non linear analysis of nearly saturated porous media theoretical and numerical formulation a formulation for a porous medium saturated with a compressible fluid undergoing large elastic and plastic deformations is presented a consistent thermodynamic formulation is proposed for the two phase mixture problem thus preserving a straightforward and robust numerical scheme a novel feature is the specification of the fluid compressibility in terms of a volumetric logarithmic strain which is energy conjugated to the fluid pressure in the entropy inequality as a result the entropy inequality is used to separate three different mechanisms representing the response effective stress response according to terzaghi in the solid skeleton fluid pressure response to compressibility of the fluid and dissipative darcy flow representing the interaction between the two phases the paper is concluded with a couple of numerical examples that display the predictive capabilities of the proposed formulation in particular we consider results for the kinematically linear theory as compared to the kinematically non linear theory

computational aspects of incrementally objective algorithms for large deformation plasticity a methodology for computationally efficient formulation of the tangent stiffness matrix consistent with incrementally objective algorithms for integrating finite deformation kinematics and with closest point projection algorithms for integrating material response is developed in the context of finite deformation plasticity numerical experiments illustrate an excellent performance of the proposed formulation in comparison with other algorithms copyright 1999 john wiley sons ltd

projective varieties admitting an embedding with gauss map of rank zero abstract we introduce an intrinsic property for a projective variety as follows there exists an embedding into some projective space such that the gauss map is of rank zero which we call gmrz for short it turns out that gmrz imposes strong restrictions on rational curves on projective varieties in fact using gmrz we show that contrary to the characteristic zero case the existence of free rational curves does not imply that of minimal free rational curves in positive characteristic case we also focus attention on segre varieties grassmann varieties and hypersurfaces of low degree in particular we give a characterisation of fermat cubic hypersurfaces in terms of gmrz and show that a general hypersurface of low degree does not satisfy gmrz

fuzzy theoretic approach to signals and systems static systems abstract fuzzy theoretic approach to signals and systems assumes all system variables and parameters as uncertain i e being characterized by membership functions develops a mathematical theory for analytically determining the membership functions on system variables and parameters derives algorithms for estimating the parameters of membership functions and establishes robustness and convergence properties of the estimation algorithms the membership functions are analytically determined via solving a variational optimization problem that maximizes the over uncertainties averaged log membership of the observed data around an initial guess this paper develops the analytical fuzzy theory for the particular case of a multi input single output static system affected by noises the theory facilitates designing an adaptive filtering algorithm the robustness of the adaptive filtering algorithm is proved theoretically via a mathematical analysis numerical experiments further demonstrate the robustness of the filtering algorithm a comparison of the algorithm with the state of art methods is made using the practical biomedical applications related to the modeling and analysis of heart rate signals for assessing the physiological state of an individual

techniques for stress and strain controlled homogenization of inelastic periodic composites abstract a framework is developed within the context of the displacement finite element method for applying periodic boundary conditions to uni period basic cells under the influence of applied macroscopically homogeneous stresses the resulting approach supplements the more common strain controlled method which is also presented and which relies on an additive decomposition of the displacement field into linear imposed and periodic unknown contributions as implemented here the stress controlled method employs a penalty formulation to insure that the displacement solution satisfies the linearperiodic decomposition the performance of both the stress and strain driven methods are demonstrated and assessed on a complete set of homogenization computations for an elasto plastic composite

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

successive identification of a fuzzy model and its applications to prediction of a complex system abstract a successive identification method of a fuzzy model is suggested the identification mechanism consists of two levels one is the supervisor level and the other is the adjustment level the supervisor level determines a policy of parameter adjustment using a set of fuzzy adjustment rules the adjustment rules are derived from the fuzzy implications of a fuzzy model and are extended to fuzzy adjustment rules by using an extended concept of zadeh s contrast intensification the adjustment level executes the policy of parameter adjustment determined with the fuzzy adjustment rules the parameter adjustment consists of premise parameter adjustment and consequent parameter adjustment both of them are realized by the weighted recursive least square algorithm finally it is shown from two examples that the method is very useful for modeling complex systems

analytical cpp in energy mapped stress space application to a modified drucker prager yield surface in conventional stress space the closest point projection cpp of computational plasticity in general does not provide the closest point in a euclidean sense but rather in an energy metric as an alternative this contribution discusses an energy mapped stress space such that cpp is indeed the closest point in a strict euclidean sense this perspective clarifies which yield surfaces can be handled analytically analytical solutions are possible if the cpp can be expressed as a polynomial of order 4 or less this is demonstrated by means of a modified drucker prager yield surface in which the hydrostatic tensile apex is removed through the use of hyperbolic meridians

