a variational analysis of the toda system on compact surfaces in this paper we consider the following toda system of equations on a compact surface we will give existence results by using variational methods in a noncoercive case a key tool in our analysis is a new moser trudinger type inequality under suitable conditions on the center of mass and the scale of concentration of the two components u1 and u2 2012 wiley periodicals inc

on liouville systems at critical parameters part 1 one bubble abstract in this paper we consider bubbling solutions to the general liouville system 0 1 g u i k j 1 n a i j j k h j e u j k h j e u j k 1 0 in m i 1 n n 2 where m g is a riemann surface and a a i j n n is a constant non negative matrix and j k j as k among other things we prove the following sharp estimates 1 the location of the blowup point 2 the convergence rate of j k j j 1 n these results are of fundamental importance for constructing bubbling solutions it is interesting to compare the difference between the general liouville system and the su 3 toda system on estimates 1 and 2

sharp estimates for solutions of multi bubbles in compact riemann surfaces in this paper we consider a sequence of multibubble solutions u k of the equation 0 1 0 u k k he uk f m he u k d 1 0 in m where h is a c 2 positive function in a compact riemann surface m and k is a constant satisfying lim k k 8m for some positive integer m 1 we prove among other things that k 8m 2 m m j 1h 1 p k j 0 log h p k j 8m 2k p k j k j e k j o e k j where p k j are centers of the bubbles of u k and k j are the local maxima of u k after adding a constant this yields a uniform bound of solutions as k converges to 8m from below provided that 0 log h p k j 8m 2k p k j 0 it generalizes a previous result due to ding jost li and wang 18 and nolasco and tarantello 31 which says that any sequence of minimizers u k is uniformly bounded if k 0 for any maximum point p of the sum of 2 log h and the regular part of the green function where k is the gaussian curvature of m the analytic work of this paper is the first step toward computing the topological degree of 0 1 which was initiated by li 24

implicit stress integration procedure for small and large strains of the gurson material model the gurson material model has broad applications in fracture mechanics large strain deformations and failure of metals void growth and void nucleation are included in the model considered in this paper an implicit stress integration procedure with calculation of the consistent tangent moduli is developed for the gurson model the general 3d deformations and the plane stress conditions are considered the procedure is robust simple and computationally efficient suitable for use within the finite element method fem it represents an application of the governing parameter method gpm for stress integration in case of inelastic material deformation a large strain formulation based on the multiplicative decomposition of the deformation gradient for material with plastic change of volume and logarithmic strains is used in the paper the developed numerical procedure for stress integration is applicable to small and large strains conditions solved examples illustrate the main features of the developed numerical algorithm copyright 2002 john wiley sons ltd

existence of bubbling solutions for chern simons model on a torus we study the existence of bubbling solutions for the the following chern simons higgs equation delta u frac1 varepsilon 2 rm e u 1 rm e u 4 pi sum i 1 2k delta p i quad text in omega where is a torus if k 1 for any critical point q of the associated sum of the green functions we introduce a quantity d q see 1 11 below we show that for any non degenerate critical point q with d q 0 the above problem has a solution ue satisfying that e 0 ue blows up at q the calculations in this paper also show that if a sequence of solutions ue blows up at q as e 0 then q must be a critical point of the associated sum of the green functions and d q leqq 0 so the condition d q 0 is almost necessary to obtain our result we also construct solutions with k bubbles for k geqq 2

a simplified canonical form algorithm with application to porous metal plasticity a canonical form for the representation of material constitutive equations within standard finite element codes has been developed which is deceptive in its simplicity substitution of different equation systems is trivial and a consistent material jacobian may be obtained automatically the process is essentially numerical and does not involve the difficult algebraic manipulation associated with more traditional approaches it is nevertheless exact because partial derivatives are derived analytically and simple because calculation of these derivatives is the only algebraic manipulation required the remainder of the process is generic in this paper the algorithm is simplified further a much more detailed and transparent explanation of the key to the method is given namely calculation of the consistent jacobian a trivial modification also extends the method to plane stress the original algorithm was validated for a simple material model the new form is used to implement the significantly more difficult modified gurson model for porous metal plasticity with hydrostatic yield dependence it is tested for single element cases involving total collapse and also used to simulate necking of a notched cylindrical bar copyright 2005 john wiley sons ltd

