a continuum model accounting for defect and mass densities in solids with inelastic material behaviour in this paper the analysis of structures with inelastic material behaviour is considered taking into account the evolution of defects and changes in mass density the underlying kinematical concept of an oriented continuum is general enough to describe the micro and macrobehaviour of material bodies appropriately based on the logical and consistent variational arguments for a lagrangian functional the dynamic balance laws boundary and transversality conditions all related to the evolution of defect density and mass changes are derived for macro and microstresses of deformational as well as of configurational type the adopted procedure which formally leaves the balance laws unaltered leads to the additional balance law for changes in defect density and additional boundary conditions for the changes in mass and defect densities driving forces or affinities associated with the evolution of defect and mass densities and a generalization of the j integral representing the thermodynamic forces on defects are obtained a nonlocal constitutive model accounting for changes in the defect density is presented

integral sliding manifold design for linear systems with additive unmatched disturbances this note offers an integral sliding manifold design method for linear systems that minimizes the impact of unmatched constant external disturbances system sensitivity upon an unmatched disturbance vector is assessed by the steady state dependent criterion function the derived procedure easily finds a unique integral sliding manifold that minimizes a quadratic optimization criterion applicability of this method in case of slowly varying disturbances is supported by determining disturbance frequency limit that guarantees satisfactory performance the proposed approach has been demonstrated on a numerical example and verified by simulations

sliding mode control of linear systems with mismatched uncertainties abstract it is well known that sliding mode control is robust to matched uncertainties that lie in the range space of the input matrix however many systems are affected by mismatched uncertainties and yet do not enjoy the matching conditions it is the purpose of this paper to present a new dynamical approach of sliding variable formulation which when the system is in sliding mode can explicitly deal with mismatched uncertainties our first step is to treat certain states as inputs to a reduced order system and use adaptive techniques to design fictitious controllers for these inputs which can then tackle the mismatched uncertainties the second step is to use sliding control to realize the adaptive fictitious controllers the design is systematic modular and intuitively simple

efficient modeling of localized material failure by means of a variationally consistent embedded strong discontinuity approach this paper is concerned with a novel embedded strong discontinuity approach suitable for the analysis of material failure at finite strains focus is on localized plastic deformation particularly relevant for slip bands in contrast to already existing models the proposed implementation allows to consider several interacting discontinuities in each finite element based on a proper re formulation of the kinematics an efficient parameterization of the deformation gradient is derived it permits to compute the strains explicitly that improves the performance significantly however the most important novel contribution of the present paper is the advocated variational constitutive update within this framework every aspect is naturally driven by energy minimization i e all unknown variables are jointly computed by minimizing the stress power the proposed update relies strongly on an extended principle of maximum dissipation this framework provides enough flexibility for different failure types and for a broad class of non associative evolution equations by discretizing the aforementioned continuous variational principle an efficient numerical implementation is obtained it shows in addition to its physical and mathematical elegance several practical advantages for instance the physical minimization principle itself specifies automatically and naturally the set of active strong discontinuities copyright 2011 john wiley sons ltd

finite elements for materials with strain gradient effects a finite element implementation is reported of the fleck hutchinson phenomenological strain gradient theory this theory fits within the toupin mindlin framework and deals with first order strain gradients and the associated work conjugate higher order stresses in conventional displacement based approaches the interpolation of displacement requires c1 continuity in order to ensure convergence of the finite element procedure for higher order theories mixed type finite elements are developed herein for the fleck hutchinson theory these elements use standard c0 continuous shape functions and can achieve the same convergence as c1 elements these c0 elements use displacements and displacement gradients as nodal degrees of freedom kinematic constraints between displacement gradients are enforced via the lagrange multiplier method the elements developed all pass a patch test the resulting finite element scheme is used to solve some representative linear elastic boundary value problems and the comparative accuracy of various types of element is evaluated copyright 1999 john wiley sons ltd

an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

an implicit bem formulation for gradient plasticity and localization phenomena the aim of this paper is to discuss a boundary element formulation for non linear structural problems involving localization phenomena in order to overcome the well known mesh dependency observed in local plasticity a gradient plasticity model is used an implicit boundary element formulation is proposed and the underlying consistent tangent operator defined this formulation is based on the classical displacement and strain integral representations combined with an integral representation of the plastic multiplier first numerical examples are presented to illustrate the application of the method copyright 2001 john wiley sons ltd

mixing heat bath and glauber dynamics damage spreading in the ising model the authors study damage spreading in the ising model on a square lattice by a monte carlo approach using a general f dynamics 0 or f or 1 which reproduces for f 0 the well known heat bath dynamics and for f 1 glauber dynamics they find for initially small damage a critical value fc 0 50 or 0 03 as the threshold for damage spreading for fc f or 1 the damage is non zero only for tc t t0 f where tc is the usual critical temperature and t0 f rises with f like t0 f tc infinity f fc alpha alpha 0 83 or 0 08 for tc or t the damage d t f seems to satisfy the scaling relation d t f approximately mod 1n f fc mod 1t 1 tc t f fc alpha

analysis and design of variable structure systems using a geometric approach multivariable variable structure systems in the sliding mode are studies using a geometric approach the properties of system order reduction and disturbance rejection are proved using projector theory new design methods for the choice of switching hyperplanes are derived for the closed loop eigenvalue eigenvector assignment problem