on the implementation of inelastic constitutive equations with special reference to large deformation problems abstract methods for finite element analysis of inelastic problems are reviewed problems with currently popular methods based on rate principles of virtual work are pointed out a formulation is presented based on the exact incremental virtual work equation the procedure for integration of the constitutive rate equations to obtain incremental constitutive equations is based on the assumption of a constant strain rate or straight strain path during the increment full newton raphson iteration is used to solve the resulting set of nonlinear equations the treatment of the constitutive equations in this newton raphson scheme leads to a linearized form which is substantially different from the classical rate equations the procedure is implemented in a finite element program and its effectiveness is shown in a number of examples

algorithmic issues for three invariant hyperplastic critical state models implicit stress integration and the consistent tangents are presented for critical state hyperplasticity models which include a dependence on the third invariant of stress an elliptical deviatoric yielding criterion 43 is incorporated within the family of geotechnical models first proposed by collins and hilder 8 an alternative expression for the yield function is proposed and the consequences of different forms of that function are revealed in terms of the stability and efficiency of the stress return algorithm errors associated with the integration scheme are presented it is shown how calibration of the two new material constants is achieved through examining one dimesional consolidation tests and undrained triaxial compression data material point simulations of drained triaxial compression tests are then compared with established experimental results strain probe analyses are used to demonstrate the concepts of energy dissipation and stored plastic work along with the robustness of the integration method over twenty finite element boundary value problems are then simulated these include single three dimensional element tests plane strain footing analyses and cavity expansion tests the rapid convergence of the global newton raphson procedure using the consistent tangent is demonstrated in small strain and finite deformation simulations

numerical solution of nonlinear differential equations with algebraic constraints i convergence results for backward differentiation formulas in this paper we investigate the behavior of numerical ode methods for the solution of systems of differential equations coupled with algebraic constraints systems of this form arise frequently in the modelling of problems from physics and engineering we study some particular examples from electrical networks fluid dynamics and constrained mechanical systems we show that backward differentiation formulas converge with the expected order of accuracy for these systems

finite strain formulation and fe implementation of a constitutive model for powder compaction abstract a finite strain formulation is developed implemented and tested for a constitutive model capable of describing the transition from granular to fully dense state during cold forming of ceramic powder this constitutive model as well as many others employed for geomaterials embodies a number of features such as pressure sensitive yielding complex hardening rules and elastoplastic coupling posing considerable problems in a finite strain formulation and numerical implementation a number of strategies are proposed to overcome the related problems in particular a neo hookean type of modification to the elastic potential and the adoption of the second piola kirchhoff stress referred to the intermediate configuration to describe yielding an incremental scheme compatible with the formulation for elastoplastic coupling at finite strain is also developed and the corresponding constitutive update problem is solved by applying a return mapping algorithm

non smooth multisurface plasticity and viscoplasticity loading unloading conditions and numerical algorithms rate independent plasticity and viscoplasticity in which the boundary of the elastic domain is defined by an arbitrary number of yield surfaces intersecting in a non smooth fashion are considered in detail it is shown that the standard kuhn tucker optimality conditions lead to the only computationally useful characterization of plastic loading on the computational side an unconditionally convergent return mapping algorithm is developed which places no restrictions aside from convexity on the functional forms of the yield condition flow rule and hardening law the proposed general purpose procedure is amenable to exact linearization leading to a closed form expression of the so called consistent algorithmic tangent moduli for viscoplasticity a closed form algorithm is developed based on the rate independent solution the methodology is applied to structural elements in which the elastic domain possesses a non smooth boundary numerical simulations are presented that illustrate the excellent performance of the algorithm

a mathematical framework for finite strain elastoplastic consolidation part 1 balance laws variational formulation and linearization a mathematical formulation for finite strain elasto plastic consolidation of fully saturated soil media is presented strong and weak forms of the boundary value problem are derived using both the material and spatial descriptions the algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the kirchhoff pore water pressure balance laws are written for the soil water mixture following the motion of the soil matrix alone it is shown that the motion of the fluid phase only affects the jacobian of the solid phase motion and therefore can be characterized completely by the motion of the soil matrix furthermore it is shown from energy balance consideration that the effective or intergranular stress is the appropriate measure of stress for describing the constitutive response of the soil skeleton since it absorbs all the strain energy generated in the saturated soil water mixture finally it is shown that the mathematical model is amenable to consistent linearization and that explicit expressions for the consistent tangent operators can be derived for use in numerical solutions such as those based on the finite element method