the relativistic non abelian chern simons equations we study ther xr system of nonlinear elliptic equations delta u a lambda sum limits b 1 r k ab e u b lambda sum limits b 1 r sum limits c 1 r e u b k ab e u c k bc 4 pi sum limits j 1 n a delta p aj a 1 2 r x r 2 where 0 is a constant parameter k kab is the cartan matrix of a semi simple lie algebra and p is the dirac measure concentrated atp r 2 this system of equations arises in the relativistic non abelian chern simons theory and may be viewed as a nonintegrable deformation of the integrable toda system we establish the existence of a class of solutions known as topological multivortices the crucial step in our method is the use of the decomposition theorem of cholesky for positive definite matrices so that a variational principle can be formulated

mean field equation of liouville type with singular data topological degree we consider the following mean field equation gv h ev mh ev 1 4 j 1n j qj 1 on m where m is a compact riemann surface with volume 1 h is a positive c1 function on m and and j are constants satisfying j 1 in this paper we derive the topological degree counting formula for noncritical values of we also give several applications of this formula including existence of the curvature 1 metric with conic singularities doubly periodic solutions of electroweak theory and a special case of self gravitating strings 2015 wiley periodicals inc

two scale analysis of heterogeneous elastic plastic materials with asymptotic homogenization and voronoi cell finite element model in this paper a multiple scale finite element model vcfem homo has been developed for elastic plastic analysis of heterogeneous porous and composite materials by combining asymptotic homogenization theory with the voronoi cell finite element model vcfem vcfem for microstructural modeling originates from dirichlet tessellation of representative material elements at sampling points in the structure structural modeling is done by the general purpose finite element code abaqus and interfacing with the microscale vcfem analysis is done through the user subroutine in abaqus for material constitutive relation umat asymptotic homogenization in umat generates macroscopic material parameters for abaqus following the macroscopic analysis a local vcfem analysis is invoked to depict the true evolution of microstructural state variables various numerical examples are executed for validating the effectiveness of vcfem homo and the effect of size shape and distribution of heterogeneities on local and global response is examined

a detailed description of the gurson tvergaard needleman model within a mixed velocity pressure finite element formulation summary in an effort to implement gurson type models into a mixed velocity pressure finite element formulation with the mini element p1 p1 the algorithm proposed by aravas ijnme 1987 to integrate the pressure dependent plasticity as well as the formulations of consistent tangent moduli have been analyzed this work firstly reviews and clarifies the mathematical basis of the formulations used by aravas ijnme 1987 and demonstrates the equality of the tangent moduli formulations proposed by govindarajan and aravas cnme 1995 and zhang cmame 1995 which are widely used in the literature a unified formulation to calculate the tangent moduli is proven and its accuracy is also investigated by the finite difference method the implementation of the gurson tvergaard needleman model is then detailed for the mixed velocity pressure finite element formulation which employs the mini element p1 p1 due to the particularity of this element one needs to calculate two tangent moduli instead of one the formulas for calculating the linear tangent modulus and the bubble tangent modulus are then detailed finally comparison tests are carried out with abaqus dassault system simulia corp providence ri usa in order to validate the present implementation for both homogeneous and heterogeneous deformations copyright 2013 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

