error estimates for galerkin approximations of the classical boussinesq system we consider the classical boussinesq system in one space dimension and its symmetric analog these systems model two way propagation of nonlinear dispersive long waves of small amplitude on the surface of an ideal fluid in a uniform horizontal channel we discretize an initial boundary value problem for these systems in space using galerkin finite element methods and prove error estimates for the resulting semidiscrete problems and also for their fully discrete analogs effected by explicit runge kutta time stepping procedures the theoretical orders of convergence obtained are consistent with the results of numerical experiments that are also presented

a three dimensional model describing stress temperature induced solid phase transformations solution algorithm and boundary value problems summary an always increasing knowledge on material properties as well as a progressively more sophisticated production technology make shape memory alloys sma extremely interesting for the industrial world at the same time sma devices are typically characterized by complex multi axial stress states as well as non homogeneous and non isothermal conditions both in space and time this aspect suggests the finite element method as a useful tool to help and improve application design and realization with this aim we focus on a three dimensional macroscopic thermo mechanical model able to reproduce the most significant sma features int j numer methods eng 2002 55 1255 1264 proposing a simple modification of such a model however the suggested modification allows the development of a time discrete solution algorithm which is more effective and robust than the one previously discussed in the literature we verify the computational tool ability to simulate realistic mechanical boundary value problems with prescribed temperature dependence studying three sma applications a spring actuator a selfexpanding stent a coupling device for vacuum tightness the effectiveness of the model to solve thermo mechanical coupled problems will be discussed in a forthcoming work copyright 2004 john wiley sons ltd

nonlinear stability of traveling waves to a hyperbolic parabolic system modeling chemotaxis we prove nonlinear stability of traveling waves of arbitrary amplitudes to a hyperbolic parabolic system modeling repulsive chemotaxis in contrast to the previous related results where various sm

variationally consistent modeling of finite strain plasticity theory with non linear kinematic hardening abstract variational constitutive updates provide a physically and mathematically sound framework for the numerical implementation of material models in contrast to conventional schemes such as the return mapping algorithm they are directly and naturally based on the underlying variational principle hence the resulting numerical scheme inherits all properties of that principle in the present paper focus is on a certain class of those variational methods which relies on energy minimization consequently the algorithmic formulation is governed by energy minimization as well accordingly standard optimization algorithms can be applied to solve the numerical problem a further advantage compared to conventional approaches is the existence of a natural distance semi metric induced by the minimization principle such a distance is the foundation for error estimation and as a result for adaptive finite elements methods though variational constitutive updates are relatively well developed for so called standard dissipative solids i e solids characterized by the normality rule the more general case i e generalized standard materials is far from being understood more precisely int j sol struct 2009 46 1676 1684 represents the first step towards this goal in the present paper a variational constitutive update suitable for a class of nonlinear kinematic hardening models at finite strains is presented two different prototypes of armstrong frederick type are re formulated into the aforementioned variationally consistent framework numerical tests demonstrate the consistency of the resulting implementation

spreading speeds and traveling waves for periodic evolution systems abstract the theory of spreading speeds and traveling waves for monotone autonomous semiflows is extended to periodic semiflows in the monostable case then these abstract results are applied to a periodic system modeling man environment man epidemics a periodic time delayed and diffusive equation and a periodic reaction diffusion equation on a cylinder

global existence and decay rate of the boussinesq burgers system with large initial data abstract in this paper we study the global existence and the long time asymptotic behavior of classical solutions to the cauchy problem for the boussinesq burgers system with large initial data more precisely we first show that the classical solutions exist globally in time with large initial data by using the l p p 2 estimates other than the conventional l 2 estimate then we prove that the global classical solutions converge to constant equilibrium states with an algebraic decay rate as time approaches infinity

global attractivity in monotone and subhomogeneous almost periodic systems abstract a global attractivity theorem is first proved for a class of skew product semiflows then this result is applied to monotone and subhomogeneous almost periodic reaction diffusion equations ordinary differential systems and delay differential equations for their global dynamics

global existence and blow up of solutions for cauchy problem of generalized boussinesq equation abstract we study the cauchy problem of generalized boussinesq equation u t t u x x u x x f u x x 0 where f u u p or u p 1 u p 1 by introducing a family of potential wells we obtain invariant sets vacuum isolating and threshold result of global existence and nonexistence of solution

a robust model of pseudoelasticity in shape memory alloys summary a model of pseudoelasticity in shape memory alloys is developed within the incremental energy minimization framework three constitutive functions are involved the helmholtz free energy and rate independent dissipation that enter incrementally the minimized energy function and the constraint function that defines the limit transformation strains the proposed implementation is based on a unified augmented lagrangian treatment of both the constitutive constraints and nonsmooth dissipation function a methodology for easy reformulation of the model from the small strain to finite deformation regime is presented finite element computations demonstrate robustness of the finite strain version of the model and illustrate the effects of tension compression asymmetry and transversal isotropy of the surface of limit transformation strains copyright 2012 john wiley sons ltd