extracting fuzzy rules for system modeling using a hybrid of genetic algorithms and kalman filter abstract this paper proposes a hybrid algorithm for extracting important fuzzy rules from a given rule base to construct a parsimonious fuzzy model with a high generalization ability this algorithm combines the advantages of genetic algorithms strong search capacity and kalman filter s fast convergence merit each random combination of the rules in the rule base is coded into a binary string and treated as a chromosome in genetic algorithms the binary string indicates the structure of a fuzzy model the parameters of the model are then estimated using the kalman filter in order to achieve a trade off between the accuracy and the complexity of a fuzzy model the schwarz rissanen criterion is used as an evaluation function in the hybrid algorithm the practical applicability of the proposed algorithm is examined by computer simulations on a human operator modeling problem and a nonlinear system modeling problem

on the numerical treatment of finite deformations in elastoviscoplasticity abstract this paper deals with the generalization of a geometric linear viscoplastic model to finite strains and its numerical application we owe the original formulation of the applied model to perzyna and chaboche it includes nonlinear isotropic and kinematic hardening as well as a nonlinear rate dependence the constitutive equations are integrated numerically in the context of a finite element formulation from theoretical considerations it is known that in the case of vanishing viscosity or slow processes rate independent plasticity arises as an asymptotic limit accordingly the numerical formulation includes this property in fact the stress algorithm corresponding to viscoplasticity is reduced to the asymptotic limit in a most simple way namely by setting the viscosity parameter equal to zero furthermore it is shown that the numerical integration of the constitutive model involves the solution of only one nonlinear equation for one scalar unknown this even applies to a sum of armstrong frederick terms the algorithm incorporates the inelastic incompressibility on the level of the gau points numerical computations of examples taken from metal forming technology show the physical significance of the model and the reliability of the numerical algorithm these calculations have been carried out by means of the finite element program psu

a formulation of the mitc4 shell element for finite strain elasto plastic analysis abstract a finite strain elasto plastic formulation is developed for the mitc4 shell element the developed formulation is based on lee s multiplicative decomposition of the deformation gradient and on the hyperelastic expression of von mises flow rule expressed in terms of hencky s strain tensor the formulation incorporates thickness stretching degrees of freedom that are condensed at the element level by imposing the classical in layer plane stress condition a symmetric and consistent tangent stiffness matrix is also developed

an integration scheme for prandtl reuss elastoplastic constitutive equations we investigate the generalized midpoint rule for the time integration of elastoplastic constitutive equations for pressure independent yield criteria the incremental equations are divided into one scalar hydrostatic pressure dilation rate equation and a stress deviator strain rate deviator tensorial equation this formulation is applied to two classical problems bulging of a tube under internal pressure and tension test on a notched specimen

on the normal bundles of smooth rational space curves in this note we consider smooth rational curves c of degree n in threedimensional projective space ip 3 over a closed field of characteristic 0 to avoid trivial exceptions we shall always assume that n 4 this does not hold however for certain auxiliary curves we shall consider let n n c be the normal bundle of c in ip 3 since degel ip3 4 and d e g c l l p 0 2 we have that d e g c l n 4 n 2 by a well known theorem of grothendieck the bundle n is a direct sum of two line bundles hence n o c 2 n l a g o c 2 n 1 a for some non negative a a c which is uniquely determined by c the question we would like to answer is an obvious one which values of a occur we shall show theorem 4 below that a value a occurs if and only if 0 0 therefore hi c n o it follows k p 150 that c represents a smooth point on the chow variety ch 3 1 n of effective cycles of dimension 1 and degree n in ip 3 since the set of all smooth rational curves with a fixed degree is obviously connected we see that the smooth c s represent a smooth irreducible 4n dimensional zariski open subset s of ch 3 1 n in a for thcoming paper e v we shall prove the following

operator split methods for the numerical solution of the elastoplastic dynamic problem the elastoplastic dynamic problem is first formulated in a form that facilitates the application of product formula techniques the additive decomposition of the dynamic equations into elastic and plastic parts is taken as a basis for the definition of product algorithms that exploit such decomposition in the context of a finite element discretization these product algorithms entail for every time step the solution of an elastic problem followed by the application of plastic algorithms that operate on the stresses and internal variables at the integration points and bring in the plastic constitutive relations suitable plastic algorithms are discussed for the cases of perfect and hardening plasticity and viscoplasticity the proposed formalism does not depend on any notion of smoothness of the yield surface and is applicable to arbitrary convex elastic regions with or without corners the stability properties of the product algorithm are identical to those of the elastic algorithm used whereas the computational expense is practically equal to that of an elastic problem

implicit explicit schemes for nonlinear consolidation abstract a general analytical procedure capable of performing linear and nonlinear consolidation analysis of saturated porous media is proposed a brief review of the coupled field equations is included and the constitutive assumptions are stated explicitly time integration of the resulting nonlinear semidiscrete finite element equations is performed by using an implicit explicit predictor multicorrector scheme developed by hughes and co workers it is shown that the algorithm can be simply and concisely implemented the technique allows for a convenient selection of implicit and explicit elements and for a convenient implicit explicit split of the various operators appearing in the equations the procedure proves to be extremely effective in dealing with consolidation problems numerical results which demonstrate the versatility and accuracy of the proposed procedures are presented

