nonlinear kolmogorov equations in infinite dimensional spaces the backward stochastic differential equations approach and applications to optimal control solutions of semilinear parabolic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations parabolic equations are intended in a mild sense that reveals to be suitable also towards applications to optimal control

equivalent spatial and material descriptions of finite deformation elastoplasticity in principal axes abstract a spatial description of the theory of rate independent finite deformation elastoplasticity in which the stress tensor is defined through the strain energy function is discussed the main assumption of isotropic elastic response and invariance requirements under superposed rigid body motion restrict the acceptable forms of the strain energy function to those given in terms of principal values of the strain measure of elastic distortion the formulation is developed on a manifold and the corresponding material description is obtained simply by pull back of the derived spatial form by appealing to the notion of covariance the method of principal axes is systematically exploited to derive the explicit expression for the stress tensor computation for an arbitrary form of the strain energy function and the explicit form of the evolution equation for an arbitrary form of the yield function a model problem of volume preserving plastic flow is discussed in the closure

control of the stochastic burgers model of turbulence we consider a control problem for a stochastic burgers equation this problem is motivated by a model from the control of turbulence see choi et al j fluid mech 253 1993 pp 509 543 we study a sequence of approximated hamilton jacobi equations by using dynamic programming

bellman equations associated to the optimal feedback control of stochastic navier stokes equations in this paper we study infinite dimensional second order hamilton jaco bi bellman equations associated to the feedback synthesis of stochastic navier stokes equations forced by space time white noise uniqueness and existence of viscosity solutions are proven for these infinite dimensional partial differential equations c 2004 wiley periodicals inc

frameworks for finite strain viscoelastic plasticity based on multiplicative decompositions part i continuum formulations abstract the present work deals with studies on viscoelastic plasticity at finite strains different forms can be proposed for the combination of plasticity and viscoelasticity mechanisms in the present work we propose two different formulations each of them is motivated by a distinct simple one dimensional rheological model these different rheological models suggest different kinematic assumptions at finite strains which in turn lead to different local governing equations issued from thermodynamically consistent frameworks however one of the common features characterizing the two formulations is the use of local multiplicative decompositions of the deformation gradient model examples issued from these formulations are proposed they are suitable for the simulation of filled rubbers polymers and polymeric foams computational aspects and numerical examples within the framework of the finite element method are addressed in detail in part ii of this work

global regular solutions of second order hamilton jacobi equations in hilbert spaces with locally lipschitz nonlinearities abstract this paper is devoted to the study of a second order hamilton jacobi equation in infinite dimensions with a locally lipschitz continuous hamiltonian h related with a stochastic optimal control problem driven by white noise in an earlier paper the author studied the case of globally lipschitz continuous hamiltonian h this paper is concerned with the case of locally lipschitz continuous h that include e g the quadratic case which appears very frequently in the applications existence uniqueness and c 2 regularity of a local solution follow by methods given previously the heart of the work is the proof of a priori estimates of the c 1 norm of the local solution this has been done by studying properties of nonlinear transition semigroups and by a careful application of them to our problem the results have been applied to a stochastic optimal control problem proving existence of feedback optimal controls

on the spatial formulation of anisotropic multiplicative elasto plasticity abstract this contribution aims at a thermodynamically consistent and modular formulation of anisotropic multiplicative elasto plasticity embedded in the well established framework of non standard dissipative materials we adopt as a key ingredient the introduction of additional symmetric arguments typically structural tensors into the relevant scalar valued isotropic tensor functions on this basis the fundamental covariance relation leads us to a formulation which allows itself to be set up directly in terms of spatial arguments and thus guarantees a convenient implementation within a finite element setting

viscosity solutions for hamilton jacobi equations with unbounded nonlinear term a simplified approach abstract in a previous paper the author defined a notion for hamilton jacobi equations with an unbounded nonlinear term ax du and for such solutions proved existence and uniqueness results here we define an equivalent notion of solution for such equations which in addition has the advantage of being simpler and more intuitive

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

optimal control of a stochastic delay heat equation with boundary noise and boundary control in this paper a controlled stochastic delay heat equation with neumann boundary noise and boundary control is considered the existence and uniqueness of the mild solution for the associated hamilton jacobi bellman equations are obtained by means of the backward stochastic differential equations which is applied to the optimal control problem

numerical aspects associated with the implementation of a finite strain elasto viscoelastic viscoplastic constitutive theory in principal stretches this paper treats the numerical implementation of a finite strain elasto viscoelastic viscoplastic constitutive model for semi crystalline polymers written in principal stretches a parallel configuration of the three model elements is used that enables the decoupled algorithmic treatment of each response within a stress update numerical scheme the numerical aspects associated with the use of principal stretch constitutive expressions in a tensor space numerical environment are initially developed for the general cases of any elastic or inelastic constitutive element included is the formulation of the closed form consistent tangential modulus tensor the principal space algorithmic treatments of the elastic viscoelastic and viscoplastic elements are then used as specific examples of particular importance is the development of a principal space closest point projection return mapping algorithm for viscoplasticity including isotropic strain hardening preliminary numerical examples are presented to illustrate the versatility of the model

infinite horizon backward stochastic differential equations and elliptic equations in hilbert spaces solutions of semilinear elliptic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations the backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition elliptic equations are intended in a mild sense suitable also for applications to optimal control we finally notice that due to the lack of smoothing properties the elliptic partial differential equation considered here could not be treated by analytic methods

