multi scale second order computational homogenization of multi phase materials a nested finite element solution strategy this paper presents the detailed implementation and computational aspects of a novel second order computational homogenization procedure which is suitable for a multi scale modelling of macroscopic localization and size effects the second order scheme is an extension of the classical first order computational homogenization framework and is based on a proper incorporation of the gradient of the macroscopic deformation gradient tensor into the kinematical macro micro scale transition from the microstructural analysis the macroscopic stress and higher order stress tensors are obtained thus delivering a microstructurally based constitutive response of the macroscopic second gradient continuum the higher order macroscopic constitutive tangents are derived through static condensation of the microscopic global tangent matrix for the solution of the second gradient equilibrium problem on the macrolevel a mixed finite element formulation is developed as an example the second order computational homogenization approach is applied for the multi scale analysis of simple shear of a constrained heterogeneous strip where a pronounced boundary size effect appears

loss surface of xor artificial neural networks training an artificial neural network involves an optimization process over the landscape defined by the cost loss as a function of the network parameters we explore these landscapes using optimization tools developed for potential energy landscapes in molecular science the number of local minima and transition states saddle points of index one as well as the ratio of transition states to minima grow rapidly with the number of nodes in the network there is also a strong dependence on the regularization parameter with the landscape becoming more convex fewer minima as the regularization term increases we demonstrate that in our formulation stationary points for networks with n h hidden nodes including the minimal network required to fit the xor data are also stationary points for networks with n h 1 hidden nodes when all the weights involving the additional node are zero hence smaller networks trained on xor data are embedded in the landscapes of larger networks our results clarify certain aspects of the classification and sensitivity to perturbations in the input data of minima and saddle points for this system and may provide insight into dropout and network compression

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

nonlocal models for damage and fracture comparison of approaches abstract the paper analyzes nonlocal constitutive models used in simulations of damage and fracture processes of quasibrittle materials a number of nonlocal formulations found in the literature are classified according to the type of variable subjected to nonlocal averaging analytical and numerical solutions of a simple one dimensional localization problem are presented it is shown that some of the formulations inevitably lead to residual stresses even at very late stages of the deformation process and consequently they are not capable of modeling complete separation in a widely open macroscopic crack the mechanisms leading to this specific type of stress locking are explained based on a theoretical analysis of the nonlocal constitutive equations it is also pointed out that the nonlocal approach distorts the shape of the stress strain diagram which has to be taken into account when designing an appropriate local softening law

non local boundary integral formulation for softening damage a strongly non local boundary element method bem for structures with strain softening damage treated by an integral type operator is developed a plasticity model with yield limit degradation is implemented in a boundary element program using the initial stress boundary element method with iterations in each load increment regularized integral representations and boundary integral equations are used to avoid the difficulties associated with numerical computation of singular integrals a numerical example is solved to verify the physical correctness and efficiency of the proposed formulation the example consists of a softening strip perforated by a circular hole subjected to tension the strain softening damage is described by a plasticity model with a negative hardening parameter the local formulation is shown to exhibit spurious sensitivity to cell mesh refinements localization of softening damage into a band of single cell width and excessive dependence of energy dissipation on the cell size by contrast the results for the non local theory are shown to be free of these physically incorrect features compared to the classical non local finite element approach an additional advantage is that the internal cells need to be introduced only within the small zone or band in which the strain softening damage tends to localize within the structure copyright 2003 john wiley sons ltd

dead beat control of linear periodic discrete time systems in this paper the dead beat control of linear periodic discrete time systems subject to periodic disturbances is studied necessary and sufficient conditions are given for the existence of a linear periodic controller such that both output dead beat control under periodic disturbances and state dead beat control under no disturbance are performed moreover synthesis procedures of the controller as well as of state dead beat observers are given which can be applied also to a class of bilinear systems

