consistent tangent matrices for substepping schemes a very simple and general expression of the consistent tangent matrix for substepping time integration schemes is presented if needed the derivatives required for the computation of the consistent tangent moduli can be obtained via numerical differentiation these two strategies substepping and numerical differentiation lead to quadratic convergence in complex nonlinear inelasticity problems

asymptotic behavior of the solution to the non isothermal phase field equation we consider the penrose fife phase field model thermodynamically consistent models of phase field type for the kinetics of phase transitions physica d 43 1990 44 62 with homogeneous neumann boundary condition to the nonlinear heat flux q 1 i e q 0 on the boundary where 0 is the temperature there is a unique h1 solution globally in time with the non empty connected compact limit set composed of stationary solutions and the linearized stable stationary solution is dynamically stable

a non isothermal phase separation with constraints and dirichlet boundary condition for temperature abstract we consider non isothermal phase separation models of the penrose fife type which were proposed in o penrose p c fife thermodynamically consistent models of phase field type for the kinetics of phase transitions physica d 43 1990 44 62 in the present paper we impose a non homogeneous dirichlet boundary condition on the nonlinear heat flux moreover we consider two cases as boundary conditions for the conserved order parameter one is the homogeneous neumann boundary condition and the other is the signorini boundary condition which is nonlinear we show the existence and uniqueness of solutions to these models

variational inequalities of navier stokes type with time dependent constraints abstract we consider a class of parabolic variational inequalities with time dependent obstacle of the form u x t p x t where u is the velocity field of a fluid governed by the navier stokes variational inequality the obstacle function p p x t imposed on u consists of three parts which are respectively the degenerate part p x t 0 the finitely positive part 0 p x t and the singular part p x t in this paper we shall propose a sequence of approximate obstacle problems with everywhere finitely positive obstacles and prove an existence result for the original problem by discussing convergence of the approximate problems the crucial step is to handle the nonlinear convection term in this paper we propose a new approach to it

a filtration model with hysteresis abstract we study a filtration model for which a hysteresis effect is accounted in the saturation versus pressure constitutive relation the problem is formulated in a quasi variational inequality we prove the existence of a time global solution

nonconvergence of formal integrals ii improved estimates for the optimal order of truncation we investigate the asymptotic properties of formal integral series in the neighbourhood of an elliptic equilibrium in nonlinear 2 dof hamiltonian systems in particular we study the dependence of the optimal order of truncation nopt on the distance from the elliptic equilibrium by numerical and analytical means the function nopt determines the region of nekhoroshev stability of the orbits and the time of practical stability we find that the function nopt decreases by abrupt steps the decrease is roughly approximated with an average power law nopt o a with a 1 we find an analytical explanation of this behaviour by investigating the accumulation of small divisors in both the normal form algorithm via lie series and in the direct construction of first integrals precisely we find that the series exhibit an apparent radius of convergence that tends to zero by abrupt steps as the order of the series tends to infinity our results agree with those obtained by servizi g et al 1983 phys lett a 95 11 for a conservative map of the plane moreover our analytical considerations allow us to explain the results of our previous paper contopoulos g et al 2003 j phys a math gen 36 8639 including in particular the different behaviour observed for low order and higher order resonances

dynamics in the center manifold of the collinear points of the restricted three body problem this paper focuses on the dynamics near the collinear equilibrium points l1 2 3 of the spatial restricted three body problem rtbp it is well known that the linear behavior of these three points is of the type center center saddle to obtain an accurate description of the dynamics in an extended neighborhood of those points two different but complementary strategies are used first the hamiltonian of the problem is expanded in power series around the equilibrium point then a partial normal form scheme is applied in order to uncouple up to high order the hyperbolic directions from the elliptic ones skipping the remainder we have that the truncated hamiltonian has an invariant manifold tangent to the central directions of the linear part the restriction of the hamiltonian to this manifold is the so called reduction to the center manifold the study of the dynamics of this reduced hamiltonian now with only two degrees of freedom gives a qualitative description of the phase space near the equilibrium point finally a lindstedt poincare procedure is applied to explicitly compute the invariant tori contained in the center manifold these tori are obtained as the fourier series of the corresponding solutions the frequencies being a power expansion of some parameters amplitudes this allows for an accurate quantitative description of these regions in particular the well known halo orbits are obtained