strongly order preserving semiflows generated by functional differential equations the aim of this paper is to apply some recently developed improvements in the theory of monotone dynamical systems due to the authors 12 13 j to certain systems of functional differential equations fde s which do not enjoy the quasimonotone property considered by one of us in 9 the present work extends our previous results in this direction for scalar equations in 111 to systems in the fundamental paper s m w hirsch establishes that most orbits of a strongly monotone scmiflow on a strongly ordered space x tend to the set e of equilibria employing ideas of hirsch and of h matano 7 the authors have extended the theory to obtain some improvements in the results of hirsch and matano under matano s weaker assumption that the semiflow is strongly order preserving recently in 13 we gave sufficient conditions for most orbits of a strongly order preserving semiflow to converge to an equilibrium these conditions require additional smoothness of the semiflow and a certain strong monotonicity condition for the linearized flow determined by the variational equation about each equilibrium p policik s has also given sufficient conditions for most orbits to converge for semilinear parabolic evolution equations possessing certain strong monotonicity properties in this paper wc apply the convergence results developed in 131 to nonquasimonotone fde s in this introduction wc briefly review the application of monotone dynamical systems theory to fde s enjoying the quasimonotone property this research appeared in 9 133 then we state one of the main results of this paper which applies when the quasimonotone property fails but when another property m holds some simple examples are given which

a climate based malaria transmission model with structured vector population in this paper we present a malaria transmission model with periodic birth rate and age structure for the vector population we first introduce the basic reproduction ratio for this model and then show that there exists at least one positive periodic state and that the disease persists when mathcal r 0 1 it is also shown that the disease will die out if mathcal r 0 1 provided that the invasion intensity is not strong we further use these analytic results to study the malaria transmission cases in kwazulu natal province south africa some sensitivity analysis of mathcal r 0 is performed and in particular the potential impact of climate change on seasonal transmission and populations at risk of the disease is analyzed

on general isotropic tensor functions of one tensor this paper discusses general isotropic real symmetric tensor valued functions of one real symmetric tensor by exploiting the eigenprojection based spectral representation of such functions eigenprojection based closed formulae for the function derivatives are derived the derived formulae provide an alternative to the eigenvector based derivative expressions proposed by chadwick and ogden arch rat mech anal 1971 44 54 68 for the same class of functions and are an extension of the eigenprojection based derivative expressions obtained by carlson and hoger quart appl math 1986 44 3 409 423 for a subset of the present class of functions the material presented here is restricted to two and three dimensional spaces which are of particular relevance to continuum mechanics for completeness algorithms for closed form computation of the isotropic tensor functions as well as their derivatives based on the eigenprojection representation are also presented these should be of interest to computational mechanics researchers dealing with functions of the present type copyright 2004 john wiley sons ltd

global periodic solutions of a generalized n species gilpin ayala competition model abstract in this paper we investigate a generalized n species gilpin ayala competition system with several deviating arguments in periodic environment which is more general and more realistic than the classical lotka volterra competition systems by using the method of coincidence degree a set of easily verifiable sufficient conditions are derived for the existence of at least one strictly positive componentwise periodic solution some new results are obtained as applications we also apply our main results to some special cases of the system we consider here including the classical n species lotka volterra competition systems and n species gilpin ayala competition model which have been studied extensively in the literature some known results are improved and generalized the examples show that our criteria are new general and easily verifiable

numerical simulation of martensitic phase transitions in shape memory alloys using an improved integration algorithm the numerical simulation of structures made of shape memory materials is of increasing interest in different fields among others the computation of pipe connectors or medical devices like endoscopic instruments and stents is a challenge in such practical applications the pseudoelastic effect as well as the one way and two way shape memory effects are utilized these material properties are caused by martensitic phase transitions between austenite and martensite in the present contribution a recently proposed constitutive theory is numerically treated in the context of the finite element method this constitutive theory is formulated in the framework of continuum thermomechanics for geometrically linear problems and is able to represent the occurring martensitic phase transitions in shape memory alloys for the numerical integration of the evolution equations the backward euler method is applied in spite of the complexity of the constitutive theory it is shown that an improved integration procedure can be formulated which merely involves the solution of three non linear equations for three scalar valued unknown variables numerical examples show the capability of the proposed model and the improved integration algorithm copyright 2006 john wiley sons ltd

a 3d sma constitutive model in the framework of finite strain the aim of the present paper is to propose a phenomenological thermodynamically consistent 3d model for shape memory alloys sma in the finite strain range in particular a model able to predict the main features of sma materials such as the superelastic and the shape memory effects is proposed the model is based on the assumption of the local multiplicative split of the deformation gradient into an elastic and a phase transformation part the governing state and evolutive equations are written in the undeformed configuration the material parameters of the model are characterized by a clear physical meaning so that they can be determined by simple experimental tests the finite deformation sma model is also reformulated in the framework of small strain linearizing the strain and stress measures in order to obtain a consistent constitutive model preserving the nonlinear material response a robust algorithm is adopted in order to integrate the nonlinear evolutive equations 2d and 3d finite elements are implemented in a numerical code considering finite and small deformations some numerical applications are carried out showing the performances of the proposed model and the developed numerical procedure to describe the superelastic and the shape memory effects of sma devices comparisons of different results obtained by the small and finite strain formulations are reported copyright 2009 john wiley sons ltd