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

elliptic functions green functions and the mean field equations on tori we show that the green functions on flat tori can have either 3 or 5 critical points only there does not seem to be any direct method to attack this problem instead we have to employ sophisticated non linear partial differential equations to study it we also study the distribution of number of critical points over the moduli space of flat tori through deformations the functional equations of special theta values provide important inequalities which lead to a solution for all rhombus tori the general picture is also emerged though some of the necessary technicality is still to de developed 1 introduction and statement of results the study of geometric or analytic problems on two dimensional tori is the same as the study of problems on r 2 with doubly periodic data such situations occur naturally in sciences and mathematics since early days the mathematical foundation of elliptic functions was subsequently devel oped in the 19th century it turns out that these special functions are rather deep objects by themselves tori of different shape may result in very dif ferent behavior of the elliptic functions and their associated objects arith metic on elliptic curves is perhaps the eldest and the most vivid example in this paper we show that this is also the case for certain non linear par tial differential equations indeed researches on doubly periodic problems in mathematical physics or differential equations often restrict the study to rectangular tori for simplicity this leaves the impression that the theory for general tori may resemble much the same way as for the rectangular case however this turns out to be false we will show that the solvability of themean field equation dependson the shape of the green function which in turn depends on the geometry of the tori in an essential way recall that the green function g z w on a flat torus t c z 1 z 2 is the unique function on t t which satisfies zg z w w z 1 t

a topological degree counting for some liouville systems of mean field type let a a ij n n be an invertible matrix and a 1 a ij n n be the inverse of a in this paper we consider the generalized liouville system n 0 1 g u i n a ij j h j e u j h j e u j 1 0 in m j 1 where 0 h j c 1 m and j and prove that under the assumptions of h 1 and h 2 see introduction the leray schauder degree of 0 1 is equal to m 1 m n n if 1 n satisfies 8 n n n i 1 i 1 i j n a ij i j 8 n 1 n n i 1 i equation 0 1 is a natural generalization of the classic liouville equation and is the euler lagrangian equation of the nonlinear function u 1 2 m 1 i j n a ij g u i g u j n n i 1 m i u i n n i 1 i log m h i e u i the liouville system 0 1 has arisen in many different research areas in mathematics and physics our counting formulas are the first result in degree theory for liouville systems

moser trudinger inequalities for singular liouville systems in this paper we prove a moser trudinger inequality for the euler lagrange functional of general singular liouville systems on a compact surface we characterize the values of the parameters which yield coercivity for the functional hence the existence of energy minimizing solutions for the system and we give necessary conditions for boundedness from below we also provide a sharp inequality under assuming the coefficients of the system to be non positive outside the diagonal the proofs use a concentration compactness alternative poho aev type identities and blow up analysis

numerical implementation and analysis of a class of metal plasticity models coupled with ductile damage this paper deals with a class of rate independent metal plasticity models which exhibit non linear isotropic hardening non linear kinematic hardening chaboche marquis model and ductile damage lemaitre chaboche model the backward euler scheme is used to integrate the rate constitutive relations the non linear equations obtained are solved by the newton method the consistent tangent operator is obtained by exact linearization of the algorithm despite the complexity of the constitutive equations closed form expressions are derived without any approximations analytical numerical and experimental results are presented acid discussed

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

explicit consistent tangent moduli with a return mapping algorithm for pressure dependent elastoplasticity models abstract in order to preserve the quadratic rate of asymptotic convergence for the widely used iterative schemes based on newton s method it is crucial to ensure consistency between the tangent moduli and the integration algorithm by exact linearization of the algorithm and decomposition of the stresses into hydrostatic and deviatoric parts a method is presented whereby an explicit expression for the tangent moduli consistent with a closest point return mapping algorithm may be developed for generalized pressure dependent elastolasticity models one significant advantage of this method is that no matrix inversion is necessary in the consistent tangent moduli expression for classical j 2 elastoplasticity associated with an isotropic hardening rule problem the present consistent tangent moduli coincide with consistent tangent moduli given by others application is made to fixed gurson based model as well as gurson based model the excellent convergence performance of the consistent tangent moduli is illustrated in numerical experiments