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

a thermodynamically motivated implicit gradient damage framework and its application to brick masonry cracking a new gradient damage model is derived starting from thermodynamic statements nonstandard terms are added to the free energy potential for this purpose in contrast with existing approaches these terms are related to the kinematics of the problem and therefore come into play already in the elastic regime following the argument that the second law of thermodynamics need only be satisfied globally for a nonlocal continuum an energy balance equation is derived which must be solved together with the usual equilibrium equations numerical solutions of this coupled set of equations have been generated for a one dimensional problem in order to study the localisation behaviour of the new model in the limit where the elastic modulus related to the energy balance goes to 0 an earlier gradient damage model is retrieved this simplified model is used to study cracking of brick masonry under the influence of mechanical loading

uniqueness studies in boundary value problems involving some second gradient models abstract enhanced models such as second gradient models have been mainly theoretically developed during the sixties and the seventies new attention has been paid to these models recently when it has been recognized that classical inelastic constitutive equations especially the ones not obeying a normality rule induce ill posed boundary value problems however little work has been done to study the well posedness properties of boundary value problems involving these enhanced models the aim of this paper is a partial study of this point only uniqueness of solution of numerical discretization of boundary value problems involving second gradient models is considered we extend to second gradient models a numerical search method to find non uniqueness already established for classical media in the case of loss of uniqueness for the underlying model our numerical results show clearly that in some cases uniqueness is lost for second gradient model as well it seems that second gradient extensions of classical models do not restore the uniqueness properties but only the objectivity of the numerical computation finally our numerical experiments show once more that post peak behavior is a structural effect they also suggest that some constitutive equations often used in geomaterials modeling may be questionable and may not be complete because even adding second gradient enhancement to these models yields non unique solutions

gradient elasticity in statics and dynamics an overview of formulations length scale identification procedures finite element implementations and new results in this paper we discuss various formats of gradient elasticity and their performance in static and dynamic applications gradient elasticity theories provide extensions of the classical equations of elasticity with additional higher order spatial derivatives of strains stresses and or accelerations we focus on the versatile class of gradient elasticity theories whereby the higher order terms are the laplacian of the corresponding lower order terms one of the challenges of formulating gradient elasticity theories is to keep the number of additional constitutive parameters to a minimum we start with discussing the general mindlin theory that in its most general form has 903 constitutive elastic parameters but which were reduced by mindlin to three independent material length scales further simplifications are often possible in particular the aifantis theory has only one additional parameter in statics and opens up a whole new field of analytical and numerical solution procedures we also address how this can be extended to dynamics an overview of length scale identification and quantification procedures is given finite element implementations of the most commonly used versions of gradient elasticity are discussed together with the variationally consistent boundary conditions details are provided for particular formats of gradient elasticity that can be implemented with simple linear finite element shape functions new numerical results show the removal of singularities in statics and dynamics as well as the size dependent mechanical response predicted by gradient elasticity

numerical technique in plasticity including solution advancement control numerical techniques applied to the consistent formulation of plasticity which is based on convex analysis are investigated for each time step the stress is found as the projection in complementary energy of the elastic stress onto the set of plastically admissible stresses while the velocity field is the extremal of a non quadratic functional explicit formulas for von mises yield criterion with mixed hardening are developed and the nonlinear equations arising from finite element discretization are solved for comparison by a number of newton type iteration procedures with line search and are length control a few numerical examples with proportional and non proportional loading are analyzed

a general framework for softening regularisation based on gradient elasticity a general non local approach to regularise strain softening continua is presented the key idea is to introduce the gradient type enrichment at the level of displacements rather than some internal variable so the model is formulated with two distinct displacement fields in fact gradient models based on two displacement fields are usual in non local elasticity where the goal is to avoid the shortcomings of classical local elasticity i e strain singularities in statics non dispersive behaviour in dynamics we show that such a gradient elasticity backbone model can be combined with any standard nonlinear constitutive driver to render a regularised model for softening inelasticity to illustrate the generality of the approach two prototype models isotropic damage and von mises plasticity are discussed the numerical examples show that the regularised models exhibit all of the desired features mesh insensitivity imperfection size insensitivity and description of size effects

comments on sliding mode control of linear systems with mismatched uncertainties abstract in the above paper kwan 1995 sliding mode control of linear systems with mismatched uncertainties automatica 31 303 307 a sliding mode control for handling mismatched uncertainties explicitly was proposed in this correspondence it is pointed out that the proof of stability the adaptation law and the control given by kwan are incorrect previously published results for handling mismatched uncertainties explicitly are cited an alternative treatment of the problem is suggested