finite deformation plasticity in principal axes from a manifold to the euclidean setting abstract this contribution presents a link between early developments in finite deformation plasticity where the notion of a covariant formulation is introduced and employed and more recent developments where rediscovery of a fundamental work of hill on the method of principal axes led to a very efficient implementation scheme more precisely we demonstrate how to develop a covariant theory of finite deformation plasticity in an invariant form by making use of the elastic principal stretches we also show how to implement principal axis formulation in the framework of manifold to carry out all the necessary manipulations by exploiting the lie derivative formalism and eventually to simplify the final result to the euclidean setting much of our work on numerical implementation reflects the fruitful cross fertilization of ideas with those from theoretical formulation in particular we show how the operator split method which is typically used to simplify the plastic flow computation can also be used to reduce the computational cost related to the special finite element interpolation schemes based on incompatible modes the latter proves to be an indispensable ingredient for accommodating the near incompressibility constraint arising in the finite deformation deviatoric plasticity an important advantage of the proposed formulation as opposed to alternative remedies e g b bar method is that the basic structure of the governing equations need not be modified

constitutive equations for fibrous connective tissues a general multiaxial theory for the constitutive relations in fibrous connective tissues is developed on the basis of microstructural and thermodynamic considerations it is compatible with existing general material theories in elastic tissues the theory considers the strain energy function to be the sum of strain energies of the tissue s components the stresses are derived from this strain energy function viscoelastic constitutive relations are obtained in an analogous manner few examples are developed in detail the results of the present strain energy based theory are identical with those of the author s previous structural models lanir 1979a b which are based on detailed equilibrium analysis it turns out however that the analytical work involved in solving boundary value problems is considerably shorter if the present theory is used the advantages of structural theories in avoiding ambiguity in material characterization and in offering an insight into the function structure and mechanics of tissue components are discussed

efficient implicit integration for finite strain viscoplasticity with a nested multiplicative split abstract an efficient and reliable stress computation algorithm is presented which is based on implicit integration of the local evolution equations of multiplicative finite strain plasticity viscoplasticity the algorithm is illustrated by an example involving a combined nonlinear isotropic kinematic hardening numerous backstress tensors are employed for a better description of the material behavior the considered material model exhibits the so called weak invariance under arbitrary isochoric changes of the reference configuration and the presented algorithm retains this useful property even more the weak invariance serves as a guide in constructing this algorithm the constraint of inelastic incompressibility is exactly preserved as well the proposed method is first order accurate concerning the accuracy of the stress computation the new algorithm is comparable to the euler backward method with a subsequent correction of incompressibility ebmsc and the classical exponential method em regarding the computational efficiency the new algorithm is superior to the ebmsc and em some accuracy tests are presented using parameters of the aluminum alloy 5754 o and the 42crmo4 steel fem solutions of two boundary value problems using msc marc are presented to show the correctness of the numerical implementation

on uniqueness and existence of viscosity solutions of fully nonlinear second order elliptic pde s we prove several comparison and existence theorems for viscosity solutions of fully nonlinear degenerate elliptic equations one of them extends some recent uniqueness results by jensen some establish the uniqueness of solutions for second order isaacs equations and hence include the uniqueness results for bellman equations by p l lions our comparison results apply even for discontinuous solutions and so perron s method readily yields the existence of continuous solutions

an implicit multi patch b spline interpolation for kirchhoff love space rod abstract the paper presents a novel formulation for the isogeometric analysis of assemblies of kirchhoff love space rod elements introducing a multi patch implicit g 1 formulation so that an automatic non singular stiffness operator is obtained without the need of adding continuity conditions the goal is achieved using a polar decomposition of the deformation of the first and last segments of the control polygon that allows to introduce directly the end rotations as degrees of freedom both parametric and geometric continuity can be obtained in this way we use bezier and b spline interpolations and we show that they are able to attain very good accuracy for developing a 3d exact curve element with geometric torsion pre twisted rod in the paper the performance of the multi patch elements is examined comparing the rates of convergence of the l 2 error norm for the multi patch and single patch formulations it is shown that the rate of convergence remains the same although in certain cases the accuracy is lower for the multi patch solutions

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

material symmetry group of the non linear polar elastic continuum we extend the material symmetry group of the non linear polar elastic continuum by taking into account microstructure curvature tensors as well as different transformation properties of polar and axial tensors the group consists of an ordered triple of tensors which makes the strain energy density of polar elastic continuum invariant under change of reference placement an analog of the noll rule is established four simple specific cases of the group with corresponding reduced forms of the strain energy density are discussed definitions of polar elastic fluids solids liquid crystals and subfluids are given in terms of members of the symmetry group within polar elastic solids we discuss in more detail isotropic hemitropic cubic symmetric transversely isotropic and orthotropic materials and give explicitly corresponding reduced representations of the strain energy density for physically linear polar elastic solids when the density becomes a quadratic function of strain measures reduced representations of the density are established for monoclinic orthotropic cubic symmetric hemitropic and isotropic materials in terms of appropriate joint scalar invariants of stretch wryness and undeformed structure curvature tensors

aspects of the formulation and finite element implementation of large strain isotropic elasticity the paper presents a formulation of isotropic large strain elasticity and addresses some computational aspects of its finite element implementation on the theoretical side an eulerian setting of isotropic elasticity is discussed exclusively in terms of the finger tensor as a strain measure noval aspects are a direct representation of the eulerian elastic moduli in terms of the finger tensor and their rigorous decomposition into decoupled volumetric and isochoric contributions based on a multiplicative split of the finger tensor into spherical and unimodular parts the isochoric stress response is formulated in terms of the eigenvalues of the unimodular part of the finger tensor a constitutive algorithm for the computation of the stresses and tangent moduli for plane problems is developed and applied to a model problem of rubber elasticity on the computational side the implementation of the constitutive model in three possible finite element formulations is discussed after pointing out algorithmic techniques for the treatment of incompressible elasticity several numerical simulations are presented which show the performance of the proposed constitutive algorithm and the convergence behaviour of the different finite element fomulations for compressible and incompressible elasticity