an energy momentum map for the time reversal symmetric 1 1 resonance with z 2 z 2 symmetry abstract we present a general analysis of the bifurcation sequences of periodic orbits in general position of a family of reversible 1 1 resonant hamiltonian normal forms invariant under z 2 z 2 symmetry the rich structure of these classical systems is investigated both with a singularity theory approach and geometric methods the geometric approach readily allows to find an energy momentum map describing the phase space structure of each member of the family and a catastrophe map that captures its global features quadrature formulas for the actions periods and rotation number are also provided

well posedness for solid liquid phase transitions with a fourth order nonlinearity abstract a phase field system which describes the evolution of both the absolute temperature and the phase variable f during first order transitions in thermal insulators is considered a thermodynamic approach is developed by regarding the order parameter as a phase field and its evolution equation as a balance law by virtue of the special form of the internal energy a third order nonlinearity g 2 f appears in the energy balance in place of the customarily constant latent heat as a consequence the bounds 0 f 1 hold whenever is positive valued in addition a nonlinear fourier law with conductivity proportional to temperature is assumed well posedness for the resulting initial and boundary value problem are then established in a suitable setting

the dynamics around the collinear equilibrium points of the rtbp this paper is devoted to the analysis of an extended neighborhood of the collinear equilibrium points of the restricted three body problem the analysis is done using numerical tools for the determination of periodic orbits and invariant 2d tori all the relevant information of the neutrally stable behavior of the dynamics in the vicinity of the three libration points is given the results in this paper extend those given in physica d 132 1999 189 since they avoid the convergence restrictions of the semi analytical approach used in this reference

retrieving topological information for phase field models the phase field approach has become a popular tool in modeling interface motion microstructure evolution and more recently the shape transformation of vesicle membranes under elastic bending energy while it is advantageous to employ phase field models in numerical simu lations to automatically handle topological changes to the microstructures or the configurations of vesicle membranes detecting topological events may also become important for many applications such as those in the simulation of blood cells motivated by such considerations a new quantity is formulated to retrieve some topological information based on the phase field formulation and to capture the occurrence of topological events it can also be used as a control method to avoid unphys ical changes of topology due to the numerical methods should it become necessary for particular practical applications through numerical experiments we demonstrate the effectiveness and the robustness of the new quantity in detecting the topology of fluid bubbles and vesicle membranes

a system of odes with a hysteresis effect abstract the paper deals with a class of ordinary differential systems which contains a differential inclusion describing input output relations of hysteresis type existence and uniqueness of local and global solutions of the systems under consideration are proved

continuity of the temperature in the two phase stefan problem the classical two phase stefan problem a model for ice water melting gives rise to a singular nonlinear partial differential equation which admits a unique weak solution here we prove that this solution and therefore the temperature in the stefan problem are continuous

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

bogolyubov type theorem with constraints induced by a control system with hysteresis effect abstract we consider the problem of minimization of an integral functional with nonconvex with respect to the control integrand we minimize our functional over the solution set of a control system described by two ordinary differential equations subject to a control constraint given by a multivalued mapping with closed nonconvex values the coefficients of the equations and the constraint depend on the phase variables one of the equations contains the subdifferential of the indicator function of a closed convex set depending on the unknown phase variable the equation containing the subdifferential describes an input output relation of hysteresis type along with the original problem we also consider the problem of minimizing the integral functional with the convexified with respect to the control integrand over the solution set of the same system with the convexified control constraint under sufficiently general assumptions we prove that this relaxed problem has an optimal solution which is the limit of a minimizing sequence of the original problem the convergence takes place simultaneously with respect to the trajectory the control and the functional and is uniform in appropriate topologies