dynamics in a periodic competitive model with stage structure in this paper we consider a time delayed periodic system which describes the competition among mature populations by appealing to theories of monotone dynamical systems periodic semiflows and uniform persistence we analyze the evolutionary behavior of the system and establish sufficient conditions for competitive coexistence and exclusion

design of simple low order finite elements for large strain analysis of nearly incompressible solids a simple four node quadrilateral and an eight node hexahedron for large strain analysis of nearly incompressible solids are proposed based on the concept of deviatoric volumetric split and the replacement of the compatible deformation gradient with an assumed modified counterpart the formulation developed is applicable to arbitrary material models the closed form of the corresponding exact tangent stiffnesses which have a particularly simple structure is derived it ensures asymptotically quadratic rates of convergence of the newton raphson scheme employed in the solution of the implicit finite element equilibrium equations from a practical point of view the incorporation of the proposed elements into existing codes is straightforward it requires only small changes in the routines of the standard displacement based 4 node quadrilateral and 8 node brick a comprehensive set of numerical examples involving hyperelasticity as well as multiplicative elasto plasticity is provided it illustrates the performance of the proposed elements over a wide range of applications including strain localisation problems metal forming simulation and adaptive analysis

asymptotic stability of traveling waves of a chemotaxis model with singular sensitivity abstract this paper establishes the nonlinear stability of traveling wave solutions to a chemotaxis model with singular or logarithmic sensitivity and its transformed parabolic hyperbolic system depending on the parameter signs we discuss the linear instability of traveling wave solutions using the spectral analysis and nonlinear asymptotic stability of traveling wave solutions with zero end state by the weighted energy estimates where the latter result solves the open question left in a previous work li and wang 2009 7

a variational formulation of rate independent phase transformations using an extremum principle we propose a rate independent mesoscopic model for the hysteretic evolution of phase transformations in shape memory alloys the model uses the deformation and phase indicator function as basic unknowns and the potentials for the elastic energy and for the dissipation as constitutive laws using the associated functionals admissible processes are defined to be the ones which are stable at all times and which satisfy the energy inequality

generalized plasticity and shape memory alloys the theory of the generalized plasticity model is reviewed a special form for multiaxial behavior based on the drucker prager flow potential is proposed the model is applied to a simplified representation of the behavior of shape memory alloys with numerical examples

error estimates for space time discretizations of a rate independent variational inequality this paper deals with error estimates for space time discretizations in the context of evolutionary variational inequalities of rate independent type after introducing a general abstract evolution problem we address a fully discrete approximation and provide a priori error estimates the application of the abstract theory to a semilinear case is detailed in particular we provide explicit space time convergence rates for classical strain gradient plasticity and the isothermal souza auricchio model for shape memory alloys

a hyperelastic based large strain elasto plastic constitutive formulation with combined isotropic kinematic hardening using the logarithmic stress and strain measures summary this paper addresses the formulation of a set of constitutive equations for finite deformation metal plasticity the combined isotropic kinematic hardening model of the infinitesimal theory of plasticity is extended to the large strain range on the basis of three main assumptions i the formulation is hyperelastic based ii the stress strain law preserves the elastic constants of the infinitesimal theory but is written in terms of the hencky strain tensor and its elastic work conjugate stress tensor and iii the multiplicative decomposition of the deformation gradient is adopted since no stress rates are present the formulation is of course numerically objective in the time integration it is shown that the model gives adequate physical behaviour and comparison is made with an equivalent constitutive model based on the additive decomposition of the strain tensor

asymptotic behaviors of competitive lotka volterra system with stage structure in this paper a two species competitive model with stage structure is presented and studied results on the global extinction and permanence are given which generalize the well known three theorems for the two species competitive system and moreover they confirm the negative effect of stage structure on the permanence of populations as well as estimate the degree of such effect conclusions in this paper suggest that for a competitive community stage structure is also one of the important reasons that cause permanence and extinction

on the boussinesq burgers equations driven by dynamic boundary conditions abstract we study the qualitative behavior of the boussinesq burgers equations on a finite interval subject to the dirichlet type dynamic boundary conditions assuming h 1 h 2 initial data which are compatible with boundary conditions and utilizing energy methods we show that under appropriate conditions on the dynamic boundary data there exist unique global in time solutions to the initial boundary value problem and the solutions converge to the boundary data as time goes to infinity regardless of the magnitude of the initial data