on the formulation and numerical solution of problems in anisotropic finite plasticity abstract this article discusses an extension of the green naghdi finite plasticity theory to explicitly include anisotropic effects in the stress response yield condition flow rule and hardening rule constitutive models are developed within the context of the extended theory and used in formulating implicit integration algorithms which inherit the characteristics of the classical return mapping scheme of isotropic plasticity representative numerical simulations demonstrate the applicability and predictive capacity of the proposed model in the presence of large plastic deformations

b spline interpolation of kirchhoff love space rods the paper deals with the isogeometric analysis via b splines of space rods under kirchhoff love hypotheses the approach was used by gontier and vollmer 12 for developing a plane curve element within the framework of the timoshenko rod model but they adopted only one patch to represent entirely the geometry of the rod furthermore the authors developed their theory only for plane elements in this work we develop an isogeometric approach for the numerical analysis of the 3d kirchhoff love rod theory we use b splines and bezier interpolations and we show that they are able to attain very good accuracy for rod structures particularly for developing a 3d exact curve element with geometric torsion the paper presents an original parametrization of the geometric torsion that proves to be very effective the use of b splines allows to avoid discontinuities on the geometrical quantities and particularly on the normal fields so that even relatively low order interpolation functions are able to yield accurate results

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

a dynamic programming approach to nonlinear boundary control problems of parabolic type abstract in this paper we study a hamilton jacobi equation related to the boundary control of a parabolic equation with neumann boundary conditions the state space of this problem is a hilbert space and the equation is defined classically only on a dense subset of the state space moreover the hamiltonian appearing in the equation contains fractional powers of an unbounded operator these facts render the problem difficult in this paper we give a revised definition of a viscosity solution to accommodate the unboundness of the hamiltonian we then obtain existence and uniqueness results for viscosity solutions in particular we show that under suitable assumptions the value function of the boundary control problem is the unique viscosity solution of the related hamilton jacobi equation

hamilton jacobi equations in infinite dimensions i uniqueness of viscosity solutions soient un espace de banach v son dual v et des solutions d une equation h x u du 0 dans etablies dans un sous ensemble de v h v r v r est continue on demontre que des solutions classiques sont determinees de facon unique par leurs valeurs limites on montre que l extension de la notion de solutions viscosite aux espaces de banach reussit dans des espaces munis de la propriete de radon nikodym

a model of finite strain viscoplasticity based on unified constitutive equations theoretical and computational considerations with applications to shells abstract a model of multiplicative finite strain viscoplasticity is developed hereby the elastic internal potential is assumed to depend quadratically on the elastic strain measure ce by means of corresponding invariants hence possible extension of the model to take anisotropy into account is straightforward the evolution equation of the unified type due to bodner and partom asme j appl mech 42 1975 385 are modified so as to fit into the framework adopted the numerical treatment of the problem is fully developed specifically the algorithmic aspects of the resulting non additive structure are intensively discussed hereby the treatment of the exponential map of a non symmetric argument is of a central importance two consistent methods are developed various applications to shell problems are considered hereby a shell theory with seven degrees of freedom together with a 4 node enhanced strain finite element formulation are used a central feature of the shell formulation is its eligibility to the application of a three dimensional constitutive law

on the existence of optimal controls for spdes with boundary noise and boundary control we consider a stochastic optimal control problem for a heat equation with boundary noise and boundary control under suitable assumptions on the coefficients we prove existence of optimal controls in a strong sense by solving the related stochastic hamiltonian system

riccati equation arising in a boundary control problem with distributed parameters global existence is proved for the solution of a riccati differential equation connected with the synthesis of a boundary control problem governed by parabolic partial differential equations

frameworks for finite strain viscoelastic plasticity based on multiplicative decompositions part ii computational aspects abstract computational aspects of the two formulations of viscoelastic plasticity at finite strains proposed in part i of this work are examined in detail these formulations are based upon distinct kinematic assumptions resulting from different multiplicative decompositions of the deformation gradient however the corresponding sets of local evolution equations consistent with continuum thermodynamics and adopted in this work have globally the same structures and therefore lead to similar algorithmic treatments the key idea in the design of the integration algorithms is the systematic use of the nowadays well known exponential mapping algorithms in conjunction with the notion of operator split methodology these numerical approximations are then applied to the model examples proposed in part i together with their extensions to incorporate rate dependent plasticity the implementation within the framework of the finite element method is described in detail and finally we present a set of representative numerical simulations to illustrate the features of the proposed models

on anisotropic flow rules in multiplicative elastoplasticity at finite strains abstract hill s anisotropic formulation of the flow rule is extended so as to fit in the realm of multiplicative finite strain plasticity the anisotropic hill type yield criterion is formulated in terms of purely material quantities the list of arguments of the flow function includes a non symmetric material eshelby like stress tensor as well as structural tensors that describe the anisotropy at hand the formulation is exemplified on orthotropy where three structural tensors are employed the fact that the stress tensor is not symmetric necessitates a special treatment of the flow function where representation theorems of tensor valued function with non symmetric arguments are invoked the consequences of such a definition on the resulting inelastic rate are discussed in full it is shown that the corresponding resulting rate as defined at the actual configuration is not symmetric any more accordingly the rate naturally includes a plastic material spin moreover we deal with the theoretically interesting question of how to define spin free rates it is also demonstrated that the flow function must depend not only on the stress tensor and on adequate structural tensors but also on the deformation itself in form of the right cauchy green tensor c however this surprising dependency which must obey a specific form can be justified as physically meaningful various numerical examples of large plastic deformations of structural components are presented that underpin the capabilities of the formulation