hydromechanical modeling of an initial boundary value problem studies of non uniqueness with a second gradient continuum a non uniqueness study for a hydromechanical boundary value problem is performed a fully saturated porous medium is considered using an elasto plastic constitutive equations to describe the mechanical behavior of the skeleton a real hydromechanical experiment which consists in a hollow cylinder test on a boom clay sample is modelled it is shown that the time step discretisation of the numerical problem has an effect on the initialisation of the newton raphson algorithm on a given time step different solutions for the same initial boundary value problem can consequently be found

correlation analysis of the damage spreading problem in a 2 dimensional ising model abstract we have studied the time dependence of the damage spreading in a 2 dimensional ising model using time series analysis we have found that the signal has a hurst exponent 0 5 in high temperatures and it approaches 1 near the temperature t d where the damage goes to zero we have also measured the correlation of the signal and found that it is strongly correlated near t d and describes a persistent fractional brownian motion fbm therefore the hamming distance in the ising model can be used to generate fbm near t d we suggest that the system presents a 1 f spectrum in the transition temperature t d

dynamical phase transitions in the classical heisenberg model damage spreading in the 2d and 3d heisenberg model is considered for the 3d model there is critical temperature t1 1 15 between a frozen phase and a chaotic phase at low temperature there is another critical temperature t2 0 3 below which the final damage depends on its initial value for the 2d case there is a transition at t0 0 5 between a frozen phase and a low temperature chaotic phase which might be characterized by the existence of infinite critical points

plastic continuum with microstructure local second gradient theories for geomaterials localization studies many plastic second gradient models have been developed in the last 10 years however some plastic second gradient models are nonlocal ones this paper is an attempt to give a general framework to deal with local second gradient theories within theories with microstructure keeping in mind future applications for geomaterials it is advocated that particular elasto plastic local models with microstructure namely local second gradient and cosserat second gradient models which are the least developed in the literature have some advantages which are somewhat promising one main objective of this paper is to present these two families of models the first one cosserat second gradient model is shown to be well adapted to granular materials the second model family is likely to be a good model for cohesive geomaterials another aim of this work is to give a method to obtain basic solutions which can be seen as localization analysis in one and two dimensions cases the key point of this method is the use of patch conditions between loading and unloading parts

numerical algorithms and mesh dependence in the disturbed state concept the disturbed state concept dsc provides a unified approach for constitutive modelling of engineering materials including such factors as elastic plastic and creep strains microcracking damage and softening and sti ening responses the interacting mechanisms in the material mixture composed of the relative intact and fully adjusted states provide implicitly for various factors such as microcrack interaction and character istic dimension the dsc model can allow for well posedness reduction or elimination of spurious mesh dependence and localization a number of problems are solved to illustrate convergence and uniqueness of the finite element procedures localization spurious mesh dependence and validation with respect to observed behavior of simulated and practical problems 1997 by john wiley sons ltd

a nonlocal model with strain based damage a thermodynamically consistent formulation of nonlocal damage in the framework of the internal variable theories of inelastic behaviours of associative type is presented the damage behaviour is defined in the strain space and the effective stress turns out to be additively splitted in the actual stress and in the nonlocal counterpart of the relaxation stress related to damage phenomena an important advantage of models with strain based loading functions and explicit damage evolution laws is that the stress corresponding to a given strain can be evaluated directly without any need for solving a nonlinear system of equations a mixed nonlocal variational formulation in the complete set of state variables is presented and is specialized to a mixed two field variational formulation hence a finite element procedure for the analysis of the elastic model with nonlocal damage is established on the basis of the proposed two field variational formulation two examples concerning a one dimensional bar in simple tension and a two dimensional notched plate are addressed no mesh dependence or boundary effects are apparent

nonlinear integral type sliding surface for both matched and unmatched uncertain systems this note presents a new nonlinear integral type sliding surface which incorporates a virtual nonlinear nominal control to achieve prescribed specifications first the plant with matched uncertainties is considered the resultant closed loop system during ideal sliding mode behaves exactly like the nominal plant under the nonlinear nominal control which completely nullifies the matched uncertainties and consequently satisfies the prescribed specifications second the stability analysis of the proposed sliding mode for the systems with unmatched uncertainties is performed to exploit the stability conditions numerical results demonstrate the validity of the proposed concept

equivalent plastic strain gradient enhancement of single crystal plasticity theory and numerics we propose a visco plastic strain gradient plasticity theory for single crystals the gradient enhancement is based on an equivalent plastic strain measure two physically equivalent variational settings for the problem are discussed a direct formulation and an alternative version with an additional micromorphic like field variable which is coupled to the equivalent plastic strain by a lagrange multiplier the alternative formulation implies a significant reduction of nodal degrees of freedom the local algorithm and element stiffness matrices of the finite element discretization are discussed numerical examples illustrate the advantages of the alternative formulation in three dimensional simulations of oligo crystals by means of the suggested formulation complex boundary value problems of the proposed plastic strain gradient theory can be solved numerically very efficiently

theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity the paper presents the theory and the numerics of a thermodynamically consistent formulation of gradient plasticity at small strains starting from the classical local continuum formulation which fails to produce physically meaningful and numerically converging results within localization computations a thermodynamically motivated gradient plasticity formulation is envisioned the model is based on an assumption for the helmholtz free energy incorporating the gradient of the internal history variable a yield condition and the postulate of maximum dissipation resulting in an associated structure as a result the driving force conjugated to the hardening evolution is identified as the quasi non local drag stress which incorporates besides the strictly local drag stress essentially the divergence of a vectorial hardening flux at the numerical side besides the balance of linear momentum the algorithmic consistency condition has to be solved in weak form thereby the crucial issue is the determination of the active constraints exhibiting plastic loading which is solved by an active set search algorithm borrowed from convex non linear programming moreover different discretization techniques are proposed in order to compare the fe performance in local plasticity with the advocated gradient formulation both for hardening and softening copyright 2001 john wiley sons ltd

spectral analysis of localization in nonlocal and over nonlocal materials with softening plasticity or damage the paper shows that spectral wave propagation analysis reveals in a simple and clear manner the effectiveness of various regularization techniques for softening materials i e materials for which the yield limits soften as a function of the total strain both plasticity and damage models are considered it is verified analytically in a simple way that the nonlocal integral type model with degrading yield limit depending on the total strain works correctly if and only one adopts an unconventional nonlocal formulation introduced in 1994 by vermeer and brinkgreve and in 1996 by planas and by stromberg and ristinmaa which is here called for the sake of brevity over nonlocal because it uses a linear combination of local and nonlocal variables in which a negative weight imposed on the local variable is com pensated by assigning to the nonlocal variable weight greater than 1 this is equivalent to a nonlocal variable with a smooth positive weight function of total weight greater than 1 normalized by superposing a negative delta function spike at the center the spectral approach readily confirms that the nonlocal integral type generalization of softening plasticity with an additive format gives correct localization properties only if an over nonlocal formulation is adopted by contrast the nonlocal integral type generalization of softening plasticity with a multiplicative format provides real istic localization behavior just like the nonlocal integral type damage model and thus does not necessitate an over non local formulation the localization behavior of explicit and implicit gradient type models is also analyzed a simple analysis shows that plasticity and damage models with gradient type localization limiter whether explicit or implicit have very different localization behaviors 2005 elsevier ltd all rights reserved

strain localization and bifurcation in a nonlocal continuum abstract the conditions for localization and wave propagation in a strain softening material described by a nonlocal damage based constitutive relation are derived in closed form localization is understood as a bifurcation into a harmonic mode the criterion for bifurcation is reduced to the classical form of singularity of a pseudo acoustic tensor this tensor is not a material property as it involves the wavelength of the bifurcation mode through the fourier transform of the weight function used in the definition of the nonlocal damage a geometrical solution is provided to analyse localization the conditions for the onset of bifurcation are found to coincide in the nonlocal and in the corresponding local cases in the nonlocal continuum the wavelength of the localization mode is constrained to remain below a threshold which is proportional to the characteristic length of the continuum the analysis in dynamics exhibits the well known property of wave dispersion in some instances i e for large wavelength modes wave celerities become imaginary but waves with a sufficiently short wavelength are found to propagate during softening in all the situations

gradient plasticity theory with a variable length scale parameter the definition and magnitude of the intrinsic length scale are keys to the development of the gradient plasticity theory that incorporates size effects however a fixed value of the material length scale is not always realistic and different problems could require different values moreover a linear coupling between the local and nonlocal terms in the gradient plasticity theory is not always realistic and that different problems could require different couplings this work addresses the proper modifications required for the full utility of the current gradient plasticity theories in solving the size effect problem it is shown that the current gradient plasticity theories do not give sound interpretations of the size effects in micro bending and micro torsion tests if a definite and fixed length scale parameter is used a generalized gradient plasticity model with a non fixed length scale parameter is proposed based on dislocation mechanics this model assesses the sensitivity of predictions to the way in which the local and nonlocal parts are coupled or to the way in which the statically stored and geometrically necessary dislocations are coupled in addition a physically based relation for the length scale parameter as a function of the course of deformation and the material microstructural features is proposed the proposed model gives good predictions of the size effect in micro bending tests of thin films and micro torsion tests of thin wires