on the numerical study of nonlinear initial boundary value problems or initial value problems this paper deals with a numerical study for two problems first of which is a system of nonlinear initial boundary value problems for a certain version of boussinesque system of equations by using two quadratic forms the second one is to investigate and construct the numerical solution for a system of nonlinear initial value problems which is generated by a system of hyper elliptic type in some hilbert space

closed form matrix exponential and its application in finite strain plasticity summary a new method to compute numerically efficient closed form representation of matrix exponential and its derivative is developed for 3 3 matrices with real eigenvalues the matrix exponential is obtained by automatic differentiation of an appropriate scalar generating function in a general case and highly accurate asymptotic expansions are derived for special cases in which the general formulation exhibits ill conditioning for instance for almost equal eigenvalues accuracy and numerical efficiency of the closed form matrix exponential as compared with the truncated series approximation are studied the application of the closed form matrix exponential in the finite strain elastoplasticity is also presented to this end several time discrete evolution laws employing the exponential map are discussed for j2 plasticity with isotropic hardening and nonlinear kinematic hardening of armstrong frederick type the discussion is restricted to the case of elastic isotropy and implicit time integration schemes in this part the focus is on a general automatic differentiation based formulation of finite strain plasticity models numerical efficiency of the corresponding incremental schemes is studied in the context of the fem copyright 2014 john wiley sons ltd

phase transitions in shape memory alloys a non isothermal ginzburg landau model abstract we propose a model to describe non isothermal transitions from the austenite to the martensite phase occurring in shape memory materials the phenomenon is set in the context of the ginzburg landau theory of phase transitions postulating a free energy depending on the temperature the stress and the order parameter in the one dimensional case when only two martensitic variants are involved and stress and deformation have a fixed direction our choice of free energy allows us to deduce a phase diagram describing the main features of a typical sma the ginzburg landau equation ruling the evolution of the order parameter is coupled with the equations of thermoelasticity by assuming a constitutive equation relating stress strain and order parameter the consistency of the model with the second law of thermodynamics in the form of the clausius duhem inequality is proved finally a possible generalization to a three dimensional model is proposed by introducing a tensor valued order parameter

global existence and asymptotic behavior of the boussinesq burgers system abstract this paper is concerned with the boussinesq burgers system which models the propagation of bores by combing the dissipation dispersion and nonlinearity we establish the global existence and asymptotical behavior of classical solutions of the initial value boundary problem of the boussinesq burgers system with the help of a lyapunov functional and the technique of moser iteration particularly we show that the solution converges to the unique constant stationary solution exponentially as time tends to infinity

long time existence for the boussinesq full dispersion systems abstract we establish the long time existence of solutions for the boussinesq full dispersion systems modeling the propagation of internal waves in a two layer system for the two dimensional hamiltonian case b d 0 a 0 c 0 we study the global existence of small solutions of the corresponding system

existence of solutions for a mathematical model related to solid solid phase transitions in shape memory alloys we consider a strongly nonlinear pde system describing solid solid phase transitions in shape memory alloys the system accounts for the evolution of an order parameter related to different symmetries of the crystal lattice in the phase configurations of the stress and the displacement u and of the absolute temperature the resulting equations present several technical difficulties to be tackled in particular we emphasize the presence of nonlinear coupling terms higher order dissipative contributions possibly multivalued operators as for the evolution of temperature a highly nonlinear parabolic equation has to be solved for a right hand side that is controlled only in l 1 we prove the existence of a solution for a regularized version by use of a time discretization technique then we perform suitable a priori estimates which allow us pass to the limit and find a weak global in time solution to the system

basic reproduction ratios for almost periodic compartmental models with time delay abstract the theory of basic reproduction ratio r 0 is established for a large class of almost periodic and time delayed compartmental population models we first present some dynamical properties for linear almost periodic functional differential systems by using the product space and evolution semigroup approach we then prove that r 0 1 has the same sign as the exponential growth bound of an associated linear system as an application we apply the developed theory to an almost periodic seir model with an incubation period and obtain a threshold result on its global dynamics in terms of r 0 finally we present some numerical simulations numerical simulations indicate that prolonging the length of incubation period is beneficial for the control of the disease in addition a simple model shows that the basic reproduction ratio may be underestimated or overestimated if an almost periodic coefficient is approximated by a periodic one

on discretized plasticity problems with bifurcations abstract a spatially discretized non linear rate problem for a time independent plastic solid is examined with particular reference to bifurcation constitutive non linearity in a general form encompassing the yield surface vertex effect is considered under the restriction that the tangent stiffness matrix for the whole system is symmetric theorems concerning existence uniqueness and stability of solutions are presented as an outcome of the theoretical analysis a computational method is proposed for crossing bifurcation points with automatic rejection of an unstable postbifurcation branch an illustrative example of plane strain tension is calculated by using the finite element method