mild solutions of semilinear elliptic equations in hilbert spaces abstract this paper extends the theory of regular solutions c 1 in a suitable sense for a class of semilinear elliptic equations in hilbert spaces the notion of regularity is based on the concept of g derivative which is introduced and discussed a result of existence and uniqueness of solutions is stated and proved under the assumption that the transition semigroup associated to the linear part of the equation has a smoothing property that is it maps continuous functions into g differentiable ones the validity of this smoothing assumption is fully discussed for the case of the ornstein uhlenbeck transition semigroup and for the case of invertible diffusion coefficient covering cases not previously addressed by the literature it is shown that the results apply to hamilton jacobi bellman hjb equations associated to infinite horizon optimal stochastic control problems in infinite dimension and that in particular they cover examples of optimal boundary control of the heat equation that were not treatable with the approaches developed in the literature up to now

adaptive boundary and point control of linear stochastic distributed parameter systems an adaptive control problem for the boundary or the point control of a linear stochastic distributed parameter system is formulated and solved in this paper the distributed parameter system is modeled by an evolution equation with an infinitesimal generator for an analytic semigroup since there is boundary or point control the linear transformation for the control in the state equation is also an unbounded operator the unknown parameters in the model appear affinely in both the infinitesimal generator of the semigroup and the linear transformation of the control strong consistency is verified for a family of least squares estimates of the unknown parameters an ito formula is established for smooth functions of the solution of this linear stochastic distributed parameter system with boundary or point control the certainty equivalence adaptive control is shown to be self tuning by using the continuity of the solution of a stationary riccati equation as a function of parameters in a uniform operator topology for a quadratic cost functional of the state and the control the certainty equivalence control is shown to be self optimizing that is the family of average costs converges to the optimal ergodic cost some examples of stochastic parabolic problems with boundary control and a structurally damped plate with random loading and point control are described that satisfy the assumptions for the adaptive control problem solved in this paper

on the amplitude modulation and localization phenomena in interactive buckling problems the postcritical behavior of a 3d system of elastically restrained beams which can manifest overall and local modes is analyzed the secondary bifurcation in the overall postcritical range is studied by applying the multiple scale perturbation method it is found that the amplitude modulation phenomenon is governed by a differential equation of the second order an approximate analytical expression of the amplitude modulating function is obtained by the wkb asymptotic method the occurrence of a turning point which is responsible for the strong localization is revealed close analogies with localization of vibrations in imperfect systems are highlighted

generalized solutions of hjb equations applied to stochastic control on hilbert space abstract in this paper we prove the existence of borel measurable optimal control laws for infinite dimensional nonstationary stochastic control problems on hilbert space this is based on some recent results on existence of generalized solutions of hjb equations on hilbert space l2 h where is a suitable reference measure on h for illustration some examples are presented

the complexity of selecting maximal solutions many important computational problems involve finding a maximal with respect to set inclusion solution in some combinatorial context we study such maximality problems from the complexity point of view and categorize their complexity precisely in terms of tight upper and lower bounds our results give characterizations of conp dp p2 fpnp fnp optp log n and fp p 2 in terms of subclasses of maximality problems an important consequence of our results is that finding an x minimal satisfying truth assignment for a given cnf boolean formula is complete for fnp optplog n solving an open question by papadimitriou proceedings of the 32nd ieee symposium on the foundations of computer science 1991 pp 163 169

strongly orthotropic continuum mechanics and finite element treatment despite successful application to orthotropic analysis any lagrangian strain tensor that is symmetric can be classified as an isotropic metric while the infinitely orthotropic case can be accurately dealt with using one dimensional elements structural tensors or kinematic constraints in this paper we present a strongly orthotropic continuum mechanics basis that models the exact kinematic behavior of the intermediary class of materials and also show its application to multi axial media and treatment using the finite element method by asserting that mechanistic strain metrics must be material property dependent and satisfy equilibrium we are able to derive a novel orthotropic linear strain tensor that is asymmetric and thus capable of describing all levels of orthotropy while maintaining generality to the well established isotropic approach subsequently formulated are a material principal rotation tensor extended orthotropic compliance tensor and an extended mohr s plot for strain relying on an additional metric denoted as aspectual strain using the developed finite element formulation it is shown that identical stress results to conventional theory for an orthotropic linear problem are predicted while offering a more informative analysis a second numerical example demonstrates the unique capability of this approach to solve the erroneous response of strongly orthotropic materials under trellis shear as compared with a number of conventional and contemporary approaches and thus its ability to produce kinematically exact results copyright 2008 john wiley sons ltd

an anisotropic viscoelastic fibre matrix model at finite strains continuum formulation and computational aspects this paper presents a fully three dimensional constitutive model for anisotropic vis coelasticity suitable for the macroscopic description of fibre reinforced composites that experience finite strains an essential feature of the model is that the matrix and the fibres are treated separately allowing then as many bundles of fibres as desired moreover the relaxation and or creep response is based on the multiplica tive viscoelastic split of the deformation gradient combined with the assumption of viscoelastic potentials for each compound here the composite is thought to be the superposition of an isotropic matrix material and further one dimensional continua each of them representing one family of fibres the deformation gradient and its multiplicative decomposition apply to all the continua linking them implicitly the global anisotropic response is obtained by an assembly of all the contributions con stitutive models for orthotropic and transversely isotropic materials are included as special cases it is shown how the continuum thermodynamics is crucial in setting the correct forms for the constitutive and evolution equations for the algorithmic design within the context of the finite element method the numerical eort is of the order of that devoted for isotropic computations in fact only a single scalar valued resolution procedure is added for each fibre bundle the algorithmic tangent moduli are derived for each compound and their assembly leads to consistent vis coelastic tangent modulus which is suitable for a quadratic rate of convergence when the newton raphson iterative scheme is employed the numerical eciency of the model is illustrated through a set of representative simulations