studies in anisotropic plasticity with reference to the hill criterion algorithms based upon the notion of return mapping have been developed for the hill yield function of anisotropic plasticity the relative accuracy of two algorithms is assessed by means of iso error maps the choice of the algorithm turns out to be much more critical for the orthotropic hill criterion than for the underlying isotropic von mises plasticity model a tangent operator that is consistent with the developed integration algorithm is formulated and its efficiency is assessed compared with the classical continuum tangent operator the model has been applied to three shell plate structures

variational principles for softening gradient dependent plasticity abstract a gradient dependent plasticity model is analysed in which the yield function not only depends on the stress tensor and an invariant plastic strain measure but also on the spatial derivatives of the latter quantity a minimum variational principle is obtained by analysing the structure discretized into sufficiently small plastic elements and thus the uniqueness of fe solutions can be ensured for softening plasticity the positive definiteness of the variational functional is determined only by the sign of the diffuse coefficient associated with the highest order derivative of the plastic multiplier in the yield function in order to adopt mix hybrid elements several general variational principles are obtained by relaxing the associated constraints on the displacement strain stress and or plastic multiplier gradient radiation fields

multiscale computational analysis in mechanics using finite calculus an introduction abstract the paper introduces a general procedure for computational analysis of a wide class of multiscale problems in mechanics using a finite calculus fic formulation the fic approach is based in expressing the governing equations in mechanics accepting that the domain where the standard balance laws are established has a finite size this introduces naturally additional terms into the classical equations of infinitesimal theory in mechanics which are useful for the numerical solution of problems involving different scales in the physical parameters the discrete nodal values obtained with the fic formulation and the finite element method fem can be effectively used as the starting point for obtaining a more refined solution in zones where high gradients of the relevant variables occur using hierarchical or enriched fem typical multiscale problems in mechanics which can be solved with the fic method include convection diffusion reaction problems with high localized gradients incompressible problems in solid and fluid mechanics localization problems such as prediction of shear bands in solids and shock waves in compressible fluids turbulence etc the paper presents an introduction of the treatment of multiscale problems using the fic approach in conjunction with the fem examples of application of the fic fem formulation to the solution of simple multiscale convection diffusion problems are given

a finite element formulation to solve a non local constitutive model with stresses and strains due to slip gradients solving constitutive models that incorporate the effects of plasticity and slip gradients is often complicated by the non local nature of the models this work presents a finite element solution to a crystal plasticity constitutive model that includes kinematic and stress effects due to slip gradients the foundation of the model is a three term multiplicative decomposition of the deformation gradient that results in a second order differential equation in terms of the stress that drives slip converting the equation into a weak form results in an integral equation that includes first order derivatives of the stress as well as boundary conditions for the stress and gradients of slip rate for each slip system using this weak form an incremental finite element method is developed to solve the constitutive model within a finite element solution to the equilibrium equation results for the compression of a two dimensional plate show the effects of including slip gradient effects in the constitutive model and indicate the tendency for localization of the slip and dislocation density into narrow bands separating regions of nearly constant dislocation density and long range strain

an algorithm and a method to search bifurcation points in non linear problems this paper is devoted to a numerical method able to help the determination of the bifurcation threshold in non linear time independent continuum mechanic problems first some theoretical results about uniqueness are recalled in the framework of the large strain assumption the differences between the classical finite step problem and the rate problem are presented an iterative algorithm able to solve the rate problem is given using different initializations it is seen in some numerical experiments that it is possible with this algorithm to get different solutions when the underlying mathematical problem solved does not enjoy a uniqueness property the constitutive equations used have been chosen to be simple enough to deduce some theoretical knowledge about the corresponding uniqueness problems finally a method is given which is able in some case to give an upper bound of the bifurcation threshold copyright 2001 john wiley sons ltd

mixed stabilized finite element methods in nonlinear solid mechanics part ii strain localization this paper deals with the question of strain localization associated with materials which exhibit softening due to tensile straining a standard local isotropic rankine damage model with strain softening is used as exemplary constitutive model both the irreducible and mixed forms of the problem are examined and stability and solvability conditions are discussed lack of uniqueness and convergence difficulties related to the strong material nonlinearities involved are also treated from this analysis the issue of local discretization error in the pre localization regime is deemed as the main difficulty to be overcome in the discrete problem focus is placed on low order finite elements with continuous strain and displacement fields triangular p1p1 and quadrilateral q1q1 although the presented approach is very general numerical examples show that the resulting procedure is remarkably robust it does not require the use of auxiliary tracking techniques and the results obtained do not suffer from spurious mesh bias dependence

post necking behaviour modelled by a gradient dependent plasticity theory abstract the delay of the onset of localization and the post necking behaviour for stretched thin sheets are determined by three dimensional effects thus a 2 d finite element analysis based on a local plasticity theory will give a physically unrealistic mesh dependent solution this in spite of the fact that the stress state is essentially two dimensional by incorporating a length scale with relation to the thickness of the sheet it is demonstrated how a 2 d finite element analysis based on a gradient dependent plasticity theory can give a good approximation of the post necking behaviour this is illustrated by numerical comparison of results from a full 3 d finite element analysis with results from a 2 d finite element model based on a finite strain version of a gradient dependent j 2 flow theory some numerical problems in the modeling will be discussed briefly

theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage this paper presents the theory and the numerics of an isotropic gradient damage formulation within a thermodynamical background the main motivation is provided by localization computations whereby classical local continuum formulations fail to produce physically meaningful and numerically converging results we propose a formulation in terms of the helmholtz free energy incorporating the gradient of the damage field a dissipation potential and the postulate of maximum dissipation as a result the driving force conjugated to damage evolution is identified as the quasi nonlocal energy release rate which essentially incorporates the divergence of a vectorial damage flux besides the strictly local energy release rate on the numerical side besides balance of linear momentum the algorithmic consistency condition must be solved in weak form thereby the crucial issue is the selection of active constraints which is solved by an active set search algorithm borrowed from convex nonlinear programming in the examples we compare the behavior in local damage with the performance of the gradient formulation

simple sliding mode control scheme applied to robot manipulators we present a simple sliding mode control scheme for robot manipulators that does not rely upon the construction of individually stable discontinuity surfaces thus greatly reducing the complexity of design we utilize the structure of the manipulator dynamics and lyapunov s second method in order to establish a sliding surface on the intersection of the switching surfaces in a direct manner a simple numerical example accompanies the theoretical development

large strain finite element analysis of a local second gradient model application to localization summary a large strainnite element formulation based on a local second gradient plasticity model is presented the corresponding constitutive equations were developed as a direct extension of microstructured siam j appl math 1973 25 3 556 575 arch rational mech anal 1964 16 51 78 or micromorphic in mechanics of generalized continua iutam symposium kroner ed springer berlin 1968 18 35 j math mech 1966 15 6 909 924 continua in which a mathematical constraint between the micro kinematics description and the usual macrodeformation gradienteld has been introduced this constraint is enforced in a weak sense by the use of lagrange multipliers in order to avoid diculties with the c 1 continuity for thenite element method correspondingnite elements are then constructed involving the lagrange multiplierseld a geometrically non linear 2 dnite element code is developed within a framework of an incremental method for every step a full newton raphson involving a numerical consistent tangent stiness operator for the complete model i e the second gradient terms as well as the classical ones is done and some numerical tests allow to validate the method and to discuss the inuence of the geometrical non linearity copyright 2002 john wiley sons ltd

h sub 2 guaranteed cost switching surface design for sliding modes with nonmatching disturbances this paper presents an extension of utkin and yang s method 1978 for sliding surface design via the minimization of a quadratic performance criterion the method proposed takes into account nonmatching disturbance signals and nonmatching system model uncertainties an upper bound for the h sub 2 norm of the disturbance to output transfer function is minimized leading to a guaranteed cost h sub 2 controller

gradient dependent plasticity formulation and algorithmic aspects a plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure hardening parameter but also on the laplacian thereof the consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity to properly solve the set of non linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements for appropriate boundary conditions this formulation can also be derived from a variational principle accordingly the theory is complete

loss of uniqueness of numerical solutions of the borehole problem modelled with enhanced media it is well known that initial boundary value problems involving constitutive equations modeling the degradation of the strength of materials are not well posed which renders computations questionable to overcome this issue it is necessary to enhance the models by incorporating some internal length it has been shown that such an enhancement restores the objectivity of the computation as spurious mesh dependency is avoided however at least for simple problems e g one dimensional ones it has been proven that uniqueness of the underlying mathematical problem itself is not restored moreover numerical modeling of element tests yields several solutions this paper demonstrates that several numerical solutions can be obtained also for less simple problems namely the borehole problems even when a defect is introduced in the computed problems different numerical solutions are found contrary to the one dimensional problem there is no proof that this loss of uniqueness comes from the underlying mathematical problem it is our opinion that this is an inherent property of initial boundary value problems where broadly speaking strong degradation of the mechanical properties is modeled in any case it is necessary to be aware of this issue for problems involving constitutive equation modeling strength degradation it is important to try to find other solutions than the one obtained by using routinely a numerical code the failure patterns of the different solutions found are however similar to experimental observations this possible loss of uniqueness can then be seen as a counterpart of the difficulties encountered when attempting to reproduce experiments this is crucial when dealing with geomaterials