exponential map algorithm for stress updates in anisotropic multiplicative elastoplasticity for single crystals this paper presents a new stress update algorithm for large strain rate independent single crystal plasticity the theoretical frame is the well established continuum slip theory based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts a distinct feature of the present formulation is the introduction and computational exploitation of a particularly simple hyperelastic stress response function based on a further multiplicative decomposition of the elastic deformation gradient into spherical and unimodular parts resulting in a very convenient representation of the schmid resolved shear stresses on the crystallographic slip systems in terms of a simple inner product of eulerian vectors the key contribution of this paper is an algorithmic formulation of the exponential map exp sl 3 sl 3 for updating the special linear group sl 3 of unimodular plastic deformation maps this update preserves exactly the plastic incompressibility condition of the anisotropic plasticity model under consideration the resulting fully implicit stress update algorithm treats the possibly redundant constraints of single crystal plasticity by means of an active set search it exploits intrinsically the simple representation of the schmid stresses by formulating the return algorithm and the associated consistent elastoplastic moduli in terms of eulerian vectors updates the performance of the proposed algorithm is demonstrated by means of a representative numerical example

an incremental variational approach to coupled thermo mechanical problems in anelastic solids application to shape memory alloys abstract we study the coupled thermo mechanical problem that is obtained by combining generalized standard materials with fourier s law for heat conduction the analysis is conducted in the framework of non smooth mechanics in order to account for possible constraints on the state variables this allows models of damage and phase transformation to be included in the analysis in view of performing numerical simulations an incremental thermo mechanical problem and corresponding variational principles are introduced conditions for existence of solutions to the incremental problem are discussed and compared with the isothermal case the numerical implementation of the proposed approach is studied in detail in particular it is shown that the incremental thermo mechanical problem can be recast as a concave maximization problem and ultimately amounts to solve a sequence of linear thermal problems and purely mechanical i e at a prescribed temperature field problems therefore using the proposed approach thermo mechanical coupling can be implemented with low additional complexity compared to the isothermal case while still relying on a sound mathematical framework as an application thermo mechanical coupling in shape memory alloys is studied the influence of the loading strain rate on the phase transformation and on the overall stress strain response is investigated as well as the influence of the thermal boundary conditions the numerical results obtained by the proposed approach are compared with numerical and experimental results from the literature

superelastic and shape memory effects in laminated shape memory alloy beams a simple shape memory alloy sma model to simulate the superelastic behavior as well as the shape memory effect is proposed it considers only the transformations from austenite to single variant martensite and from single variant martensite to austenite taking into account the ine uence of the temperature in the constitutive relationship the proposed sma constitutive model is employed in a novel layerwise beam theory to develop new sma beam e nite element models with suitable interpolation of the e eld variables involved the e nite element models developed herein account for the time evolution sma constitutive equations in particular the developed e nite elements treat the sma material as reinforcement of elastic beams several applications are presented to assess the validity of the constitutive model and the proposed numerical procedure

finite element analysis of the behavior of shape memory alloys and their applications abstract a nonlinear finite element procedure is developed which incorporates a thermodynamically derived constitutive law for shape memory alloy material behavior the constitutive equations include the necessary internal variables to account for the material transformations and are utilized in a one dimensional finite element procedure that captures the unique shape memory alloy responses of pseudoelasticity and of the shape memory effect at all temperatures stress levels and loading conditions detailed material properties for the alloy used are necessary for the analysis the solution of the geometrically and physically nonlinear problem is achieved by application of a newton s method in which a sequence of linear problems is numerically solved due to consistent linearization a quadratic rate of convergence is obtained several test cases are presented to illustrate the potential of the finite element procedure cases simulating the stress strain behavior of a bar of shape memory alloy under simple uniaxial loading as well as restrained recovery responses at different temperatures compare well with experimental and analytical results two further generalized applications are examined the use of a shape memory alloy ring as a pipe connector and eigenfrequency tuning of a composite beam with embedded shape memory wires the results of these analyses correlate well with analytical results and the methodology for use of the finite element procedure in general cases is demonstrated the finite element procedure is thus shown to be a powerful tool for studying various applications of shape memory alloys

numerical algorithms for cyclic phase transformation hysteresis in a shape memory plate subject to axisymmetric plane stress we present numerical algorithms for calculating stress fields in an annulus composed of a shape memory material under conditions of quasi static edge loading at constant temperature the algorithms track the material microstructure in terms of the volume fraction of austenite a and martensite m the latter of which provides a transformation strain the dependence on load path imparts significant hysteresis in the stress induced transformation between a and m a previous study that was restricted to proportional loading in the direction of forward transformation j appl mech 2005 72 44 53 is here generalized to consider arbitrary loadings the shooting algorithm that was robust for the previously considered proportional loadings is found to be subject to numerical instability for the most general transformation possibilities considered here this motivates the development of an alternative iterated mapping algorithm that is found to generate a robust semi analytical finite difference procedure the algorithm efficiently determines the operative transformation type as is illustrated in cases where forward and reverse loading are occurring simultaneously at different plate locations at those locations where phase transformation is inactive the algorithm continues to account for martensite reorientation that alters the local transformation strain copyright 2006 john wiley sons ltd