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

optimization of rational powered membership functions using extended kalman filter this paper presents an extension to the application of the extended kalman filter ekf in membership function mf optimization since the ekf is a derivative based method and derivative calculations of various mf shapes are too complicated so far only triangular type has been optimized via this approach in this article the ekf is applied in optimizing the rational powered mfs which are extended form of triangular trapezoidal functions and hence can offer better performance in almost all applications in addition because of the efficiency of the singleton mfs which makes them a common and desirable choice in hardware software realization of fuzzy systems these mfs are also optimized using the ekf the corresponding analytical equations and derivative formulas are given and finally the efficiency of the ekf in mf optimization is discussed

design of fuzzy systems using neurofuzzy networks introduces a systematic approach for fuzzy system design based on a class of neural fuzzy networks built upon a general neuron model the network structure is such that it encodes the knowledge learned in the form of if then fuzzy rules and processes data following fuzzy reasoning principles the technique provides a mechanism to obtain rules covering the whole input output space as well as the membership functions including their shapes for each input variable such characteristics are of utmost importance in fuzzy systems design and application in addition after learning it is very simple to extract fuzzy rules in the linguistic form the network has universal approximation capability a property very useful in e g modeling and control applications here we focus on function approximation problems as a vehicle to illustrate its usefulness and to evaluate its performance comparisons with alternative approaches are also included both non noisy and noisy data have been studied and considered in the computational experiments the neural fuzzy network developed here and consequently the underlying approach has shown to provide good results from the accuracy complexity and system design points of view

an evaluation of substepping and implicit stress point algorithms abstract elasto plastic finite element analyses of geotechnical boundary value problems involve the use of a non linear solution strategy a popular and efficient strategy is the modified newton raphson approach of which a key element is the integration of the constitutive laws over a finite strain step two algorithms for performing such an integration are the substepping and return methods in this paper the basic assumptions behind these methods are described and the associated errors compared this comparative study is undertaken both at a fundamental level and when applied to a typical boundary value problem the errors associated with both methods are increment size dependent it is shown in the problems considered that for a particular increment size the substepping method is the more accurate

training fuzzy systems with the extended kalman filter the generation of membership functions for fuzzy systems is a challenging problem we show that for mamdani type fuzzy systems with correlation product inference centroid defuzzification and triangular membership functions optimizing the membership functions can be viewed as an identification problem for a nonlinear dynamic system this identification problem can be solved with an extended kalman filter we describe the algorithm and compare it with gradient descent and with adaptive neuro fuzzy inference system anfis based optimization of fuzzy membership functions the methods discussed in this paper are illustrated on a fuzzy filter for motor winding current estimation and are compared with butterworth filtering we demonstrate that the kalman filter can be an effective tool for improving the performance of a fuzzy system

elastoplastic consolidation at finite strain part 2 finite element implementation and numerical examples a mathematical model for finite strain elastoplastic consolidation of fully saturated soil media is implemented into a finite element program the algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the kirchhoff pore water pressure a two field mixed finite element formulation is employed in which the nodal solid displacements and the nodal pore water pressures are coupled via the linear momentum and mass balance equations the constitutive model for the solid phase is represented by modified cam clay theory formulated in the kirchhoff principal stress space and return mapping is carried out in the strain space defined by the invariants of the elastic logarithmic principal stretches the constitutive model for fluid flow is represented by a generalized darcy s law formulated with respect to the current configuration the finite element model is fully amenable to exact linearization numerical examples with and without finite deformation effects are presented to demonstrate the impact of geometric nonlinearity on the predicted responses the paper concludes with an assessment of the performance of the finite element consolidation model with respect to accuracy and numerical stability