on a navier stokes allen cahn model with inertial effects abstract a mathematical model describing the flow of two phase fluids in a bounded container is considered under the assumption that the phase transition is influenced by inertial effects the model couples a variant of the navier stokes system for the velocity u with an allen cahn type equation for the order parameter relaxed in time in order to introduce inertia at the microscopic level the resulting model is characterized by second order material derivatives which constitute the main difficulty in the mathematical analysis in order to obtain a tractable problem a viscous relaxation term is then included in the phase equation the mathematical results consist in existence of weak solutions in 3d and under additional assumptions existence and uniqueness of strong solutions in 2d a partial characterization of the long time behavior of solutions is also given and in particular some issues related to dissipation of energy are discussed

a nonsmooth newton method for elastoplastic problems in this work we reformulate the incremental small strain j2 plasticity problem with linear kinematic and nonlinear isotropic hardening as a set of unconstrained nonsmooth equations the reformul

existence of solutions to heat equations with hysteresis coupled with navier stokes equations in 2d domains abstract this paper is concerned with a system of heat equations with hysteresis and navier stokes equations in two dimensional domains there are some studies on the system of heat equations and navier stokes equations in which the temperature the solution to heat equations is controlled by obstacle functions in this paper the control of the temperature is precisely described by introducing hysteresis this paper provides the existence of solutions along the abstract theory for evolution equations with subdifferential operators

a projected newton algorithm for the dual convex program of elastoplasticity summary in this paper we study a dual optimization problem that arises when taking a mathematical programming approach to incremental state update in nonlinear problems the mathematical programming approach stems from energy based descriptions of constitutive models we describe a projected newton algorithm to solve the dual optimization problem this algorithm requires solution of an unconstrained optimization problem at the integration point level rather than a constrained one as carried out by classical return mapping schemes especially implementation of multi surface plasticity models is no more involved than that of single surface models we explore characteristics and performance of the projected newton algorithm through numerical examples insights gained from such a further exploration of mathematical programming algorithms are likely to aid in development of successive convex programming approaches to geometric nonlinear and other non convex problems such as non associated flow models copyright 2014 john wiley sons ltd

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

thermodynamically consistent models of phase field type for the kinetics of phase transitions abstract a general framework is given for the phenomenological kinetics of phase transitions in which not only the order parameter but also the temperature may vary in time and space instead of a ginzburg landau free energy functional as used in formulating the cahn hilliard equation we use the analogous entropy functional model entropy functionals and the kinetic equations resulting from them are constructed for various cases phase transitions with and without a critical point and in the former case with or without a latent heat the class considered is general enough to include the entropy functionals for the ising model in mean field approximation the van der waals fluid and a simplified version of the density functional theory of freezing a case without critical point for which the energy is conserved but the order parameter is not provides a thermodynamically consistent derivation of the phase field equations studied by caginalp fix and others and also leads in a natural way to the lyapunov functional given by langer for these equations but the treatment also suggests that a modified version of the phase field equations might provide a more realistic model of freezing

existence and uniqueness for a concrete carbonation process with hysteresis abstract a partial differential system arising in the moisture transport in concrete carbonation modeling is considered the system consists of a diffusion equation for moisture and an ordinary differential equation accounting for the hysteresis effect appearing in the process the existence of solutions for this system supplied with suitable initial boundary conditions and having fairly general nonlinear right hand sides is established when the dimension of the space domain is one the uniqueness of a solution is also provided