gradient structures for the thermomechanics of shape memory materials abstract we investigate the variational structure of a phenomenological model for the coupled thermomechanical behavior of shape memory polycrystalline materials the nonisothermal evolution of the medium is reformulated as a generalized gradient flow of the entropy with respect to an entropy production potential based on this reformulation a semi implicit time discretization of the fully coupled thermomechanical problem is presented and proved to be unconditionally stable and convergent the flexibility and robustness of the numerical method is assessed via both uniaxial and multiaxial computational tests

analysis of a model representing stage structured population growth with state dependent time delay a stage structured model of population growth is proposed where the time to ma turity is itself state dependent it is shown that under appropriate assumptions all solutions are positive and bounded criteria for the existence of positive equilibria and further conditions for the uniqueness of the equilibria are given the stability of the equilibria are also discussed in addition an attracting region is determined for solutions such that this region collapses to the unique positive equilibrium in the state independent case

shape memory behaviour modelling within continuum thermomechanics abstract a phenomenological material model to represent the multiaxial material behaviour of shape memory alloys is proposed the material model is able to represent the main effects of shape memory alloys the one way shape memory effect the two way shape memory effect due to external loads the pseudoelastic and pseudoplastic behaviour as well as the transition range between pseudoelasticity and pseudoplasticity the material model is based on a free energy function and evolution equations for internal variables by means of the free energy function the energy storage during thermomechanical processes is described evolution equations for internal variables e g the inelastic strain tensor or the fraction of martensite are formulated to represent the dissipative material behaviour in order to distinguish between different deformation mechanisms case distinctions are introduced into the evolution equations thermomechanical consistency is ensured in the sense that the constitutive model satisfies the clausius duhem inequality finally some numerical solutions of the constitutive equations for isothermal and non isothermal strain and stress processes demonstrate that the various phenomena of the material behaviour are well represented this applies for uniaxial processes and for non proportional loadings as well

global dynamics of a hyperbolic parabolic model arising from chemotaxis we prove global existence and qualitative behavior of classical solutions for a hyperbolic parabolic system describing chemotaxis on bounded domains it is shown that classical solutions to the initial boundary value problem of the one dimensional model exist globally in time for large initial data and the solutions converge to constant equilibrium states exponentially in time which rigorously demonstrates the collapsing of cell populations in chemotaxis moreover similar results are established for the multidimensional model when the initial data are small

non blowup of a generalized boussinesq burgers system with nonlinear dispersion relation and large data abstract we study the qualitative behavior of classical solutions to the cauchy problem of a generalized boussinesq burgers system in one space dimension assuming initial data belong to h 2 r and utilizing energy methods we show that there exist unique global in time classical solutions to the cauchy problem of the model and the solutions converge to constant equilibrium states as time goes to infinity regardless of the magnitude of the initial data moreover it is shown that the viscous and inviscid models are consistent in the process of vanishing viscosity limit

non convex potentials and microstructures in finite strain plasticity a mathematical model for a finite strain elastoplastic evolution problem is proposed in which one time step of an implicit time discretization leads to generally non convex minimization problems the elimination of all internal variables enables a mathematical and numerical analysis of a reduced problem within the general framework of calculus of variations and nonlinear partial differential equations the results for a single slip system and von mises plasticity illustrate that finite strain elastoplasticity generates reduced problems with non quasiconvex energy densities and so allows for non attainment of energy minimizers and microstructures

global stability of strong rarefaction waves for the generalized kdv burgers equation this paper is concerned with the global stability of strong rarefaction waves for the generalized kdv burgers equation in contrast to former results obtained by z a wang and c j zhu stability of the rarefaction wave for the generalized kdv burgers equation acta math sci 22b 3 2002 319 328 ours do not require the strength of the rarefaction waves to be small and the initial disturbance can also be chosen large c 2006 elsevier ltd all rights reserved

analysis of sma composite laminates using a multiscale modelling technique the present work deals with the analysis of smart laminates obtained as stacking sequence of fibre reinforced composite laminae and composite shape memory alloy sma layers the behaviour of composite sma csma laminate is studied developing a full micro macro approach in fact a non linear 4 node mixed interpolation of tensorial components mitc4 laminate finite element based on the first order shear deformation theory is developed the sma layer constitutive relationship is determined solving a non linear homogenization problem at each non linear iteration of each time step for each integration gauss point some numerical applications are developed in order to investigate the influence of the csma on the buckling behaviour of plates and on the transversal displacement control of plates subjected to different loading conditions copyright 2006 john wiley sons ltd