unified analysis of enriched finite elements for modeling cohesive cracks abstract aiming to provide a justified theoretical ground based on which different enriched finite elements can be systematically compared we developed in this work a unified framework for modeling cohesive cracks using the variational multiscale method the kinematics i e coarse and fine scale displacement and strain fields and statics i e coarse and fine scale equilibrium equations are thoroughly investigated in both continuum and discrete settings with respect to the fine scale kinematics and statics adopted in the embedded finite element method efem and the extended finite element method xfem we mainly discuss four groups of enriched finite elements with non uniform discontinuity modes i e the kinematically optimal symmetric efem and xfem as well as the kinematically and statically optimal non symmetric efem and xfem in all these methods the enrichment parameters can be regarded either as element wise local or continuous global variables the enriched finite elements with material element node enrichments are then exemplified in an increasing order of their respective capabilities in representing the fine scale kinematics and the interrelations between them are also discussed owing to this unified framework we are able to clarify some existing points of view related to efem and xfem it is found that if the same fine scale statics is used and the same local global property is assumed for the involved enrichment parameters xfem can be regarded as a kinematically enhanced efem since it accounts for a more general fine scale kinematics than that i e relative rigid body motions and self stretching considered in efem finally several simple but sufficiently representative numerical examples are presented to show the significance in appropriately reflecting the fine scale kinematics and statics in an enriched finite element for modeling cohesive cracks

a new class of stabilizing controllers for uncertain dynamical systems this paper is concerned with the problem of designing a stabilizing controller for a class of uncertain dynamical systems the vector of uncertain parameters q cdot is time varying and its values q t lie within a prespecified bounding set q in r p furthermore no statistical description of q cdot is assumed and the controller is shown to render the closed loop system practically stable in a so called guaranteed sense that is the desired stability properties are assured no matter what admissible uncertainty q cdot is realized within the perspective of previous research in this area this paper contains one salient feature the class of stabilizing controllers which we characterize is shown to include linear controllers when the nominal system happens to be linear and time invariant in contrast in much of the previous literature see for example 1 2 7 and 9 a linear system is stabilized via nonlinear control another feature of this paper is the fact that the

a variational principle for gradient plasticity abstract we elaborate on a generalized plasticity model which belongs to the class of gradient models suggested earlier by aifantis and co workers the generalization of the conventional theory of plasticity has been accomplished by the inclusion of higher order spatial gradients of the equivalent plastic strain in the yield condition first it is shown how these gradients affect the critical condition for the onset of localization and allow for a wavelength selection analysis leading to estimates for the width and or spacing of shear bands due to the presence of higher order gradients additional boundary conditions for the equivalent plastic strain are required this question and also the associated problem of the formulation and solution of general boundary value problems were left open in the previous work we demonstrate here that upon assuming a certain type of additional boundary conditions the structural symmetries of the gradient dependent constitutive model are such that there exists a variational principle for the displacement rates and the rate of the equivalent plastic strain the variational principle can serve as a basis for the numerical solution of boundary value problems in the sense of the finite element method explicit expressions for the tangent stillness matrix and the generalized nodal point forces are given

modeling strong discontinuities at finite strains a novel numerical implementation abstract in this paper a finite element formulation suitable for the modeling of locally embedded strong discontinuities at finite strains is presented following the enhanced assumed strain concept eas the proposed numerical model is based on an additive decomposition of the displacement gradient into a conforming and an enhanced part the enhanced part is associated with the final failure kinematics of solids which are approximated by means of a discontinuous displacement field strong discontinuities referring to the displacement jump no special assumption such as purely mode i or mode ii failure is made the same holds for the class of interface laws considered which govern the evolution of the displacement discontinuity in terms of the traction vector acting at the surface of strong discontinuities consequently the suggested numerical framework can be applied to a broad range of different interface laws including damage based models in contrast to previous works the presented finite element formulation does not require the static condensation technique to be employed more precisely instead of computing the conforming part of deformation and the displacement jump simultaneously from the weak form of equilibrium and the weak form of traction continuity the different parts of the local deformation are decomposed according to a predictor corrector algorithm the proposed predictor and the corrector step are formally identical to that of classical computational plasticity models hence subroutines designed for standard models continuous deformation can be applied with only minor modifications necessary the applicability as well as the performance of the resulting finite element formulation are demonstrated by means of a fully three dimensional analysis of shear band formation in a bar made of a ductile material

arbitrary lagrangian eulerian finite element analysis of strain localization in transient problems non local models guaranty that finite element computations on strain softening materials remain sound up to failure from a theoretical and computational viewpoint the non locality prevents strain localization with zero global dissipation of energy and consequently finite element calculations converge upon mesh refinements to non zero width localization zones one of the major drawbacks of these models is that the element size needed in order to capture the localization zone must be smaller than the internal length hence the total number of degrees of freedom becomes rapidly prohibitive for most engineering applications and there is an obvious need for mesh adaptivity this paper deals with the application of the arbitrary lagrangian eulerian ale formulation well known in hydrodynamics and fluid structure interaction problems to transient strain localization in a non local damageable material it is shown that the ale formulation which is employed in large boundary motion problems can also be well suited for non linear transient analysis of softening materials where localization bands appear the remeshing strategy is based on the equidistribution of an indicator that quantifies the interelement jump of a selected state variable two well known one dimensional examples illustrate the capabilities of this technique the first one deals with localization due to a propagating wave in a bar and the second one studies the wave propagation in a hollow sphere