upper bound limit analysis using discontinuous velocity fields abstract a new method for computing rigorous upper bounds under plane strain conditions is described it is based on a linear three noded triangular element which has six unknown nodal velocities and a fixed number of unknown plastic multiplier rates and uses the kinematic theorem to define a kinematically admissible velocity field as the solution of a linear programming problem unlike existing formulations which permit only a limited number of velocity discontinuities whose directions of shearing must be specified a priori the new formulation permits velocity discontinuities at all edges shared by adjacent triangles and the directions of shearing are found automatically the variation of the velocity jump along each discontinuity is described by an additional set of four unknowns all of the unknowns are subject to the constraints imposed by an associated flow rule and the velocity boundary conditions the objective function corresponds to the dissipated power or some related load parameter of interest and is minimised to yield the desired upper bound since plastic deformation may occur not only in the discontinuities but also throughout the triangular elements as well the method is capable of modelling complex velocity fields accurately and typically produces tight upper bounds on the true limit load the formulation is applicable to materials whose strength is cohesive frictional purely cohesive and uniform or purely cohesive and linearly varying and thus quite general the new procedure is very efficient and always requires fewer elements than existing methods to obtain useful upper bound solutions moreover because of the extra degrees of freedom introduced by the discontinuities the linear elements no longer need to be arranged in a special pattern to model incompressible behaviour accurately

three dimensional quasi static frictional contact by using second order cone linear complementarity problem a new formulation is presented for the three dimensional incremental quasi static problems with unilateral frictional contact under the assumptions of small rotations and small strains a second order cone linear complementarity problem is formulated which consists of complementarity conditions defined by bilinear functions and second order cone constraints the equilibrium configurations are obtained by using a combined smoothing and regularization method for the second order cone complementarity problem copyright 2005 john wiley sons ltd

the phase field method in the sharp interface limit the phase field pf method for solidification phenomena is an open formulation based on a free energy functional two common choices for the pf potential here referred to briefly as the caginalp and kobayashi models are compared with respect to their numeric results within the classical sharp interface limit both qualitative and quantitative behavior are addressed and an assessment of the computational effort required to approximate a sharp interface problem is made it is shown that the specific form of the free energy potential does have a strong influence on the convergence of the pf results to their sharp interface limit compliance of the pf solutions with the linear kinetic model for the interface temperature is also investigated a simple one dimensional solidification problem in the presence of kinetic undercooling is solved by the pf model and also by a deforming grid method our results support the view that if care is exercised in formulating the phase temperature coupling there is a high degree of confidence in using the pf method for the numerical modeling of general solidification phenomena

the phase field transition system with non homogeneous cauchy stefan boltzmann and homogeneous neumann boundary conditions and non constant thermal conductivity abstract the paper establishes the existence estimate uniqueness and regularity for the solution of a nonlinear parabolic system a two phase caginalp type system with non homogeneous cauchy stefan boltzmann and homogeneous neumann boundary conditions and non constant thermal conductivity it extends the already studied types of boundary conditions which makes the mathematical model to be richer and more flexible to describe the real physical phenomena including phase separation

on the formulation of closest point projection algorithms in elastoplasticity part ii globally convergent schemes this paper presents the formulation of numerical algorithms for the solution of the closest point projection equations that appear in typical implementations of return mapping algorithms in elastoplasticity the main motivation behind this work is to avoid the poor global convergence properties of a straight application of a newton scheme in the solution of these equations the so called newton cppm the mathematical structure behind the closest point projection equations identified in part i of this work delineates clearly different strategies for the successful solution of these equations in particular primal and dual closest point projection algorithms are proposed in non augmented and augmented lagrangian versions for the imposition of the consistency condition the primal algorithms involve a direct solution of the original closest point projection equations whereas the dual schemes involve a two level structure by which the original system of equations is staggered with the imposition of the consistency condition driving alone the iterative process newton schemes in combination with appropriate line search strategies are considered resulting in the desired asymptotically quadratic local rate of convergence and the sought global convergence character of the iterative schemes these properties together with the computational performance of the different schemes are evaluated through representative numerical examples involving different models of finite strain plasticity in particular the avoidance of the large regions of no convergence in the trial state observed in the standard newton cppm is clearly illustrated