relaxed cal h _ infty stabilization conditions for discrete time fuzzy systems with interval time varying delays to derive less conservative delay and range dependent h infin stabilization conditions for discrete time takagi sugeno t s fuzzy systems with interval time varying delays the use of a fuzzy weighting dependent lyapunov krasovskii functional fwlkf in which all variables are set to be affinely or quadratically dependent on fuzzy weighting functions is proposed subsequently parameterized linear matrix inequality plmi based h infin stabilization conditions are derived by following the free weighting matrix approach to fully exploit the convexity of fuzzy weighting functions the derived plmis are sequentially replaced by a finite set of lmis by considering all possible conditions associated with fuzzy weighting functions

dead beat observers of reduced order for linear periodic discrete time systems with inaccessible inputs in this paper necessary and sufficient conditions are given for the existence of a dead beat observer for a linear periodic discrete time system subject to immeasurable periodic disturbances the conditions express in terms of the disturbed system the reconstructibility of the augmented system obtained by connecting the former with the disturbance generator a synthesis procedure of the observer is also provided

a multi level computational model for multi scale damage analysis in composite and porous materials abstract an adaptive multi level methodology is developed in this paper to create a hierarchy of computational sub domains with varying resolution for multiple scale problems it is intended to concurrently predict evolution of variables at the structural and microstructural scales as well as to track the incidence and propagation of microstructural damage in composite and porous materials the microstructural analysis is conducted with the voronoi cell finite element model vcfem while a conventional displacement based fem code executes the macroscopic analysis the model introduces three levels in the computational domain which include macro macro micro and microscopic analysis it differentiates between non critical and critical regions and ranges from macroscopic computations using continuum constitutive relations to zooming in at hotspots for pure microscopic simulations coupling between the scales in regions of periodic microstructure is accomplished through asymptotic homogenization an adaptive process significantly increases the efficiency while retaining appropriate level of accuracy for each region numerical examples are conducted for composite and porous materials with a variety of microscopic architectures to demonstrate the potential of the model

the finite element method for the mechanically based model of non local continuum summary in this paper the finite element method fem for the mechanically based non local elastic continuum model is proposed in such a model each volume element of the domain is considered mutually interacting with the others beside classical interactions involved by the cauchy stress field by means of central body forces that are monotonically decreasing with their inter distance and proportional to the product of the interacting volume elements the constitutive relations of the long range interactions involve the product of the relative displacement of the centroids of volume elements by a proper distance decaying function which accounts for the decrement of the long range interactions as long as distance increases in this study the elastic problem involving long range central interactions for isotropic elastic continuum will be solved with the aid of the fem the accuracy of the solution obtained with the proposed fem code is compared with other solutions obtained with galerkins approximation as well as with finite difference method moreover a parametric study regarding the effect of the material length scale in the mechanically based model and in the kroner eringen non local elasticity has been investigated for a plane elasticity problem copyright 2011 john wiley sons ltd

recursive solutions to deadbeat observers for time varying multivariable systems this paper describes a new construction of the deadbeat observer for the state estimation of linear time varying multivariable systems the proposed design methods are computationally attractive because of their simplicity and recursive nature and are recommendable even for time invariant multivariable systems

bounds for element size in a variable stiffness cohesive finite element model the cohesive finite element method cfem allows explicit modelling of fracture processes one form of cfem models integrates cohesive surfaces along all finite element boundaries facilitating the explicit resolution of arbitrary fracture paths and fracture patterns this framework also permits explicit account of arbitrary microstructures with multiple length scales allowing the effects of material heterogeneity phase morphology phase size and phase distribution to be quantified however use of this form of cfem with cohesive traction separation laws with finite initial stiffness imposes two competing requirements on the finite element size on one hand an upper bound is needed to ensure that fields within crack tip cohesive zones are accurately described on the other hand a lower bound is also required to ensure that the discrete model closely approximates the physical problem at hand both issues are analysed in this paper within the context of fracture in multi phase composite microstructures and a variable stiffness bilinear cohesive model the resulting criterion for solution convergence is given for meshes with uniform cross triangle elements a series of calculations is carried out to illustrate the issues discussed and to verify the criterion given these simulations concern dynamic crack growth in an al2o3 ceramic and in an al2o3 tib2 ceramic composite whose phases are modelled as being hyperelastic in constitutive behaviour copyright 2004 john wiley sons ltd