on the numerical implications of multiplicative inelasticity with an anisotropic elastic constitutive law the statement that theories of inelasticity at finite strains have arrived at a high level of development is only true in conjunction with isotropic material behaviour from both points of view theoretical and computational the extension to anisotropic material behaviour seems to be a complicated task the statement is especially true when the multiplicative decomposition of the deformation gradient is considered a basis for the formulation of special interest are questions related to the mathematical form of the stored energy function or equivalently of the constitutive relation for the material stress tensor as the thermodynamical force this paper deals with the above issues the anisotropic formulation is accomplished using the notion of structural tensors here we suggest that the privileged directions of the material should be transformed in a specific way under the action of the inelastic part of the deformation gradient the inelastic behaviour is assumed to be governed by evolution equations of the unified type numerically we deal with the full multiplicative structure of the theory the numerical treatment is developed in full detail expressions concerning the local iteration as well as the tangent operator are derived various numerical examples with applications to shells are presented which demonstrate the influence of anisotropy and the applicability of the theory

on truth table reducibility to sat we show that polynomial time truth table reducibility via boolean circuits to sat is the same as logspace truth table reducibility via boolean formulas to sat and the same as logspace turing reducibility to sat in addition we prove that a constant number of rounds of parallel queries to sat is equivalent to one round of parallel queries we give an oracle relative to which 2p is not equal to the class of predicates polynomial time truth table reducible to sat

regular solutions of second order stationary hamilton jacobi equations abstract we study a second order stationary hamilton jacobi equation in infinite dimension this equation is nonlinear and convex with respect to the first order term we use properties of the transition semigroup associated to the linear equation to write the hamilton jacobi equation in integral form and we prove existence uniqueness and regularity of a solution by the theory of maximal monotone operators we also prove that this solution is the pointwise limit of a uniformly bounded sequence of classical solutions of approximating problems finally the solution is the value function of the associated optimal stochastic control problem some examples are given

stress rate formulation for elastoplastic models with internal variables based on augmented lagrangian regularisation the constitutive laws of elasto plasticity with internal variables are described through the definition of suitable dual potentials which include various hardening models a family of variational principles for inelastic problems is obtained using convex analysis tools the structural problem is analysed using the complementary energy prager hodge functional the functional is regularised introducing an augmented lagrangian regularisation for the indicator function of the elastic domain so that a smooth optimisation problem is obtained in the numerical solution the discretised problem is reformulated in a finite step form using a fully implicit integration scheme and the functional is redefined in the space of the self equilibrated nodal stresses after enforcing satisfaction of the equilibrium equations in a weak form numerical tests have shown good performance on the part of the algorithm which approaches the converged solution for a considerably smaller number of elements as compared with other algorithms the method is equally available for perfect or hardening plasticity

an explicit solution for implicit time stepping in multiplicative finite strain viscoelasticity abstract we consider the numerical treatment of one of the most popular finite strain models of the viscoelastic maxwell body this model is based on the multiplicative decomposition of the deformation gradient combined with neo hookean hyperelastic relations between stresses and elastic strains the evolution equation is six dimensional and describes an incompressible flow such that the volume changes are purely elastic for the corresponding local initial value problem a fully implicit integration procedure is considered and a simple explicit update formula is derived thus no local iterative procedure is required which makes the numerical scheme more robust and efficient the resulting integration algorithm is unconditionally stable and first order accurate the incompressibility constraint of the inelastic flow is exactly preserved a rigorous proof of the symmetry of the consistent tangent operator is provided moreover some properties of the numerical solution like invariance under the change of the reference configuration and positive energy dissipation within a time step are discussed numerical tests show that in terms of accuracy the proposed integration algorithm is equivalent to the classical implicit scheme based on the exponential mapping finally in order to check the stability of the algorithm numerically a representative initial boundary value problem involving finite viscoelastic deformations is considered a fem solution of the representative problem using msc marc is presented

on the query complexity of selecting minimal sets for monotone predicates propositional satisfiability sat solvers are routinely used for solving many function problems a natural question that has seldom been addressed is what is the number of calls to a sat solver for solving some target function problem this article improves upper bounds on the query complexity of solving several function problems defined on propositional formulas these include computing the backbone of a formula and computing the set of independent variables of a formula for the general case of monotone predicates the article improves upper bounds on the query complexity of computing a minimal set when the number of minimal sets is constant this applies for example to the computation of a minimal unsatisfiable subset mus for cnf formulas but also to the computation of prime implicants and implicates with immediate application in a number of ai settings

adaptive control for semilinear stochastic systems an adaptive ergodic cost stochastic control problem for a partially known semilinear stochastic system in an infinite dimensional space is formulated and solved the solutions of the hamilton jacobi bellman equations for the discounted cost and the ergodic cost stochastic control problems require some special interpretations because they do not typically exist in the usual sense the solutions of the parameter dependent ergodic hamilton jacobi bellman equations are obtained from some corresponding discounted cost control problems as the discount rate tends to zero the solutions of the ergodic hamilton jacobi bellman equations are shown to depend continuously on the parameter a certainty equivalence adaptive control is given that is based on the optimal controls from the solutions of the ergodic hamilton jacobi bellman equations and a strongly consistent family of estimates of the unknown parameter this adaptive control is shown to achieve the optimal ergodic cost for the known system

on theory and numerics of large viscoplastic deformation abstract a multiplicative theory and corresponding computations of finite elastic viscoplastic deformations based on unified constitutive equations are presented basic features of theory are 1 the inelastic part of the deformation gradient is understood as a material stretch type tensor no need arises for the notion of the intermediate configuration 2 in the isotropic case the use of an elastic logarithmic strain tensor is shown to lead to the identification that the elastic strains are given by the quantity c 1 p c with c p being an inelastic cauchy green type tensor 3 in spite of the fact that the logarithmic strain measure is used closed forms of the tangent operator within an implicit time integration scheme are given circumventing very involved elaborations when the spectral decomposition is used 4 evolution equations of the bodner and partom type are employed a general formalism is developed for the application of the evolution laws of the unified type within the theoretical framework the formalism can be used to generalize any unified evolution equations formulated for infinetismal strains to the range of finite strains 5 for the axisymmetric case in addition to the displacement based 4 node and 9 node finite elements an enhanced strain 4 node element is presented it is shown anyhow that in the highly nonlinear regime the enhanced strain formulation may exhibit numerical instabilities different numerical examples of finite strain deformations are presented