a re formulation of the exponential algorithm for finite strain plasticity in terms of cauchy stresses abstract the role of the stress measure to be chosen as the argument in the definition of yield functions is discussed in the context of finite strain plasticity theory motivated by physical arguments the exponential algorithm for multiplicative finite strain plasticity is revisited such that cauchy stresses are adopted as arguments in the yield function using logarithmic strain measures the return map algorithm is formulated in principal axes the algorithmic tangent moduli are obtained in a slightly modified unsymmetric format compared to the standard formulation in terms of kirchhoff stresses however the global structure of the exponential algorithm is unchanged the algorithm is applied to the re formulation of the cam clay model in terms of cauchy stresses the typical calibration procedure of the cam clay model based on cauchy stresses is demonstrated as an alternative a modification of the cam clay model which allows re calibration of cauchy stress based test data to be used within the framework of a kirchhoff based finite strain model is also discussed the relevance of the adequate choice of the stress measure is illustrated by means of selected numerical analyses

coupled plastic damaged model abstract a constitutive model that couples plasticity and damage is presented the model is thermodynamically consistent and comes from a generalization of classical plasticity theory and isotropic damage theory of kachanov coupling between plasticity and damage is achieved through a simultaneous solution of the plastic and the damage problem after a description of the model a numerical algorithm for the integration of the resulting constitutive equations is presented it is an euler backward type of algorithm that is particularly suitable to solve plain stress non linear problems with a 2d finite element program the consistent stiffness matrix is also derived the paper is completed with some application examples that show that the model presented accurately reproduces the behaviour of elastic plastic damaged materials

strain localization in frictional materials exhibiting displacement jumps abstract this paper presents a mathematical model for analyzing strain localization in frictional solids exhibiting displacement jumps precise conditions for the appearance of slip lines including their initiation and evolution are outlined for a rate independent strain softening drucker prager model and explicit analytical expressions are used to describe the orientation of the slip line a stress displacement relation obtained through the consistency condition is also formulated to describe the quasi static response in the post localization regime the mathematical model which is cast within the framework of finite element analysis employing the assumed enhanced strain method circumvents mesh dependence issues often associated with rate independent plasticity models it is shown that the enhancement equation is nothing else but the consistency condition imposed on the band numerical examples involving plane strain compression are described to demonstrate objectivity with respect to mesh refinement and insensitivity to mesh alignment of finite element solutions

symmetry preserving return mapping algorithms and incrementally extremal paths a unification of concepts in this work we seek to characterize the conditions under which an elastic plastic stress update algorithm preserves the symmetries inherent to the material response from a numerical standpoint the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality for the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving for hardening plasticity symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations we show that these restrictions amount to the existence of a pseudo internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli in view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and hence in symmetric tangents we address the question of whether any connections exist between the two approaches we show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence

dynamics of porous media at finite strain we present a finite element model for the analysis of a mechanical phenomenon involving dynamic expulsion of fluids from a fully saturated porous solid matrix in the regime of large deformation momentum and mass conservation laws are written in lagrangian form by a pull back from the current configuration to the reference configuration following the solid matrix motion a complete formulation based on the motion of the solid and fluid phases is first presented then approximations are made with respect to the material time derivative of the relative flow velocity vector to arrive at a so called v p formulation which is subsequently implemented in a finite element model we show how the resulting finite element matrix equations can be consistently linearized using a compressible neo hookean hyperelastic material with a kelvin solid viscous enhancement for the solid matrix as a test function for the nonlinear constitutive model numerical examples are presented demonstrating the significance of large deformation effects on the transient dynamic responses of porous structures as well as the strong convergence profile exhibited by the iterative algorithm

capturing strain localization in dense sands with random density summary this paper presents a three invariant constitutive framework suitable for the numerical analyses of localization instabilities in granular materials exhibiting unstructured random density a recently proposed elastoplastic model for sands based on critical state plasticity is enhanced with the third stress invariant to capture the difference in the compressive and extensional yield strengths commonly observed in geomaterials undergoing plastic deformation the new three invariant constitutive model similar to its two invariant predecessor is capable of accounting for meso scale inhomogeneities as well as material and geometric nonlinearities details regarding the numerical implementation of the model into a fully nonlinear finite element framework are presented and a closed form expression for the consistent tangent operator whose spectral form is used in the strain localization analyses is derived an algorithm based on the spectral form of the so called acoustic tensor is proposed to search for the necessary conditions for deformation bands to develop the aforementioned framework is utilized in a series of boundary value problems on dense sand specimens whose density fields are modelled as exponentially distributed unstructured random fields to account for the effect of inhomogeneities at the meso scale and the intrinsic uncertainty associated with them copyright 2006 john wiley sons ltd