a polynomial characterization of mathcal a mathcal b invariant and reachability subspaces based on the state space model of p fuhrmann a link is laid between the geometric approach to linear system theory as developed by w m wonham and a s morse and the approach based on polynomial matrices in particular polynomial characterizations of a b invariant and reachability subspaces are given these characterizations are used to prove the equivalence of the disturbance decoupling problem and the exact model matching problem and also to connect the polynomial matrix and the geometric approach to the construction of observers finally constructive procedures and conditions are given for computing the supremal a b invariant subspace and reachability space and for checking the solvability of the exact model matching problem

a general existence result for the toda system on compact surfaces in this paper we consider the following toda system of equations on a compact surface u1 2 1 h1eu1 h1eu1dvg 1 2 h2eu2 h2eu2dvg 1 u1 4 j 1m 1 j pj 1 u2 2 2 h2eu2 h2eu2dvg 1 1 h1eu1 h1eu1dvg 1 u2 4 j 1m 2 j pj 1 which is motivated by the study of models in non abelian chern simons theory here h1 h2h1 h2 are smooth positive functions 1 2 1 2 two positive parameters pipi points of the surface and 1 i 2 j 1 i 2 j non negative numbers we prove a general existence result using variational methods the same analysis applies to the following mean field equation u 1 heu heudvg 1 2 he u he udvg 1 which arises in fluid dynamics

qualitative properties of solutions to some nonlinear elliptic equations in r 2 o introduction elliptic equations in this paper we investigate properties of the solutions to the au r x e u x x r 2 for functions r x which are positive near infinity equations of this kind arise from a variety of situations such as from prescribing gaussian curvature in geometry i 2 and from combustion theory in physics 3 recently a series ofworks have been sought to understand the existence and the qualitative properties of the solutions of ni i 5 and ni cheng 4 1 considered the case where r x is nonpositive mcowen 6 1 and aviles 7 investigated the situation where r x 0 in some order as ixl in our previous paper 1 we consider a special case where r is a constant we proved that the solutions are radially symmetric and hence classified all the solutions in this paper we consider more general functions r x first we obtain the asymptotic behavior of the solution near infinity consequently we prove that all the solutions satisfy an identity which is somewhat of a generalization of the well known kazdan warner condition finally using the asymptotic behavior together with the further development of the method employed in our previous paper i 1 we show that all the solutions are radially symmetric provided r is radially symmetric and nonincreasing this part can be viewed as the completion of 1 throughout this paper we assume that the function r x is positive near infinity in 1 we study the asymptotic behavior of the solution u x of let fl 1 2n r2 r x e dx under some appropriate conditions we show that the solutions approach

a micropolar formulation of the desai hierarchical model for elastoplastic porous media in this contribution the desai hierarchical model is extended to the case of 3d elasto plastic two phase micropolar continuum an unconditionally stable implicit euler backward algorithm for integration of the constitutive relations is developed and presented in detail the regularizing effect of the introduction of a length parameter to the classical desai model is demonstrated by means of several case studies of single phase and two phase porous media

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

ring fragmentation predictions using the gurson model with material stability conditions as failure criteria the gurson constitutive model used in combination with failure criteria based on material stability and bifurcation has been used in a finite element model to predict fracture and fragmentation in a dynamic expanding ring experiment integration of the constitutive relation is through a two level iteration scheme operating only on scalar equations it provides a robust solution for the large strain increments expected in shock problems numerically efficient failure criteria based on a bifurcation analysis and drucker s condition for material stability are evaluated at each integration point and at every time step the models were used to predict the fracture strain and number of fragments for thin electromagnetically loaded expanding rings the results show good predictions of time to failure predictions of the number of fragments are generally good with the model based on drucker s hypothesis being better at the higher strain rates

finite element implementation of gradient plasticity models part ii gradient dependent evolution equations abstract the variational formulation and finite element implementation of a class of plasticity models with gradient dependent yield functions is covered in detail in part i in this sequel attention is focussed upon the finite element formulation and implementation of a different class of plasticity models wherein spatial gradients of one or more internal variables enter the evolution equations for the state variables finite element solutions are obtained for the problems of localization of plastic flow in plane strain tension and of a mode i plane strain crack the pathological dependence of the finite element solution on the size of the elements in local plasticity models disappears when the gradient type model is used