continuum and discrete models for structures including quasi inextensible elasticae with a view to the design and modeling of composite reinforcements abstract inspired by some composite fiber reinforcements used in aeronautical engineering and by the need of conceiving new metamaterials some discrete models including quasi inextensible elasticae are considered a class of continuum models approximately describing the macroscopic mechanical behavior of introduced structures is then heuristically proposed some of these continuum models can be regarded as a special kind of second gradient elastic media in which the higher gradient elasticity is conferred by the flexural stiffnesses of elasticae constituting the microscopic lattice the discrete models are studied by means of suitably tailored numerical codes designed to avoid numerical instabilities and locking and a comparison of discrete versus continuum models is attempted the obtained results show that the theory of generalized continua may be useful in some engineering applications and it plays a relevant role in the mechanics of woven composites the introduced discrete and continuum models are used to describe the so called bias extension test on woven fabrics and it is shown that a good choice to correctly reproduce the targeted phenomenology is to use a second gradient continuum theory however as discussed throughout the paper in the context of rigorous micro macro identification procedures there still remain many open problems to be solved especially when dealing with systems subjected to particular constraints such as inextensibility

large deformation simulation of anisotropic material using an updated lagrangian finite element method large deformation finite element fe simulations of anisotropic material often show slow convergence or break down with increasing anisotropy and deformation large deformations are generally approximated by multiple small linearised steps this leads to poor performance and contradicting formulations here a new conceptually simple scheme was implemented in an updated lagrange formulation an appropriate decomposition of the deformation gradient results in constitutive relations defined in invariant tensors consistent tangent matrices are given for a linearly elastic fibre model and for a generalised anisotropic material the simulations are robust showing quadratic convergence for arbitrary degrees of anisotropy and arbitrary deformations with strain increments over 100 plasticity of the fibres is included without compromising the rate of convergence

improved versions of assumed enhanced strain tri linear elements for 3d finite deformation problems abstract improved three dimensional tri linear elements for finite deformation problems are developed based on an assumed enhanced strain methodology which in the linear regime incorporates the classical method of incompatible modes as a particular case three crucial modifications of a recently proposed element which reduces to wilson s brick in the linear regime are introduced to prevent locking response in distorted configurations and to maintain proper rank while preserving excellent performance in bending dominated and localization problems i a modified quadrature rule ii an additional enhancement of the divergence term and iii a modification of the isoparametric shape function derivatives for the three dimensional problem moreover these modified shape function derivatives are shown to improve the performance of the standard tri linear brick in distorted configurations in addition a strategy is described to circumvent the memory storage requirements in the static condensation procedure of the enhanced strain parameters the excellent performance of the improved methodology is illustrated in representative numerical simulations

oracles that compute values this paper focuses on complexity classes of partial functions that are computed in polynomial time with oracles in npmv the class of all multivalued partial functions that are computable nondeterministically in polynomial time concerning deterministic polynomial time reducibilities it is shown that a multivalued partial function is polynomial time computable with k adaptive queries to npmv if and only if it is polynomial time computable via 2k 1 nonadaptive queries to npmv a characteristic function is polynomial time computable with k adaptive queries to npmv if and only if it is polynomial time computable with k adaptive queries to np unless the boolean hierarchy collapses for every k k adaptive nonadaptive queries to npmv are different than k 1 adaptive nonadaptive queries to npmv nondeterministic reducibilities lowness and the difference hierarchy over npmv are also studied the difference hierarchy for partial functions does not collapse unless the boolean hierarchy collapses but surprisingly the levels of the difference and bounded query hierarchies do not interleave as is the case for sets unless the polynomial hierarchy collapses

viscosity solutions of dynamic programming equations for the optimal control of the two dimensional navier stokes equations in this paper we study the infinite dimensional hamilton jacobi equation associated with the optimal feedback control of viscous hydrodynamics we resolve the global unique solvability problem of this equation by showing that the value function is the unique viscosity solution

on inter element forces in the fem displacement formulation and implications for stress recovery this paper describes a new technique for the determination of the inter element forces and tractions as well as stress state at nodes as a post processing step after the solution of standard fe displacement calculation the work is motivated in the context of a broader development of a procedure to simulate fracture processes using a discrete approach without the need of double noded interface elements the technique easily implementable is based on the double minimization of an objective function representing the error between the inter element stress tractions and the projection of the best fit stress tensor t along the planes of the interfaces converging at an element corner node the formulation is illustrated with some basic examples in which the resulting stress tensors and inter element forces are compared to theoretical solutions and to the results obtained by using a traditional stress average smoothing method

ergodic control of semilinear stochastic equations and the hamilton jacobi equation abstract in this paper we consider optimal control of stochastic semilinear equations with lipschitz continuous drift and cylindrical noise we show existence and uniqueness up to an additive constant of solutions to the stationary hamilton jacobi equation associated with the cost functional given by the asymptotic average per unit time cost as a consequence we find the optimizing controls given in the feedback form to obtain these results we prove also some new results on the transition semigroups of semilinear diffusion acting in the spaces of continuous function with the weighted sup norms and on the optimal control of semilinear diffusions for the discounted cost functional

hamilton jacobi bellman equations for the optimal control of the duncan mortensen zakai equation abstract we study a class of hamilton jacobi bellman hjb equations associated to stochastic optimal control of the duncan mortensen zakai equation the equations are investigated in weighted l 2 spaces we introduce an appropriate notion of weak viscosity solution of such equations and prove that the value function is the unique solution of the hjb equation we apply the results to stochastic optimal control problems with partial observation and correlated noise