the b bar method and the limitation principles abstract the generalized elastic material provides a reference model to cast in a unitary framework many structural models which are based on nonlinear monotone multivalued relations such as viscoelasticity plasticity and unilateral models the modified forms of the hu washizu and hellinger reissner principles and the displacement based variational formulation are recovered for the generalized elastic material starting from a functional in the complete set of state variables the related limitation principles are derived and their specialization to elasticity and elastoplasticity with mixed hardening are provided it is shown that the interpolating fields for the pressure and the volumetric strain usually adopted in the b bar method lead to a limitation principle accordingly the same elastic and elastoplastic solutions can be obtained by means of an approximate mixed displacement pressure variational principle a second application is concerned with the conditions ensuring the coincidence of the solutions between an approximate two field mixed formulation and the displacement based method numerical examples are provided to show the coincidence of the solutions obtained from different mixed finite element formulations in elasticity or elastoplasticity under the validity of the limitation principles

a new numerically stable sequential algorithm for coupled finite strain elastoplastic geomechanics and flow abstract we propose a new numerically stable sequential implicit method for coupled flow and finite strain multiplicative elastoplastic geomechanics we find from stability analysis that the sequential method that solves the flow problem first by fixing the first piola kirchhoff total stress solving the geomechanics solid deformation problem at the next step is unconditionally stable contractive and b stable in this sense this method named the fixed first piola kirchhoff stress method is an extension of the fixed stress method in coupled flow and infinitesimal geomechanics we also study the fixed second piola kirchhoff stress method comparing it with the fixed first piola kirchhoff stress method because the constitutive relations are formulated by the second piola kirchhoff total stress although fixing the second piola kirchhoff total stress field does not provide theoretical unconditional stability in space discretization we use the finite element method for the geomechanics problem with the total lagrangian approach while employing the finite volume method for the flow problem geometrical nonlinearity from the total lagrangian approach results in full tensor permeability even if the initial permeability is isotropic to consider the full tensor permeability accurately we employ the multipoint flux approximation in solving the flow problem in time discretization the backward euler method is used then we perform numerical experiments of the two fixed stress sequential methods with various scenarios and find superiority of their numerical stability specifically the two fixed stress sequential methods provide almost identical results for elasticity for j 2 plasticity the two sequential methods yield slightly different numerical results although the trends of the results are similar for the drucker prager plasticity we find that the results from the two methods are almost identical for all the test cases the two sequential methods are numerically stable

generating rules for fuzzy logic controllers by functions abstract in this paper we introduce a method of generating control rules for fuzzy logic controllers called parametric functions method by this method we can obtain control rules by adjusting several parameters

convergence of newton type methods in incremental return mapping analysis of elasto plastic problems abstract the incremental finite element algorithm with return mapping stress computation is considered for the solution of problems of elasto plasticity this algorithm performed in load steps leads to the necessity of solving large scale nonlinear systems the properties of these systems are investigated in the presented paper together with two iterative techniques for their solution the main results of the paper are rigorous proofs of the convergence of the inexact initial stiffness method and the local quadratic convergence of the inexact newton method with the consistent tangent operator

on the formulation of closest point projection algorithms in elastoplasticity part i the variational structure we present in this paper the characterization of the variational structure behind the discrete equations defining the closest point projection approximation in elastoplasticity rate independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range the later in the context of isotropic finite strain multiplicative plasticity primal variational principles in terms of the stresses and stress like hardening variables are presented first followed by the formulation of dual principles incorporating explicitly the plastic multiplier augmented lagrangian extensions are also presented allowing a complete regularization of the problem in the constrained rate independent limit the variational structure identified in this paper leads to the proper framework for the development of new improved numerical algorithms for the integration of the local constitutive equations of plasticity as it is undertaken in part ii of this work

implicit dynamic three dimensional finite element analysis of an inelastic biphasic mixture at finite strain part 1 application to a simple geomaterial abstract based on the mixture theory formulation for a fluid saturated inelastic pressure sensitive porous solid subjected to dynamic large strain deformation a 3d finite element implementation with implicit time integration is presented a recently published 2d implementation li et al 2004 cmame v193 p3837 70 is extended to 3d porosity dependent permeability and pressure sensitive inelastic solid skeleton response at finite strain the clausius duhem inequality provides the form of the constitutive equations for the solid and fluid phases as well as the dissipation function a non associative drucker prager cap plasticity model at finite strain is formulated based on a multiplicative decomposition of the deformation gradient and numerically integrated semi implicitly in the intermediate configuration to avoid questions of incremental objectivity the elastic implementation is verified with available 1d analytical and 2d benchmark problems new numerical solutions for 3d large strain dynamic behavior of saturated inelastic porous media are presented the computational efficiency of the implemented formulation in achieving quadratic convergence is illustrated