theory and finite element computation of cyclic martensitic phase transformation at finite strain a generalized variational formulation including quasi convexification of energy wells for arbitrarily many martensitic variants in case of mono crystals for linearized strains was developed by govindjee and miehe comp meth appl mech eng 2001 191 3 5 215 238 and computationally extended by stein and zwickert comput mech 2006 in press this work is generalized here for finite strain kinematics with monotonous hyperelastic stress strain functions in order to account for large transformation strains that can reach up to 15 a major theoretical and numerical difficulty herein is the convexification of the finite deformation phase transformation pt problems for multiple phase variants n 2 a lower bound of the mixing energy is provided by the reuss bound in case of linear kinematics and an arbitrary number of variants shown by govindjee et al j mech phys solids 2003 51 4 i xxvi in case of finite strains a generalized representation of free energy of mixing is introduced for a quasi reuss bound which in general holds for n 2 numerical validation of the used micro macro material model is presented by comparing verified numerical results with the experimental data for cu82al14ni4 monocrystals for quasiplastic pt provided by xiangyang et al j mech phys solids 2000 48 2163 2182 the zigzag type experimental stress strain curve within pt at loading called yield tooth is approximated within the finite element analysis by a smoothly decreasing and then increasing axial stress which could not be achieved with linearized kinematics yielding a constant axial stress during pt copyright 2007 john wiley sons ltd

threshold dynamics of a time periodic reaction diffusion epidemic model with latent period abstract in this paper we first propose a time periodic reaction diffusion epidemic model which incorporates simple demographic structure and the latent period of infectious disease then we introduce the basic reproduction number r 0 for this model and prove that the sign of r 0 1 determines the local stability of the disease free periodic solution by using the comparison arguments and persistence theory we further show that the disease free periodic solution is globally attractive if r 0 1 while there is an endemic periodic solution and the disease is uniformly persistent if r 0 1

a periodic epidemic model with age structure in a patchy environment in this paper a periodic epidemic model with age structure in a patchy environment is introduced we investigate its global dynamics in term of the basic reproduction number mathcal r 0 and show that there exists at least one positive periodic state and the disease persists when mathcal r 0 1 while the disease will die out if mathcal r 0 1 some numerical examples are given to confirm our analytic results and to show that the age and spatial heterogeneities are important factors for the global dynamics

tangent operators and design sensitivity formulations for transient non linear coupled problems with applications to elastoplasticity tangent operators and design sensitivities are derived for transient non linear coupled problems the solution process and the formation of tangent operators are presented in a systematic manner and sensitivities for a generalized response functional are formulated via both the direct differentiation and adjoint methods the derived formulations are suitable for finite element implementations analyses of systems with materials that exhibit history dependent response may be obtained directly by applying the analyses of transient non linear coupled systems rate independent elastoplasticity is investigated as a case study and a problem with an analytical solution is analysed for demonstration purposes

asymptotic dynamics for the small data weakly dispersive one dimensional hamiltonian abcd system fondecyt postdoctorado 2017 proyecto 3170067 project france chile ecos sud c18e06 chilean research grants fondecyt 1150202 comision nacional de investigacion cientifica y tecnologica conicyt conicyt fondecyt 1191412 cmm conicyt pia afb170001

on the robustness and efficiency of integration algorithms for a 3d finite strain phenomenological sma constitutive model summary most devices based on shape memory alloys experience large rotations and moderate or finite strains this motivates the development of finite strain constitutive models together with the appropriate computational counterparts to this end in the present paper a three dimensional finite strain phenomenological constitutive model is investigated and a robust and efficient integration algorithm is proposed properly defining the variables extensively used regularization schemes are avoided and a nucleation completion criterion is defined moreover introducing a logarithmic mapping a new form of time discrete equations is proposed the solution algorithm as well as a suitable initial guess for the resultant nonlinear equations are also deeply discussed extensive numerical tests are performed to show robustness as well as efficiency of the proposed integration algorithm implementation of the integration algorithm within a user defined subroutine umat in the commercial nonlinear finite element software abaqus standard makes also possible the solution of a variety of boundary value problems the obtained results show the efficiency and robustness of the proposed approach and confirm the improved efficiency in terms of solution cpu time when a nucleation completion criterion is used instead of regularization schemes as well as when a logarithmic mapping is used for the time discrete evolution equation instead of an exponential mapping copyright 2010 john wiley sons ltd

permanence and existence of a positive periodic solution to a periodic stage structured system with infinite delay in this paper we consider a periodic non autonomous competitive stage structured system with infinite delay for the interaction between n species the adult members of which are in competition for each of the n species the model incorporates a time delay which represents the time from birth to maturity of that species infinite delay is introduced which denotes the influential effect of the entire past history of the system on the current competition interactions we first prove by using the comparison principle that if the growth rates are sufficiently large then the solutions are uniformly permanent then by using horn s fixed point theorem we show that the system with finite delay has a positive periodic solution as a consequence of this result we prove that even the system with infinite delay admits a positive periodic solution