two dimensional elastoplasticity approximation by mixed finite elements two dimensional elastoplastic problems are used to assess the performance of a family of mixed finite elements in the non linear regime in particular four node bilinear quadrilateral elements that exhibit high accuracy in coarse meshes are used to simulate plane stress plane strain axisymmetric and shear deformable plate bending problems the excellent performance of these elements is demonstrated with a number of discriminating examples selected from the literature in addition agreement is observed in the limit load predicted by the axisymmetric solid and plate bending elements

a non linear programming method approach for upper bound limit analysis this paper presents a finite element model based on mathematical non linear programming in order to determine upper bounds of colapse loads of a mechanical structure the proposed formulation is derived within a kinematical approach framework employing two simultaneous and independent field approximations for the velocity and strain rate fields the augmented lagrangian is used to establish the compatibility between these two fields in this model only continuous velocity fields are used uzawa s minimization algorithm is applied to determine the optimal kinematical field that minimizes the difference between external and dissipated work rate the use of this technique allows to bypass the complexity of the non linear aspects of the problem since non linearity is addressed as a set of small local subproblems of optimization for each finite element the obtained model is quite versatile and suitable for solving a wide range of collapse problems this paper studies 3d strut and tie structures 2d plane strain stress and 3d solid problems copyright 2007 john wiley sons ltd

an analysis of a phase field model of a free boundary a mathematical analysis of a new approach to solidification problems is presented a free boundary arising from a phase transition is assumed to have finite thickness the physics leads to a system of nonlinear parabolic differential equations existence and regularity of solutions are proved invariant regions of the solution space lead to physical interpretations of the interface a rigorous asymptotic analysis leads to the gibbs thompson condition which relates the temperature at the interface to the surface tension and curvature

shape instabilities and pattern formation in solidification a new method for numerical solution of the moving boundary problem abstract when a solidification front is advancing into a region of supercooled liquid its shape is subject to instabilities which can lead to complex modes of growth the evaluation of the growth pattern is determined by the interaction of the driving force of the instability due to heat diffusion with the restabilizing force due to surface tension and its full development is a highly nonlinear process a new method for solving the two phase heat diffusion problem under these conditions is described the method is based on a single domain treatment weak formulation of the moving boundary problem with the temperature field near the interface approximated by a piecewise linear function in the spirit of the finite element technique calculated results for a model problem are in excellent agreement with the predictions of an analytical approximation

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

reconstruction of two time independent coefficients in an inverse problem for a phase field system abstract in this paper we present stability results concerning the inverse problem of determining two time independent coefficients for a phase field system in a bounded domain r n for the dimension n 3 with a single observation on a subdomain and the sobolev norm of certain partial derivatives of the solutions at a fixed positive time 0 t over the whole spatial domain the proof of these results relies on an appropriate carleman estimate for the phase field system

exponential attractors for a conserved phase field system with memory we consider a conserved phase field system of caginalp type characterized by the assumption that both the internal energy and the heat flux depend on the past history of the temperature and its gradient respectively the model consists of a parabolic integrodifferential equation coupled with a fourth order evolution equation for the phase field this system supplemented with suitable boundary conditions can be interpreted as a dissipative dynamical system in a proper phase space in a previous joint work the last two authors have proved the existence of a global attractor of finite fractal dimension here we show the existence of an exponential attractor by means of the techniques we developed for nonconserved phase field systems with memory

analysis of an iterative scheme of fractional steps type associated to the reaction diffusion equation endowed with a general nonlinearity and cauchy neumann boundary conditions abstract the paper studies the existence uniqueness regularity and the approximation of solutions to the reaction diffusion equation endowed with a general nonlinear regular potential and cauchy neumann boundary conditions the convergence and error estimate results for an iterative scheme of fractional steps type associated to the nonlinear parabolic equation are also established the advantage of such method consists in simplifying the numerical computation necessary to be done in order to approximate the solution of nonlinear parabolic equation