multi scale boundary element modelling of material degradation and fracture in the present paper a multi scale boundary element method for modelling damage is proposed the constitutive behaviour of a polycrystalline macro continuum is described by micromechanics simulations using averaging theorems an integral non local approach is employed to avoid the pathological localization of micro damage at the macro scale at the micro scale multiple intergranular crack initiation and propagation under mixed mode failure conditions is considered moreover a non linear frictional contact analysis is employed for modelling the cohesive frictional grain boundary interfaces both micro and macro scales are being modelled with the boundary element method additionally a scheme for coupling the micro bem with a macro fem is also proposed to demonstrate the accuracy of the proposed method the mesh independency is investigated and comparisons with two macro fem models are made to validate the different modelling approaches finally microstructural variability of the macro continuum is considered to investigate possible applications to heterogeneous materials

cal h _ infty output feedback control based on an fir type quasi deadbeat observer this technical note proposes a novel output feedback control law based on a finite impulse response fir type quasi deadbeat observer for linear systems for nominal systems without disturbances this technical note first establishes the deadbeat condition that reduces the state estimation error to zero within a finite time and verifies that all the hidden poles of the closed loop system under the quasi deadbeat observer based control law are zero and that the separation principle holds true in order to enhance the disturbance rejection capability for systems with random work disturbances on the structural merit of the fir type observer we have proposed the conditions for an h infin quasi deadbeat observer and an h infin stabilizer based on the predetermined observer respectively

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

quasi deadbeat minimax filters for deterministic state space models in this note a quasi deadbeat property is introduced and a quasi deadbeat minimax filter dmf is proposed as a new class of filters for deterministic discrete time state space models constraints such as linearity quasi deadbeat property and independence of the initial state information will be required in advance in addition to a new performance index of the worst case gain between the disturbance and the current estimation error the proposed dmf is obtained by directly minimizing the new performance index with above constraints finite impulse response fir and infinite impulse response iir structures are suggested with emphasis on the fir structure the proposed dmf is represented first in a standard batch form and then in an iterative form it is shown that the dmf with fir and iir structures for deterministic systems are similar in form to the existing receding horizon unbiased fir filter rhuff and the kalman filter respectively for stochastic systems

brief a receding horizon unbiased fir filter for discrete time state space models this paper concerns with a new linear finite impulse response fir filter called the receding horizon unbiased fir rhuf filter for the state estimation in discrete time state space models to obtain the rhuf filter linearity unbiasedness and fir structure will be required beforehand in addition to a performance criteria of minimum variance the rhuf filter is obtained by directly solving an optimization problem with the unbiasedness constraint the rhuf filter has time invariance and deadbeat properties the rhuf filter is represented in both a batch form and an iterative form it is shown that the rhuf filter is equivalent to the existing receding horizon kalman fir rhkf filter whose optimality is not clear to understand the former is more systematic and logical while the latter is heuristic due to handling of infinite covariance of the initial state information

output feedback h control of systems over communication networks using a deterministic switching system approach this paper proposes a new control problem of systems over asymmetric path delay configurations on arbitrary communication networks where the criterion is the h norm minimization via dynamic output feedback controllers network delay dependent switching controllers are designed via a piecewise lyapunov function approach as well as a common lyapunov function approach the controllers are found through convex optimization over linear matrix inequalities

linear function dead beat observers with disturbance localization for linear periodic discrete time systems abstract in this paper the classical notion of a conditioned invariant subspace is extended to the case of linear periodic discrete time systems properly characterized and suitably specialized to the notion of an outer reconstructible subspace these ideas are used in order to find necessary and sufficient conditions for the existence of a linear function dead beat observer for such systems under unknown and unmeasurable disturbances and a synthesis procedure for such an observer