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

numerical aspects in the finite element simulation of the portevin le chatelier effect abstract serrated yielding and propagation of localized bands of plastic strain rate are the apparent phenomena of the portevin le chatelier plc effect the finite element modeling of this effect is investigated using a model proposed by zhang et al 74 describing dynamic strain aging and material parameters for a nickel based superalloy at 500 c this work presents 1 an efficient implicit integration scheme of the constitutive equations in the presence of instabilities 2 a numerical tool to determine the type of plastic strain rate localization bands based on results of simulations and 3 a mesh and time discretization sensitivity analysis of the model regarding the characteristics of plc bands this analysis is carried out in 2d and 3d for axisymmetric smooth and notched specimens

improved explicit integration in plasticity the article presents a simple but efficient numerical scheme for the integration of non linear constitutive equations in which the principal reason for the inaccuracy of the classical explicit schemes for example forward euler scheme is effectively eliminated in the newly developed explicit scheme where there is no need for iteration the implementation simplicity of the forward euler scheme and accuracy of the approach which is using the backward euler scheme to integrate the constitutive equations are successfully combined computational performance of the proposed next increment corrects error nice integration scheme particularly regarding the accuracy and the cpu time consumption is first analysed on a case of complex loading of a material point when comparing it to the forward euler backward euler trapezoidal and midpoint integration schemes it turns out that because of its capability of a fast and relatively accurate integration of the constitutive equations the nice scheme is very convenient for the integration of constitutive models where a direct solution technique is used to solve a boundary value problem although the deduction of the new integration scheme is general its implementation for shell applications needs particular care namely in order to satisfy the zero normal stress condition during the whole integration a through thickness strain increment has to be adequately chosen in each integration step the nice scheme which was also implemented into abaqus explicit via user material subroutine vumat interface platform has been additionally compared with the abaqus explicit default integration scheme backward euler and forward euler scheme two loading case studies namely the bending of a square plate and the stretching of a specimen including the onset of necking are considered with two constitutive models the von mises and gtn material model being adopted generally the nice scheme has demonstrated to be advantageous in cases where reasonable accuracy and very fast integration of the constitutive model is demanded which is mostly the case in engineering computations with a direct solution method for example explicit dynamics and metal forming process simulations copyright 2009 john wiley sons ltd

numerical integration of a pressure dependent non linear kinematic hardening constitutive model for large strain cyclic plasticity of metals summary a gurson based constitutive model is presented which includes non linear mixed isotropic kinematic hardening and creep and allows the analysis of problems involving arbitrarily large plastic strains this model was developed with the main objective of allowing on the basis of a single set of material parameters the numerical simulation of all the main features of cold metal forming processes which usually imply severe loading unloading cycles with very large plastic strains difficult to be correctly reproduced numerically a suitable integration scheme of the rate equations is described and implemented into a finite element code the results obtained are compared with some reference experimental ones an application of the model for the simulation of wire drawing processes is also presented copyright 2011 john wiley sons ltd

condensed structural solutions to the disturbance rejection and decoupling problems with stability in this paper it is shown that a static state feedback control law rejects the disturbance and simultaneously performs input output decoupling while ensuring internal stability of the closed loop system if and only if an integer equality holds for the global undisturbed system and the row subsystems of the combined plant where the disturbance is handled as a control input namely in terms of their respective total contents sums of the orders of the multiplicities of its infinite and finite unstable invariant zeros

classification and nondegeneracy of su n 1 toda system with singular sources we consider the following toda system open image in new window where i 1 0 is dirac measure at 0 and the coefficients a ij form the standard tri diagonal cartan matrix in this paper i we completely classify the solutions and obtain the quantization result sum j 1 n a ij int mathbb r 2 e u j dx 4 pi 2 gamma i gamma n 1 i quad forall 1 leq i leq n this generalizes the classification result by jost and wang for i 0 forall 1 leq i leq n ii we prove that if i i 1 j for all 1 i j n then any solution u i is radially symmetric w r t 0 iii we prove that the linearized equation at any solution is non degenerate these are fundamental results in order to understand the bubbling behavior of the toda system