global smooth solutions to a thermodynamically consistent model of phase field type in higher space dimensions abstract in a recent paper penrose and fife proposed a thermodynamically consistent model of phase field type for phase transition phenomena such as liquid solid phase transitions the model is based on the observation that the second law of thermodynamics postulates that the entropy functional cannot decrease along solution paths it turns out that the resulting field equations form a system of partial differential equations which is considerably more difficult than the phase field equations studied by caginalp and others for one space dimension global existence uniqueness and asymptotic behaviour of smooth solutions of the initial boundary value problem with neumann boundary data have been obtained in a recent paper by zheng in this paper we prove global existence and uniqueness in three space dimensions for the initial boundary value problem with a third boundary condition

a phase field model with temperature dependent constraint this paper is concerned with a phase field model with temperature dependent constraint for the order parameter in the kinetic equation of the order parameter we take account of diffusion as well as undercooled superheated state which is modelled by means of a hysteresis input output relation the input is the temperature field and the output is the order parameter in this paper we shall show that there exists a solution globally in time in a physically reasonable sense when the coefficient of interfacial energy is sufficiently small

on the existence uniqueness and regularity of solutions to the phase field system with a general regular potential and a general class of nonlinear and non homogeneous boundary conditions abstract this paper studies a caginalp phase field transition system endowed with a general regular potential as well as a general class in both unknown functions of nonlinear and non homogeneous depending on time and space variables boundary conditions we first prove the existence uniqueness and regularity of solutions to the allen cahn equation subject to the nonlinear and non homogeneous dynamic boundary conditions the existence uniqueness and regularity of solutions to the caginalp system in this new formulation are also proved this extends previous works concerned with regular potential and nonlinear boundary conditions allowing the present mathematical model to better approximate the real physical phenomena especially phase transitions

the numerical computation of heteroclinic connections in systems of gradient partial differential equations the numerical computation of heteroclinic connections in partial differential equations pdes with a gradient structure such as those arising in the modeling of phase transitions is considered initially a scalar reaction diffusion equation is studied structural assumptions are made on the problem to ensure the existence of absorbing sets and consequently a global attractor as a result of the gradient structure it is known that if all equilibria are hyperbolic the global attractor comprises the set of equilibria and heteroclinic orbits connecting equilibria to one another thus it is natural to consider direct approximation of the set of equilibria and the connecting orbits results are proved about the fourier spanning basis for branches of equilibria and also for certain heteroclinic connections these results exploit the oddness of the nonlinearity the reaction diffusion equation is then approximated by a galerkin spectral discretization to produce a system of ordinary differential equations

a mixed finite element model for plane strain elastic plastic analysis part ii application to the 4 node bilinear element in this paper the results of part i of this study are applied to the 4 node bilinear element the trial functions for different fields are defined consistently with the a priori conditions established the rate problem is generalized to cover finite loading steps and the solution strategy is presented computations referred to some discriminating examples from the literature demonstrate that the proposed model is actually capable of predicting the perfectly plastic collapse load for pathological plane strain problems exhibits excellent performances with coarse meshes and is rather insensitive to mesh distortion

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

parabolic pdes with hysteresis and quasivariational inequalities w0 being prescribed as an initial output of w its input output relation is illustrated in fig 1 1 see 1 part i iii 2 for the precise de nition in the gure fa and fd are continuous and nondecreasing functions on r such that fa fd on r we refer for some results on this sort of model to 1 4 as is well known 1 part i iii 2 1 2 is equivalent to the following variational inequality wt x t iu x t w x t 3 0 x t qt 1 3

normal maps inducted by linear transformations we study a certain piecewise linear manifold which we call the normal manifold associated with a polyhedral convex set and a family of continuous functions called normal maps that are induced on this manifold by continuous functions from rn to rn these normal maps occur frequently in optimization and equilibrium problems and the subclass of normal maps induced by linear transformations plays a key role our main result is that the normal map induced by a linear transformation is a lipschitzian homeomorphism if and only if the determinant of the map in each n cell of the normal manifold has the same nonzero sign