energy landscape of the finite size spherical three spin glass model we study the three spin spherical model with mean field interactions and gaussian random couplings for moderate system sizes of up to 20 spins we obtain all stationary points of the energy landscape by means of the numerical polynomial homotopy continuation method on the basis of these stationary points we analyze the complexity and other quantities related to the glass transition of the model and compare these finite system quantities to their exact counterparts in the thermodynamic limit

disturbance decoupling by measurement feedback with stability or pole placement in this paper we solve the disturbance decoupling problem by measurement feedback and requiring stability or pole placement on the closed loop system the problem is attacked using the geometric approach through the concepts of a bmod mathcal b invariant and controllability subspaces and their duals a mid k invariant and complementary observability subspaces the solution of this problem has an interesting structure consisting of a feedback processor which decomposes into i a disturbance decoupling loop ii a disturbance input stabilization or pole placement loop and iii a controlled output stabilization or pole placement loop

on the stabilization of a class of bilinear systems abstract in this paper the problem of the stabilization of a class of continuous time bilinear systems containing the class of the homogeneous ones is studied and simple stabiliza bility conditions are derived expressed in terms of the stability or stabilizability of some linear or homogeneous bilinear subsystems of the given system on this basis it is shown that this problem can be decomposed into subproblems and reduced to the stabilization of homogeneous subsystems of the system obtained through successive decompositions of it a sufficient condition for the stabilization of a homogeneous bilinear system is also given

periodic solutions of periodic riccati equations for periodically time varying matrix riccati equations controllability and observability in the usual sense are shown to be sufficient for the existence of a unique positive definite periodic solution

computational homogenization for heterogeneous thin sheets in this paper a computational homogenization technique for thin structured sheets is proposed based on the computational homogenization concepts for first and second order continua the actual three dimensional 3d heterogeneous sheet is represented by a homogenized shell continuum for which the constitutive response is obtained from the nested analysis of a microstructural representative volume element rve incorporating the full thickness of the sheet and an in plane representative cell of the macroscopic structure at an in plane integration point of the macroscopic shell the generalized strains i e the membrane deformation and the curvature are used to formulate the boundary conditions for the microscale rve problem at the rve scale all microstructural constituents are modeled as an ordinary 3d continuum described by the standard equilibrium and the constitutive equations upon proper averaging of the rve response the macroscopic generalized stress and the moment resultants are obtained in this way an in plane homogenization is directly combined with a through thickness stress integration from a macroscopic point of view a numerical generalized stress strain constitutive response at every macroscopic in plane integration point is obtained additionally the simultaneously resolved microscale rve local deformation and stress fields provide valuable information for assessing the reliability of a particular microstructural design

topology trivialization and large deviations for the minimum in the simplest random optimization finding the global minimum of a cost function given by the sum of a quadratic and a linear form in n real variables over n 1 dimensional sphere is one of the simplest yet paradigmatic problems in optimization theory known as the trust region subproblem or constraint least square problem when both terms in the cost function are random this amounts to studying the ground state energy of the simplest spherical spin glass in a random magnetic field we first identify and study two distinct large n scaling regimes in which the linear term magnetic field leads to a gradual topology trivialization i e reduction in the total number mathcal n tot of critical stationary points in the cost function landscape in the first regime mathcal n tot remains of the order n and the cost function energy has generically two almost degenerate minima with the tracy widom tw statistics in the second regime the number of critical points is of the order of unity with a finite probability for a single minimum in that case the mean total number of extrema minima and maxima of the cost function is given by the laplace transform of the tw density and the distribution of the global minimum energy is expected to take a universal scaling form generalizing the tw law though the full form of that distribution is not yet known to us one of its far tails can be inferred from the large deviation theory for the global minimum in the rest of the paper we show how to use the replica method to obtain the probability density of the minimum energy in the large deviation approximation by finding both the rate function and the leading pre exponential factor