cam clay plasticity part iv implicit integration of anisotropic bounding surface model with nonlinear hyperelasticity and ellipsoidal loading function abstract this paper describes a fully implicit stress point integration algorithm for a class of anisotropic bounding surface plasticity models with ellipsoidal loading function the plasticity model is coupled with a nonlinear hyperelastic model to ensure that the elastic component of the combined model is energy conserving a key feature of the integration algorithm for the combined model is a return mapping in strain space which allows fully implicit integration and consistent linearization of the constitutive equations for this class of bounding surface models the consistency condition on the bounding surface is shown to be mathematically equivalent to the consistency condition on the loading surface thus allowing practically all attributes of the standard return mapping algorithm of classical plasticity theory to be carried over to the bounding surface theory with little modification as a specific example the infinitesimal version of modified cam clay theory is used to represent the bounding surface model and an exponential function is used to interpolate the plastic modulus on the loading surface isoerror maps are generated describing the accuracy of the integration algorithm on the stress point level finally a boundary value problem involving a strip footing on lightly overconsolidated clay is analyzed to demonstrate the robustness of the algorithm in a finite element setting

cam clay plasticity part v a mathematical framework for three phase deformation and strain localization analyses of partially saturated porous media we present a mathematical framework for deformation and strain localization analyses of partially saturated granular media using three phase continuum mixture theory first we develop conservation laws governing a three phase mixture to identify energy conjugate expressions for constitutive modeling energy conjugate expressions identified relate a certain measure of effective stress to the deformation of the solid matrix the degree of saturation to the matrix suction the pressure in each phase to the corresponding intrinsic volume change of this phase and the seepage forces to the corresponding pressure gradients from the second of law of thermodynamics we obtain the dissipation inequality from the principle of maximum plastic dissipation we derive a condition for the convexity of the yield function then we formulate expressions describing conditions for the onset of tabular deformation bands under locally drained and locally undrained conditions finally we cast a specific constitutive model for partially saturated soils within the proposed mathematical framework and implement it in the context of return mapping algorithm of computational plasticity the proposed constitutive model degenerates to the classical modified cam clay model of soil mechanics in the limit of full saturation numerical examples are presented to demonstrate the performance of the return mapping algorithm as well as illustrate the localization properties of the model as functions of imposed deformation and matrix suction histories

nonlinear context adaptation in the calibration of fuzzy sets abstract in this note we elaborate on the concept and use of context adaptation the underlying idea hinges upon a nonlinear transformation of an actual reference unit universe of discourse into a subset of reals say a b that is implied by actually available data current context assuming a collection of fuzzy sets a a1 a2 an defined over 0 1 the adaptation gives rise to a new frame of cognition a a1 a2 an expressed over a b owing inherent nonlinearity of the developed mapping different elements fuzzy sets of a can be stretched or expanded according to the given experimental data proposed is a neural network as a relevant optimization tool

adaptive return mapping algorithms for j2 elasto viscoplastic flow in this paper a new class of integration algorithms for elasto viscoplastic constitutive equations is proposed it is based on the generalized trapezoidal rule which is a weighted combination of the start and end of the increment but instead of taking constant weights the weights are a function of the plastic multiplier in this way the magnitude of the plastic strain increment determines the way the integration is performed the stress update and consistent tangent are derived for the case of j2 flow several candidates within the class of adaptive return mapping algorithms are investigated it is shown numerically that some of the proposed algorithms are more accurate than commonly used algorithms such as mean normal and radial return

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

variational principles for a class of finite step elastoplastic problems with non linear mixed hardening a class of elastoplastic relations with non linear mixed hardening is addressed in the framework of an internal variable theory the relevant finite step structural problem resulting from the time integration of the constitutive laws according to a backward difference scheme is then formulated in a geometrically linear range convex analysis and potential theory for monotone multi valued operators are shown to provide the rationale for the development of a consistent variational theory as a special result a convex minimum principle in the final values of displacements plastic strains and plastic parameters is formulated and a critical comparison with an analogous result proposed in the literature is presented

on the numerical integration of three invariant elastoplastic constitutive models abstract we investigate the performance of a numerical algorithm for the integration of isotropically hardening three invariant elastoplastic constitutive models with convex yield surfaces the algorithm is based on a spectral representation of stresses and strains for infinitesimal and finite deformation plasticity and a return mapping in principal stress directions smooth three invariant representations of the mohr coulomb model such as the lade duncan and matsuoka nakai models are implemented within the framework of the proposed algorithm among the specific features incorporated into the formulation are the hardening softening responses and the tapering of the yield surfaces toward the hydrostatic axis with increasing confining pressure isoerror maps are generated to study the local accuracy of the numerical integration algorithm finally a boundary value problem involving loading of a strip foundation on a soil is analyzed with and without finite deformation effects to investigate the performance of the integration algorithm in a full scale non linear finite element simulation