a temperature dependent beam for shape memory alloys constitutive modelling finite element implementation and numerical simulations this paper presents a thermomechanical one dimensional constitutive model based on the use of strain and temperature as control variables and able to reproduce the basic responses of shape memory materials such as superelasticity the shape memory behavior different response in tension and compression single variant martensite reorientation process the model time integration is performed and a robust algorithm for the solution of the time discrete model is addressed together with the algorithmically consistent tangent the model is also implemented in a small deformation beam finite element which is used to simulate the following applications exploiting the superelastic and or the shape memory effect tensile pure bending and three point bending tests orthodontic wires two way linear and angular mechanisms the numerical investigations show that the proposed procedure is an effective computational tool for the simulation of a broad range of applications based on shape memory materials

extinction and permanence in nonautonomous competitive system with stage structure in this paper the n species nonautonomous stage structured competitive system is constructed and considered sufficient conditions for its extinction and permanence are obtained results here generalize and unify some previous ones moreover it is concluded that stage structure in this system is one of the important factors that effect the extinction and permanence of species

an incremental energy minimization state update algorithm for 3d phenomenological internal variable sma constitutive models based on isotropic flow potentials summary an incremental energy minimization approach for the solution of the constitutive equations of 3d phenomenological models for shape memory alloys sma is presented a robust algorithm for the solution of the resulting nonsmooth constrained minimization problem is devised without introducing any regularization in the dissipation or chemical terms the proposed algorithm is based on a thorough detection of the singularities relevant to the incremental energy formulation in conjunction with a newton raphson method equipped with a wolfe line search dealing with regular solutions the saturation constraint on the transformation strain is treated by means of an active set strategy thus avoiding any need for a two stage return mapping algorithm a parametrization of the saturation constraint manifold is introduced thus reducing the problem dimensionality with improved computational performance finally an efficient algorithm for the computation of the dissipation function in terms of haigh westergaard invariants is presented allowing for a quite general choice of deviatoric transformation functions numerical results confirm the robustness and consistency of the proposed state update algorithm copyright 2015 john wiley sons ltd

on the modelling of non linear kinematic hardening at finite strains with application to springback comparison of time integration algorithms the paper discusses the derivation and the numerical implementation of a finite strain material model for non linear kinematic and isotropic hardening the kinematic hardening component represents a continuum extension of the classical rheological model of armstrong frederick kinematic hardening in addition a comparison between several numerical algorithms for the integration of the evolution equations is conducted in particular a new form of the exponential map that preserves the plastic volume and the symmetry of the internal variables as well as two modifications of the backward euler scheme are discussed finally the applicability of the model for springback prediction is demonstrated by performing simulations of the draw bending process and a comparison with experiments the results show an excellent agreement between simulation and experiment copyright 2007 john wiley sons ltd

long time existence results for bore type initial data for bbm boussinesq systems abstract in this paper we deal with the long time existence for the cauchy problem associated to bbm type boussinesq systems of equations which are asymptotic models for long wave small amplitude gravity surface water waves as opposed to previous papers devoted to the long time existence issue we consider initial data with nontrivial behavior at infinity which may be used to model bore propagation

a multi variant martensitic phase transformation model formulation and numerical implementation the development of models for shape memory alloys and other materials that undergo martensitic phase transformations has been moving towards a common generalized thermodynamic framework several promising models utilizing single martensitic variants and some with multiple variants have appeared recently in this work we develop a model in a general multi variant framework for single crystals that is based upon lattice correspondence variants and the use of dissipation arguments for the generation of specialized evolution equations the evolution equations that appear are of a unique nature in that not only are the thermodynamic forces restricted in range but so are their kinematic conjugates this unusual situation complicates the discrete time integration of the evolution equations we show that the trial elastic state method that is popular in metal plasticity is inadequate in the present situation and needs to be replaced by a non linear programming problem with a simple geometric interpretation the developed integration methodology is robust and leads to symmetric tangent moduli example computations show the behavior of the model in the pseudoelastic range of particular interest is the fact that the model can predict the generation of habit plane like variants solely from the lattice correspondence variants this is demonstrated through a comparison to the experimental work of shield j mech phys solids 43 1995 869

analysis of an age structured model for tick populations subject to seasonal effects abstract we investigate an age structured hyperbolic equation model by allowing the birth and death functions to be density dependent and periodic in time with the consideration of seasonal effects by studying the integral form solution of this general hyperbolic equation obtained through the method of integration along characteristics we give a detailed proof of the uniqueness and existence of the solution in light of the contraction mapping theorem with additional biologically natural assumptions using the tick population growth as a motivating example we derive an age structured model with time dependent periodic maturation delays which is quite different from the existing population models with time independent maturation delays for this periodic differential system with seasonal delays the basic reproduction number r 0 is defined as the spectral radius of the next generation operator then we show the tick population tends to die out when r 0 1 while remains persistent if r 0 1 when there is no intra specific competition among immature individuals due to the sufficient availability of immature tick hosts the global stability of the positive periodic state for the whole model system of four delay differential equations can be obtained with the observation that a scalar subsystem for the adult stage size can be decoupled the challenge for the proof of such a global stability result can be overcome by introducing a new phase space based on which a periodic solution semiflow can be defined which is eventually strongly monotone and strictly subhomogeneous