a variational principle for gradient plasticity abstract we elaborate on a generalized plasticity model which belongs to the class of gradient models suggested earlier by aifantis and co workers the generalization of the conventional theory of plasticity has been accomplished by the inclusion of higher order spatial gradients of the equivalent plastic strain in the yield condition first it is shown how these gradients affect the critical condition for the onset of localization and allow for a wavelength selection analysis leading to estimates for the width and or spacing of shear bands due to the presence of higher order gradients additional boundary conditions for the equivalent plastic strain are required this question and also the associated problem of the formulation and solution of general boundary value problems were left open in the previous work we demonstrate here that upon assuming a certain type of additional boundary conditions the structural symmetries of the gradient dependent constitutive model are such that there exists a variational principle for the displacement rates and the rate of the equivalent plastic strain the variational principle can serve as a basis for the numerical solution of boundary value problems in the sense of the finite element method explicit expressions for the tangent stillness matrix and the generalized nodal point forces are given

multi scale constitutive modelling of heterogeneous materials with a gradient enhanced computational homogenization scheme a gradient enhanced computational homogenization procedure that allows for the modelling of microstructural size effects is proposed within a general non linear framework in this approach the macroscopic deformation gradient tensor and its gradient are imposed on a microstructural representative volume element rve this enables us to incorporate the microstructural size and to account for non uniform macroscopic deformation fields within the microstructural cell every microstructural constituent is modelled as a classical continuum and the rve problem is formulated in terms of standard equilibrium and boundary conditions from the solution of the microstructural boundary value problem the macroscopic stress tensor and the higher order stress tensor are derived based on an extension of the hill mandel condition this automatically delivers the microstructurally based constitutive response of the higher order macro continuum and deals with the microstructural size in a natural way several examples illustrate the approach particularly the microstructural size effects

simulation of the multi scale convergence in computational homogenization approaches although the asymptotic homogenization is known to explicitly predict the thermo mechanical behaviors of an overall structure as well as the microstructures the current developments in engineering fields introduce some kinds of approximation about the microstructural geometry in order for the homogenization method for periodic media to apply for general heterogeneous ones the problems arising from mathematical modeling are examined in the framework of representative volume element rve analyses here the notion of homogenization convergence allows us to eliminate the geometrical periodicity requirement when the size of rve is sufficiently large then the numerical studies in this paper realize the multi scale nature of the convergence of overall material properties as the unit cell size is increased in addition to such dependency of the macroscopic field variables on the selected size of unit cells the convergence nature of microscopic stress values is also studied quantitatively via the computational homogenization method similar discussions are made for the elastoplastic mechanical responses in both macro and microscopic levels in these multi scale numerical analyses the specific effects of the microstructural morphology are reflected by using the digital image based dib finite element fe modeling technique which enables the construction of accurate microstructural models

a canonical decomposition of linear periodic discrete time systems in this paper a linear periodic discrete time system is studied on the basis of simple properties of the subspaces of controllable states and of unreconstructible ones a canonical structure theorem is derived this generalizes 1o such a system the classical kalman decomposition while preserving the constant dimensionality of the four subsystems which arise when a periodic continuous time system is decomposed the dynamic matrices of the non controllable and or non reconstructible subsystems are shown to be non singular at each time instant as those for a time invariant discrete time system are

energy landscape of the finite size mean field 2 spin spherical model and topology trivialization motivated by the recently observed phenomenon of topology trivialization of potential energy landscapes pels for several statistical mechanics models we perform a numerical study of the finite size 2 spin spherical model using both numerical polynomial homotopy continuation and a reformulation via non hermitian matrices the continuation approach computes all of the complex stationary points of this model while the matrix approach computes the real stationary points using these methods we compute the average number of stationary points while changing the topology of the pel as well as the variance histograms of these stationary points are presented along with an analysis regarding the complex stationary points this work connects topology trivialization to two different branches of mathematics algebraic geometry and catastrophe theory which is fertile ground for further interdisciplinary research