existence of minimizers for a finite strain micromorphic elastic solid we investigate geometrically exact generalized continua of micromorphic type in the sense of eringen the two field problem for the macrodeformation and the affine microdeformation p gl 3 r in the quasistatic conservative load case is investigated in a variational form depending on material constants two existence theorems in sobolev spaces are given for the resulting nonlinear boundary value problems these results comprise existence results for the micro incompressible case p sl 3 r and the cosserat micropolar case p so 3 r in order to treat external loads a new condition called bounded external work has to be included which overcomes the conditional coercivity of the formulation the possible lack of coercivity is related to fracture of the micromorphic solid the mathematical analysis uses an extended korn first inequality the methods of choice are the direct methods of the calculus of variations

second order hamilton jacobi equations in infinite dimensions some second order hamilton jacobi equations connected to stochastic optimal control problems for infinite dimensional systems driven by a white noise are studied a direct method to prove existence and uniqueness of mild solutions is developed then this solution is identified as the value function of the related stochastic control problem and a feedback formula for optimal controls is derived

on a numerical implementation of a formulation of anisotropic continuum elastoplasticity at finite strains in a recent theoretical study see c sansour i karsaj j soric a formulation of anisotropic continuum elastoplasticity at finite strains part i modelling international journal of plasticity 22 2006 2346 2365 a constitutive model for anisotropic elastoplasticity at finite strains has been developed the model is based on the multiplicative decomposition of the deformation gradient the stored energy function as well as the flow rule has been considered as quadratic functions of their arguments in both cases the list of arguments is extended to include structural tensors which describe the anisotropy of the material response at hand non linear isotropic hardening is considered as well in this paper the integration of the constitutive law is presented the associative flow rule is integrated using the exponential map which preserves the plastic incompressibility condition the numerical treatment of the problem is fully developed and expressions related to the local iteration and the consistent tangent operator are considered in detail it is shown that while the consistent linearisation of the model is quite complicated it still can be achieved if various intriguing implicit dependencies are identified and correctly dealt with various numerical examples of three dimensional deformations of whole structural components are presented the examples clearly illustrate the influence of anisotropy on finite elastoplastic deformations

minimal sets on propositional formulae problems and reductions abstract boolean satisfiability sat is arguably the archetypical np complete decision problem progress in sat solving algorithms has motivated an ever increasing number of practical applications in recent years however many practical uses of sat involve solving function as opposed to decision problems concrete examples include computing minimal unsatisfiable subsets minimal correction subsets prime implicates and implicants minimal models backbone literals and autarkies among several others in most cases solving a function problem requires a number of adaptive or non adaptive calls to a sat solver given the computational complexity of sat it is therefore important to develop algorithms that either require the smallest possible number of calls to the sat solver or that involve simpler instances this paper addresses a number of representative function problems defined on boolean formulae and shows that all these function problems can be reduced to a generic problem of computing a minimal set subject to a monotone predicate this problem is referred to as the minimal set over monotone predicate msmp problem this work provides new ways for solving well known function problems including prime implicates minimal correction subsets backbone literals independent variables and autarkies among several others moreover this work also motivates the development of more efficient algorithms for the msmp problem finally the paper outlines a number of areas of future research related with extensions of the msmp problem

ergodic boundary point control of stochastic semilinear systems a controlled markov process in a hilbert space and an ergodic cost functional are given for a control problem that is solved where the process is a solution of a parameter dependent semilinear stochastic differential equation and the control can occur only on the boundary or at discrete points in the domain the linear term of the semilinear differential equation is the infinitesimal generator of an analytic semigroup the noise for the stochastic differential equation can be distributed boundary and point some ergodic properties of the controlled markov process are shown to be uniform in the control and the parameter the existence of an optimal control is verified to solve the ergodic control problem the optimal cost is shown to depend continuously on the system parameter

second order hamilton jacobi equations in hilbert spaces and stochastic boundary control the paper is concerned with fully nonlinear second order hamilton jacobi bellman isaacs equations of elliptic type in separable hilbert spaces which have unbounded first and second order terms the viscosity solution approach is adapted to the equations under consideration and the existence and uniqueness of viscosity solutions are proved a stochastic optimal control problem driven by a parabolic stochastic pde with control of dirichlet type on the boundary is considered it is proved that the value function of this problem is the unique viscosity solution of the associated hamilton jacobi bellman equation

maximum principle for an optimal control problem associated to a spde with nonlinear boundary conditions abstract we study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain perturbed by noise we allow the control to act on the boundary and set boundary conditions which result in a stochastic differential equation for the trace of the solution on the boundary this work provides necessary and sufficient conditions of optimality in the form of a maximum principle we also provide a result of existence for the optimal control in the case where the control acts linearly

strain gradient elastic homogenization of bidimensional cellular media the present paper aims at introducing an homogenization scheme for the determination of strain gradient elastic coefficients this scheme is based on a quadratic extension of homogeneous boundary condition hbc it allows computing strain elastic effective tensors this easy to handle computational procedure will then be used to construct overall honey comb like materials behavior and to verify some theoretical predictions about strain gradient elasticity

infinite dimensional hamilton jacobi equations and dirichlet boundary control problems of parabolic type the paper is concerned with an infinite dimensional hamilton jacobi equation this equation is related to boundary control problems of dirichlet type for semilinear parabolic systems the viscosity solution approach is adapted to the equation under consideration using the properties of fractional powers of generators of analytic semigroups an existence and uniqueness result for such problem is obtained

viscosity solutions for a class of hamilton jacobi equations in hilbert spaces we study hamilton jacobi equations with an unbounded term in hilbert spaces we introduce a new variant of the notion of viscosity solution for a class of hamilton jacobi equations and obtain comparison and existence results for viscosity solutions we also examine the usefulness of the notion of viscosity solution in optimal control