bubbling solutions for the su 3 chern simons model on a torus we consider the following nonlinear system derived from the su 3 chern simons models on a torus where denotes the dirac measure at when if we look for a solution with then 0 1 is reduced to the chern simons higgs equation the existence of bubbling solutions to 0 1 has been a longstanding problem in this paper we prove the existence of such solutions such that even if 2012 wiley periodicals inc

on a sharp sobolev type inequality on two dimensional compact manifolds motivated by the asymptotic analysis of double vortex condensates in the chern simons higgs theory we construct a suitable minimizing sequence for a sharp sobolev inequality a la moser for two dimensional compact manifolds as a consequence we first obtain a direct proof of the sharp character of such an inequality secondly and more interestingly we use such minimizing sequence to show that for the flat torus the corresponding extremal problem attains its infimum

a complement about almost controllability subspaces abstract we show that for any almost controllability subspace there exist a maximal input chain and a family of state feedbacks which lead to the well known feedback chain expression for this subspace

on the numerical integration of a class of pressure dependent plasticity models with mixed hardening radial return algorithms for both three dimensional and plane stress situations are developed for a class of pressure dependent plasticity models formulated in state variables with mixed hardening the consistent tangent matrix has been developed which among other advantages does not require numerical inversion the algorithms for gurson s mixed hardening model are incorporated in a finite element program to solve several simple uniaxial tension problems when compared with numerically integrated solutions the results from the finite element analysis show excellent agreement finally results of the axisymmetric necking problem using gurson s mixed hardening model are presented as an example of application

finite element implementation of non linear elastoplastic constitutive laws using local and global explicit algorithms with automatic error control implicit stress integration algorithms have been demonstrated to provide a robust formulation for finite element analyses in computational mechanics but are difficult and impractical to apply to increasingly complex non linear constitutive laws this paper discusses the performance of fully explicit local and global algorithms with automatic error control used to integrate general non linear constitutive laws into a non linear finite element computer code the local explicit stress integration procedure falls under the category of return mapping algorithm with standard operator split and does not require the determination of initial yield or the use of any form of stress adjustment to prevent drift from the yield surface the global equations are solved using an explicit load stepping with automatic error control algorithm in which the convergence criterion is used to compute automatically the coarse load increment size the proposed numerical procedure is illustrated here through the implementation of a set of elastoplastic constitutive relations including isotropic and kinematic hardening as well as small strain hysteretic non linearity a series of numerical simulations confirm the robustness accuracy and efficiency of the algorithms at the local and global level published in 2001 by john wiley sons ltd

harmonic maps of the two sphere into a complex grassmann manifold ii where qt is a complex valued one form defined up to a factor of absolute value 1 this form qp defines a complex structure on m for x e m the space f x has an orthogonal space f x of dimension n k we denote by f x and f x their corresponding projective spaces of dimensions k 1 and n k 1

analytic aspects of the toda system i a moser trudinger inequality in this paper we analyze solutions of the open toda system and establish an optimal moser trudinger type inequality for this system let be a closed surface with area 1 and k aij n n the cartan matrix for su n 1 i e we show that has a lower bound in h1 n if and only if this inequality is optimal as a direct consequence if mj for 4 for j 1 2 n m has a minimizer u that satisfies 2001 john wiley sons inc

