nonlocal thermodynamic theories are critically revisited. A relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so called current multipliers. The treatment is restricted to deal with nonlocality connected to dynamic thermodynamic variables. Several classical equations are derived, including Guyer-Krumhansl, Ginzburg-Landau and Cahn-Hilliard type equations. [source] | ||||||||||