elasto plasticity revisited numerical analysis via reproducing kernel particle method and parametric quadratic programming aiming to simplify the solution process of elasto plastic problems this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto plasticity the parametric quadratic programming theory is useful and effective for the assessment of certain features of structural elasto plastic behaviour and can also be exploited for numerical iteration examples are presented to illustrate the essential aspects of the behaviour of the model proposed and the flexibility of the coupled parametric quadratic programming formulations with the reproducing kernel particle method copyright 2002 john wiley sons ltd

local minimisers and singular perturbations we construct local minimisers to certain variational problems the method is quite general and relies on the theory of convergence the approach is demonstrated through the model problem it is shown that in certain nonconvex domains n and for e small there exist nonconstant local minimisers u e satisfying u e 1 except in a thin transition layer the location of the layer is determined through the requirement that in the limit u e u 0 the hypersurface separating the states u 0 1 and u 0 1 locally minimises surface area generalisations are discussed with for example vector valued u and anisotropic perturbations replacing u 2

variational inequalities for a system of elliptic parabolic equations abstract we create a general framework for mathematical study of variational inequalities for a system of elliptic parabolic equations in this paper we establish a solvability theorem concerning the existence of solutions for the vector valued elliptic parabolic variational inequality with time dependent constraint moreover we give some applications of the system for example time dependent boundary obstacle problem and time dependent interior obstacle problem

an interior point algorithm for elastoplasticity the problem of small deformation rate independent elastoplasticity is treated using convex programming theory and algorithms a finite step variational formulation is first derived after which the relevant potential is discretized in space and subsequently viewed as the lagrangian associated with a convex mathematical program next an algorithm based on the classical primal dual interior point method is developed several key modifications to the conventional implementation of this algorithm are made to fully exploit the nature of the common elastoplastic boundary value problem the resulting method is compared to state of the art elastoplastic procedures for which both similarities and differences are found finally a number of examples are solved demonstrating the capabilities of the algorithm when applied to standard perfect plasticity hardening multisurface plasticity and problems involving softening copyright 2006 john wiley sons ltd

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

a class of nonlinear elliptic parabolic equations with time dependent constraints on etudie les equations d evolutions non lineaires de la forme f t du t dt t v t v t bu t 0 t t dans un espace de hilbert h ou t est la sous differentielle d une fonction convexe t definie sur h b est un operateur monotone maximal dans h on considere l existence et l unicite des solutions ainsi que des estimations a priori

on a system of nonlinear pde s for phase transitions with vector order parameter and convective effect the paper deals with a system of nonlinear pde s which describes a phase field model with convection and temperature dependent constraint to the vector order parameter existence of solutions for the system under consideration is proved by the method of yosida approximation and fixed point arguments

computation of sharp phase boundaries by spreading the planar and spherically symmetric cases abstract the sharp interface that arises from any of the major transition problems classical or modified stefan etc can be smoothed using the phase field approach as a numerical tool the basic idea is that the thickness of the interface can be regarded as a mathematical free parameter which can be stretched beyond its physical value for computational convenience the computations in one dimensional space and n dimensions with radial symmetry indicate that this is an efficient method for dealing with stiff equations and results in a very accurate interface determination without explicit tracking the question of optimizing the interfacial thickness with respect to grid size is also considered empirically the technique also provides a numerical verification of the concept of an unstable critical radius of solidification