degree counting and shadow system for toda system of rank two one bubbling abstract we initiate the program for computing the leray schauder topological degree for toda systems of rank two this program still contains a lot of challenging problems for analysts as the first step we prove that if a sequence of solutions u 1 k u 2 k blows up then one of h j e u j k m h j e u j k d v g j 1 2 tends to a sum of dirac measures this is so called the phenomena of weak concentration our purposes in this article are i to introduce the shadow system due to the bubbling phenomena when one of parameters i crosses 4 and j 4 n where 1 i j 2 ii to show how to calculate the topological degree of toda systems by computing the topological degree of the general shadow systems iii to calculate the topological degree of the shadow system for one point blow up we believe that the degree counting formula for the shadow system would be useful in other problems

fully implicit integration and consistent tangent modulus in elasto plasticity this paper deals with the numerical integration of a class of rate independent elasto plastic models the backward euler scheme is used to integrate the rate constitutive relations the non linear equations obtained are solved by the newton method the consistent tangent modulus is obtained by exact linearization of the algorithm in the case of j 2 elastoplasticity with non linear isotropic hardening and non linear kinematic hardening chaboche marquis model explicit formulas are derived without any approximations

degree counting for toda system with simple singularity one point blow up abstract in this paper we study the degree counting formula of the rank two toda system with simple singular source when 1 0 4 4 8 and 2 4 n the key step is to derive the degree formula of the shadow system which arises from the bubbling solutions as 1 tends to 4 in order to compute the topological degree of the shadow system we need to find some suitable deformation during this deformation we shall deal with new difficulty arising from the phenomenon blow up does not necessarily imply concentration of mass this phenomenon occurs due to the collapsing of singularities this is a continuation of the previous work 25

the partial model matching or partial disturbance rejection problem geometric and structural solutions the partial model matching problem or equivalently the partial disturbance rejection problem is revisited it has been initially introduced in emre and silverman 1980 and amounts to matching the first k markov parameters of the plant with those of the model this obviously finds all its interest when no solution exists to the exact problem the authors give both geometric and structural solutions to these problems the geometric solution is in terms of the steps of the well known supremal output nulling controlled invariant subspace algorithm the structural conditions amount to comparing some list of integers namely some orders of zeros at infinity

line search methods in general return mapping algorithms with application to porous plasticity the present paper focuses on the application of line search methods in general return mapping algorithms two inexact line search methods and an exact line search method are investigated regarding their convergence properties within an automatic time incrementation in finite element calculations as an example for the assessment of the algorithms an elastic plastic and an elastic viscoplastic version of gurson s porous plasticity model are used in simulations of the necking of a tensile bar it is shown that larger time increments are possible and therefore a smaller number of increments are required when using line search methods the exact line search method shows the best performance concerning the required number of increments but takes more cpu time to complete the simulation the application of the inexact line search methods in general lowers the number of increments along with a reduction in the cpu time as compared with the case when no line search is used copyright 2007 john wiley sons ltd

on a class of constitutive equations in viscoplasticity formulation and computational issues the viscoplastic constitutive model is formulated based on the existence of the dissipation potential which embodies the notion of the gauge minkowski function of the convex set a perturbation method is used for a solution of stiff differential equations characterizing the associated problem of evolution it relies on a discrete formulation of viscoplasticity which results from the regularized version of the principle of maximum plastic dissipation the operator split methodology and the newton raphson method are used to obtain the numerical solution of the discretized equations of evolution the consistent tangent modulus is expressed in a closed form as a result of the exact linearization of the discretized evolution equations for several variants of the flow potential function including some representative stiff functional forms numerical tests of the integration algorithm based on iso error maps are provided finally a numerical example is presented to illustrate the robustness and the effectiveness of the proposed approach

on the accuracies of numerical integration algorithms for gurson based pressure dependent elastoplastic constitutive models abstract a class of generalized mid point algorithms for pressure dependent elastoplastic models is formulated in the paper the accuracies of the formulated generalized mid point algorithms including the euler backward algorithm and the one step euler forward algorithm are systematically analyzed against the exact solution for gurson based pressure dependent elastoplastic model the accuracies of the algorithms are assessed by means of iso error maps results show that the formulated generalized mid point algorithms are reasonably accurate in both small and large increment steps it is found that in all the cases considered the maximum errors in the presence of volumetric strain increments are less than those without volumetric strain increments when the deviatoric strain increments are given in the radial direction the true mid point algorithm is the most accurate one furthermore the optimal value of the generalized mid point algorithms in terms of maximum errors is observed between 0 5 and 1 for both small and large increment steps the one step euler forward algorithm gives the worst accuracy