a generalized midpoint algorithm for the integration of a generalized plasticity model for sands this paper describes a method of performing the integration of generalized plasticity models in which unlike classical elastoplasticity the yield surface is not explicitly defined the algorithm is based on a generalized midpoint scheme and is applied to a specific generalized plasticity model for sands in which a hyperelastic formulation is introduced to describe the reversible component of the soil response instead of the hypoelastic approach originally proposed in this way an efficient integration scheme is developed in the elastic strain space the consistent algorithmic tangent operator is derived isoerror maps are generated to study the local accuracy of the numerical integration algorithm results from a series of numerical examples based on the simulation of drained triaxial tests are given to illustrate the accuracy and convergence properties of the algorithm both at the local and at the global level finally an example is given of the simulation of a cyclic triaxial test to illustrate the improvement on accuracy caused by the use of a hyperelastic law into the constitutive equations as opposed to the hypoelastic formulation initially adopted in the model copyright 2008 john wiley sons ltd

implicit j2 bounding surface plasticity using prager s translation rule a bounding surface j2 plasticity model that uses prager s translation rule is presented the model preserves masing s rules and is developed from the same ideas as classical infinitesimal j2 plasticity resulting in the same formulation with the exception of the algorithm for the computation of the hardening function instead of utilizing a loading surface as in a previous formulation hardening surfaces are introduced the formulation is similar to that of multilayer plasticity using prager s rule presented in previous work an implicit algorithm based on the radial return concept is used and the consistent elastoplastic tangent is also developed in closed form examples illustrating anisotropic behaviour are presented and compared to that predicted by a multilayer j2 plasticity model the model is also applied to a soil dynamics problem to show the robustness of the algorithm and its applicability to complex loading copyright 2002 john wiley sons ltd

a genetic learning process for the scaling factors granularity and contexts of the fuzzy rule based system data base abstract in this contribution we propose a new method to automatically learn the knowledge base of a fuzzy rule based system by finding an appropriate data base using a genetic algorithm and considering a simple generation method to derive the rule base our genetic process learns all the components of the data base number of labels working ranges and membership function shapes for each linguistic variable using a non linear scaling function to adapt the fuzzy partition contexts

cam clay plasticity part iii extension of the infinitesimal model to include finite strains the infinitesimal version of the modified cam clay model of critical state soil mechanics is reformulated to include finite deformation effects central to the formulation are the choice of a hardening law that is appropriate for cases involving large plastic volumetric strains and the use of a class of two invariant stored energy functions appropriate for cam clay type models that includes as special cases the constant elastic shear modulus approximation as well as the pressure dependent shear modulus elastic model the analytical model is cast within the framework of finite deformation theory based on a multiplicative decomposition of the deformation gradient for the fully elasto plastic case return mapping is done implicitly in the space defined by the invariants of the elastic logarithmic principal stretches which requires the solution at each stress point of no more than three simultaneous non linear equations a finite element analysis of a strip footing problem is presented to illustrate a prototype example where finite deformation effects significantly impact the predicted response

remarks on rate constitutive equations for finite deformation problems computational implications it is explicitly shown that if the spatial elasticity tensor of an elastic material is taken as isotropic for all possible configurations then its coefficients cannot be constants they must depend nontrivially on the jacobian determinant of the deformation gradient moreover the assumption typically made for computational purposes that its coefficients remain constant for all possible configurations is incompatible with elasticity it is further shown that an assumption widely used in the computational literature in the context of finite deformation plasticity namely relating an objective stress rate to the rate of deformation tensor through a fourth rank constant isotropic tensor is also incompatible with elasticity thus furnishing an example of an hypoelastic material which is not elastic

formulation and finite element implementation of a multiplicative model of coupled poro plasticity at finite strains under fully saturated conditions in this paper we present the formulation and numerical analysis of a finite deformation model of coupled poro plasticity fully saturated conditions are assumed the model is based on a multiplicative decomposition of the deformation gradient in elastic and plastic parts together with an additive elastoplastic decomposition of the fluid content the final relations describing the evolution of the different fields are then obtained in the thermodynamic framework furnished by the principle of maximum plastic dissipation the particular case of an associated drucker prager model in effective stresses is considered as a model example a complete characterization of the dissipative structure of the problem of evolution is described through the derivation of an a priori stability estimate we describe in detail the finite element implementation of the model in the context of staggered algorithms for the solution of the physically coupled problem finally we present representative numerical simulations to illustrate the features of the proposed models in particular the case of strain localization in globally undrained conditions is studied in the proposed framework