a direct complementarity approach for the elastoplastic analysis of plane stress and plane strain structures this paper presents a direct complementarity approach for carrying out the elastoplastic analysis of plane stress and plane strain structures founded on a traditional finite step formulation our approach however avoids the typically cumbersome implementation of iterative predictorcorrector procedures associated with the ubiquitous return mapping algorithm instead at each predefined step the governing formulationcast in its most natural mathematical programming format known as a mixed complementarity problemis directly solved by using a complementarity solver run from within a mathematical modeling system we have chosen the industry standard general algebraic modeling system path mixed complementarity problem solver that is called from within the general algebraic modeling system environment we consider both von mises and tresca materials with perfect or hardening kinematic and isotropic behaviors our numerical tests five benchmark examples of which are presented in this paper have been carried out using models constructed from the mixed finite element of capsoni and corradi comput methods appl mech eng 1997 141 6793 which beneficially offers a locking free behavior and coarse mesh accuracy the results indicate in addition to an isochoric locking free behavior good accuracy and the ability to circumvent the difficult singularity problem associated with the corners of tresca yield surfaces

halo orbits around the collinear points of the restricted three body problem abstract we perform an analytical study of the bifurcation of the halo orbits around the collinear points l 1 l 2 l 3 for the circular spatial restricted three body problem following a standard procedure we reduce to the center manifold constructing a normal form adapted to the synchronous resonance introducing a detuning which measures the displacement from the resonance and expanding the energy in series of the detuning we are able to evaluate the energy level at which the bifurcation takes place for arbitrary values of the mass ratio in most cases the analytical results thus obtained are in very good agreement with the numerical expectations providing the bifurcation threshold with good accuracy care must be taken when dealing with l 3 for small values of the mass ratio between the primaries in that case the model of the system is a singular perturbation problem and the normal form method is not particularly suited to evaluate the bifurcation threshold

relaxation and optimisation of a phase field control system with hysteresis abstractthe present paper is concerned with a nonlinear partial differential control system arising in phase transition modelling the control constraint is given by a state dependent nonconvex valued multivalued mapping we study the problem of minimisation of a given integral cost functional over solutions to the above system the cost integrand is nonconvex in the control variable relaxation results of bogolyubov type are obtained for this problem

convergence of the newton raphson algorithm in elastic plastic incremental analysis a spatially continuous time discrete formulation of the loading of an elastic perfectly plastic body governed by a von mises yield condition is presented it is assumed that incremental changes in strain occur along minimum work paths which is equivalent to a backward difference implicit integration algorithm or the radial return method

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

a new computational model for tresca plasticity at finite strains with an optimal parametrization in the principal space abstract a new computational model for the rate independent elasto plastic solids characterized by yield surfaces containing singularities and general nonlinear isotropic hardening is presented within the context of fully implicit return mapping algorithms a numerical scheme for integration of the constitutive equations is formulated in the space of principal stresses as a direct consequence of the principal stress approach the representation of a yield surface is cast in terms of optimal parameterization which for the tresca yield criterion takes a simple linear form the associated return mapping equations then reduce to a remarkably simple format in addition due to assumed isotropy of the models the associated algorithmic incremental constitutive functionals can be identified as particular members of a class of isotropic tensor functions of one tensor in which the function eigenvalues are expressed in terms of the eigenvalues of the argument this observation leads to a simple closed form derivation of the consistent tangent moduli associated with the described integration algorithms the extension of the present model to finite strains is carried out following standard multiplicative plasticity described in terms of logarithmic stretches and exponential approximation to the flow rule the efficiency and robustness of the computational model are illustrated on a range of numerical examples

periodic solutions to a heat equation with hysteresis in the source term this paper is concerned with a parabolic problem with hysteresis effects in the heat source which models the feedback control the existence of periodic solutions is proved by the viscosity approach when the heat force changes periodically in time more precisely with the help of the subdifferential operator theory and the poincare map the existence of solutions to the approximation problem is shown and the solution of the periodic problem is obtained under consideration by using a passage to limit procedure

resonance tongues in hill s equations a geometric approach abstract the geometry of resonance tongues is considered in mainly reversible versions of hill s equation close to the classical mathieu case hill s map assigns to each value of the multiparameter the corresponding poincare matrix by an averaging method the geometry of hill s map locally can be understood in terms of cuspoid whitney singularities this adds robustness to the result the algorithmic nature of the averaging method enables a pull back to the resonance tongues of the original system