three dimensional incompressible viscoelasticity in large strains formulation and numerical approximation abstract this paper considers viscoelastic incompressible solids in large deformations a three dimensional thermodynamical model is first proposed it leads to a nonlinear variational problem which is approximated in space by mixed finite elements and in time by a first order implicit scheme this approximation is analyzed on the corresponding linearized problem finally an elimination strategy is described which reduces each step of the discrete problem to the solution of a standard hyperelastic problem to be solved by newton s method

path dependent hamilton jacobi equations in infinite dimensions abstract we propose notions of minimax and viscosity solutions for a class of fully nonlinear path dependent pdes with nonlinear monotone and coercive operators on hilbert space our main result is well posedness existence uniqueness and stability for minimax solutions a particular novelty is a suitable combination of minimax and viscosity solution techniques in the proof of the comparison principle one of the main difficulties the lack of compactness in infinite dimensional hilbert spaces is circumvented by working with suitable compact subsets of our path space as an application our theory makes it possible to employ the dynamic programming approach to study optimal control problems for a fairly general class of delay evolution equations in the variational framework furthermore differential games associated to such evolution equations can be investigated following the krasovski subbotin approach similarly as in finite dimensions

determining inference semantics for disjunctive logic programs abstract in a seminal paper gelfond and lifschitz 34 introduced simple disjunctive logic programs where in rule heads the disjunction operator is used to express incomplete information and defined the answer set semantics called gl semantics for short based on a program transformation called gl reduct and the minimal model requirement our observations reveal that the requirement of the gl semantics i e an answer set should be a minimal model of rules of the gl reduct may sometimes be too strong a condition and exclude some answer sets that would be reasonably acceptable to address this we present an alternative more permissive answer set semantics called the determining inference di semantics specifically we introduce a head selection function to formalize the operator and define answer sets as follows i given an interpretation i and a selection function sel we transform a disjunctive program into a normal program s e l i called a disjunctive program reduct ii given a base answer set semantics x for normal programs we define i to be a candidate answer set of w r t x if i is an answer set of s e l i under x and iii we define i to be an answer set of w r t x if i is a minimal candidate answer set the di semantics is general and applicable to extend any answer set semantics x for normal programs to disjunctive programs by replacing x with the gl n l p semantics defined by gelfond and lifschitz 33 we induce a di semantics for simple disjunctive programs and by replacing x with the well justified semantics defined by shen et al 65 we further induce a di semantics for general disjunctive programs we also establish a novel characterization of the gl semantics in terms of a disjunctive program reduct which reveals the essential difference of the di semantics from the gl semantics and leads us to giving a satisfactory solution to the open problem presented by hitzler and seda 36 about characterizing split normal derivatives of a simple disjunctive program such that answer sets of the normal derivatives are answer sets of under the gl semantics finally we give computational complexity results in particular we show that in the propositional case deciding whether a simple disjunctive program has some di answer set is np complete this is in contrast to the gl semantics and equivalent formulations such as the flp semantics 24 where deciding whether has some answer set is 2 p complete while brave and cautious reasoning are 2 p and 2 p complete respectively for both gl and di answer sets for general disjunctive programs with compound formulas as building blocks the complexity of brave and cautious reasoning increases under di semantics by one level of the polynomial hierarchy which thus offers higher problem solving capacity

finite element analysis of internally balanced elastic materials abstract this paper provides a finite element treatment for a generalized hyperelastic theory in which the deformation gradient is subject to the multiplicative two factor decomposition that is commonly used in large strain plasticity the multiplicative decomposition in the present context is motivated by a theory of balanced internal variables one of which is the first factor in the decomposition previous studies have shown how the associated continuum mechanical formulation then leads not only to the stress equations of equilibrium but also to an additional tensor balance equation that serves to determine the individual factors in the decomposition such a theory has been shown to predict loading thresholds associated with the emergence of slip surfaces at grip locations in well posed boundary value problems however previous numerical treatments focused on shooting method procedures that failed to resolve loading plateaus and other key features associated with the emergence of such singular surfaces in the present work we describe a finite element treatment that resolves such previously obscure details additional finite element simulations illustrate new aspects of singular surface emergence in this type of theory including the emergence of singular surfaces in the interior of the computational domain

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

removing redundancy from a clause abstract this paper deals with the problem of removing redundant literals from a given clause we first consider condensing a weak type of redundancy elimination a clause is condensed if it does not subsume any proper subset of itself it is often useful and sometimes necessary to replace a non condensed clause c by a condensation i e by a condensed subset of c which is subsumed by c after studying the complexity of an existing clause condensing algorithm we present a more efficient algorithm and provide arguments for the optimality of the new method we prove that testing whether a given clause is condensed is co np complete and show that several problems related to clause condensing belong to complexity classes that are probably slightly harder than np we also consider a stronger version of redundancy elimination a clause c is strongly condensed iff it does not contain any proper subset c such that c logically implies c we show that the problem of testing whether a clause is strongly condensed is undecidable

on the compressibility of mathcal np instances and cryptographic applications we study compression that preserves the solution to an instance of a problem rather than preserving the instance itself our focus is on the compressibility of mathcal np decision problems we consider mathcal np problems that have long instances but relatively short witnesses the question is whether one can efficiently compress an instance and store a shorter representation that maintains the information of whether the original input is in the language or not we want the length of the compressed instance to be polynomial in the length of the witness and polylog in the length of original input such compression enables succinctly storing instances until a future setting will allow solving them either via a technological or algorithmic breakthrough or simply until enough time has elapsed in this paper we first develop the basic complexity theory of compression including reducibility completeness and a stratification of mathcal np with respect to compression we then show that compressibility say of sat would have vast implications for cryptography including constructions of one way functions and collision resistant hash functions from any hard on average problem in mathcal np and cryptanalysis of key agreement protocols in the bounded storage model when mixed with time complexity based cryptography

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