brief designing robust sliding hyperplanes for parametric uncertain systems a riccati approach in this paper we propose a method to design robust sliding hyperplanes in the presence of mismatched parametric uncertainty based on quadratic stability the robust sliding hyperplane is constructed from a riccati inequality associated with quadratic stabilizability the proposed method enables us to deal with structured uncertainty and optimize the sliding motion by applying the guaranteed cost control idea

adaptive sliding mode control of multi input nonlinear systems with perturbations to achieve asymptotical stability a design of adaptive sliding surfaces for a class of multi input mi nonlinear systems with matched and mismatched perturbations is proposed in this note to solve regulation problems based on the lyapunov stability theorem and backstepping technique by using some adaptive gains designed in the sliding surface function the virtual input and the controllers not only the mismatched perturbations are automatically overcome during the sliding mode but also the property of asymptotical stability of controlled systems is achieved at the same time furthermore the knowledge of the upper bound of partial perturbations is not required controlling a two link robot manipulator is given to demonstrate the feasibility of the proposed control scheme

numerical approximation of incremental infinitesimal gradient plasticity we investigate a representative model of continuum infinitesimal gradient plasticity the formulation is an extension of classical rate independent infinitesimal plasticity based on the additive decomposition of the symmetric strain tensor into elastic and plastic parts it is assumed that dislocation processes contribute to the storage of energy in the material whereby the curl of the plastic distortion appears in the thermodynamic potential and leads to an additional nonlocal backstress tensor the formulation is cast into a numerical framework by a saddle point approximation of the corresponding minimization problem in each incremental loading step this allows one to reformulate the nonlocal dissipation inequality to a point wise flow rule and yields a solution scheme which is a direct extension of the standard approach in classical plasticity our numerical results show the regularizing effects of the additional physically motivated terms copyright 2008 john wiley sons ltd

three dimensional isogeometric solutions to general boundary value problems of toupin s gradient elasticity theory at finite strains abstract we present to the best of our knowledge the first complete three dimensional numerical solutions to a broad range of boundary value problems for a general theory of finite strain gradient elasticity we have chosen for our work toupin s theory toupin 1962 one of the more general formulations of strain gradient elasticity our framework has three crucial ingredients the first is isogeometric analysis hughes et al 2005 which we have adopted for its straightforward and robust representation of c 1 continuity the second is a weak treatment of the higher order dirichlet boundary conditions in the formulation which control the development of strain gradients in the solution the third ingredient is algorithmic automatic differentiation which eliminates the need for linearization by hand of the rather complicated geometric and material nonlinearities in gradient elasticity at finite strains we present a number of numerical solutions to demonstrate that the framework is applicable to arbitrary boundary value problems in three dimensions we discuss length scale effects the role of higher order boundary conditions and perhaps most importantly the relevance of the framework to problems with elastic free energy density functions that are non convex in strain space

a new controller design for manipulators using the theory of variable structure systems a controller design for manipulators using the theory of variable structure systems vss is presented to deal with the set point regulation problem the major obstacle of vss vector control with strong dynamic coupling is overcome for a class of systems with positive symmetric inertia matrices parameter variations can easily be considered in the design methodology which is readily extendable to a higher number of links the problem of chattering is solved by the introduction of sliding sectors

time dependent thermodynamic properties of the ising model from damage spreading the relationship between damage spreading and static thermodynamic properties in the ising model developed by coniglioet al is here extended to include time dependent thermodynamic quantities we exploit this new result to measure the time dependent spin correlation function from damage spreading in the ising model with heat bath and glauber dynamics until now only static thermodynamic quantities have been correctly determined from damage spreading and even then only with heat bath dynamics we also show that there are significant differences between the kinetics of damage spreading as found in heat bath and glauber dynamics

a finite element method for poro mechanical modelling of geotechnical problems using local second gradient models in this paper a new finite element method is described and applied it is based on a theory developed to model poromechanical problems where the mechanical part is obeying a second gradient theory the aim of such a work is to properly model the post localized behaviour of soils and rocks saturated with a pore fluid beside the development of this new coupled theory a corresponding finite element method has been developed the elements used are based on a weak form of the relation between the deformation gradient and the second gradient using a field of lagrange multipliers the global problem is solved by a system of equations where the kinematic variables are fully coupled with the pore pressure some numerical experiments showing the effectiveness of the method ends the paper

existence and uniqueness theorems for boundaryvalue problems involving incrementally non linear models abstract sufficient conditions for existence and uniqueness of rate boundary value probleminvolving an incrementally non linear constitutive equation useful for geomaterials are proved the models considered are incrementally non linear models not descending from a rate potentialand thus are not included into the hill theory framework results are given in the framework ofsmall strain assumption the main assumption is the positiveness of the second order work theexistence theorem is a generalisation of the lax milgram theorem whereas uniqueness theoremis based on the well known hill exclusion functional