topological degree for a mean field equation on riemann surfaces we consider the following mean field equations 0 1 where m is a compact riemann surface with volume 1 h is a positive continuous function on m is a real number 0 2 and where is a bounded smooth domain h is a c1 positive function on and based on our previous analytic work 14 we prove among other things that the degree counting formula for 0 1 is given by for 8m 8 m 1 2003 wiley periodicals inc

an implicit integration algorithm for the finite element implementation of a nonlinear anisotropic material model including hysteretic nonlinearity abstract fully implicit integration schemes have been demonstrated to be very robust and efficient for nonlinear elastoplastic and elastic viscoplastic models and enjoy widespread use in finite element formulations the paper introduces a new form of fully implicit local and global algorithms for the integration of nonlinear elastoplastic constitutive laws including anisotropic plasticity and hysteretic small strain elastic nonlinearity the local stress integration algorithm is based on a single step backward differentiation method with iterative solution for the predictor as well as the corrector steps the global system of implicit nonlinear equations is solved with a quasi newton technique using a numerical tangent computed every load step by finite difference and optimized with iterative updating using the broyden fletcher goldfarb shano bfgs procedure the proposed numerical procedure is illustrated here through the implementation of a set of nonlinear constitutive equations describing the response of lightly overconsolidated cohesive materials numerical simulations of single element tests as well as a boundary value problem confirm the robustness accuracy and efficiency of the proposed algorithm at the local and global level

a generalized approach to formulate the consistent tangent stiffness in plasticity with application to the gld porous material model abstract it has been shown that the use of the consistent tangent moduli is crucial for preserving the quadratic convergence rate of the global newton iterations in the solution of the incremental problem in this paper we present a general method to formulate the consistent tangent stiffness for plasticity the robustness and efficiency of the proposed approach are examined by applying it to the isotropic material with j2 flow plasticity and comparing the performance and the analysis results with the original implementation in the commercial finite element program abaqus the proposed approach is then applied to an anisotropic porous plasticity model the gologanu leblond devaux model performance comparison between the consistent tangent stiffness and the conventional continuum tangent stiffness demonstrates significant improvement in convergence characteristics of the overall newton iterations caused by using the consistent tangent matrix

on the numerical integration of a class of pressure dependent plasticity models an unconditionally stable algorithm for the numerical integration of elastoplastic pressure dependent constitutive relations is analysed in detail in this paper the application of the method to plane stress problems in which the out of plane strain component is not defined kinematically is discussed the tangent moduli resulting from this integration algorithm are obtained by consistent linearization of the elastoplastic constitutive equations the algorithm is applied to gurson s constitutive model some one dimensional problems are solved and comparisons with exact solutions are made the paper closes with a numerical study of the necking of an axi symmetric specimen using gurson s plasticity model to describe the constitutive behaviour of the material

a canonical form return mapping algorithm for rate independent plasticity a canonical form for the representation of elastic predictor radial return plasticity algorithms is presented which is deceptive in its simplicity iterative application of the corrector is in a form used universally in the solution of ordinary differential equations and substitution of different yield functions and state variable evolution equations is trivial the consistency condition is maintained by an additional constraint equation via what is in effect a lagrange multiplier a consistent material jacobian may be obtained automatically by applying partial elimination to the same set of equations the process is numerical and requires no additional algebraic manipulation to demonstrate the validity of such a simple technique existing apparently more complex formulations are derived through the simple expedient of static condensation as a practical example of the application of the method a standard von mises plasticity model is implemented and results are presented for two standard benchmarks that test quadratic convergence for large increments copyright 2001 john wiley sons ltd