computational plasticity for composite structures based on mathematical homogenization theory and practice abstract this paper generalizes the classical mathematical homogenization theory for heterogeneous medium to account for eigenstrains starting from the double scale asymptotic expansion for the displacement and eigenstrain fields we derive a close form expression relating arbitrary eigenstrains to the mechanical fields in the phases the overall structural response is computed using an averaging scheme by which phase concentration factors are computed in the average sense for each micro constituent and history data is updated at two points reinforcement and matrix in the microstructure one for each phase macroscopic history data is stored in the database and then subjected in the post processing stage onto the unit cell in the critical locations for numerical examples considered the cpu time obtained by means of the two point averaging scheme with variational micro history recovery with 30 seconds on sparc 10 51 as opposed to 7 hours using classical mathematical homogenization theory at the same time the maximum error in the microstress field in the critical unit cell was only 3 5 in comparison with the classical mathematical homogenization theory

thermo mechanical analysis of nonlinear heterogeneous materials by second order reduced asymptotic expansion approach an effective second order reduced asymptotic expansion srae approach is proposed to analyze the thermo mechanical coupling problems of nonlinear periodic heterogeneous materials the first order and second order nonlinear unit cell solutions at a microscale obtained by calculating the different multiscale cell functions are given at first then the homogenization coefficients are evaluated and the nonlinear homogenized equations defined on whole structure are solved successively also the temperature and displacement fields are constructed as second order multiscale approximate solutions by assembling the distinct local cell solutions and homogenized solutions the main features of the proposed approach are i an effective model reduction scheme for computing high order nonlinear unit cell problems and ii an asymptotic high order homogenization solution that does not need high order continuity of the macroscale solutions further the corresponding finite element difference algorithms based on the srae approach are given in detail finally by some typical numerical examples the availability and correctness of the proposed algorithms are confirmed the computational results clearly demonstrate that the srae approach reported in this work are efficient and valid to predict the macroscopic thermo mechanical properties and can catch the microscale information of the heterogenous materials accurately

a multiscale projection method for macro microcrack simulations we present a new multiscale method for crack simulations this approach is based on a two scale decomposition of the displacements and a projection to the coarse scale by using coarse scale test functions the extended finite element method xfem is used to take into account macrocracks as well as microcracks accurately the transition of the field variables between the different scales and the role of the microfield in the coarse scale formulation are emphasized the method is designed so that the fine scale computation can be done independently of the coarse scale computation which is very efficient and ideal for parallelization several examples involving microcracks and macrocracks are given it is shown that the effect of crack shielding and amplification for crack growth analyses can be captured efficiently copyright 2007 john wiley sons ltd

effective properties of composite materials with periodic microstructure a computational approach abstract this study reviews several problems which are specific of composites with periodic microstructure composed of linear or nonlinear constituents the theoretical background of the method is recalled first two different families of numerical methods are considered to solve the problem the first is based on the finite element method the concept of macroscopic degrees of freedom is presented the implementation of periodicity conditions is discussed a general framework permitting either a strain or stress control is proposed the second numerical method is based on fast fourier transforms it considers first the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain the solution of this problem is based on the explicit form of the periodic green s function of the reference medium the relative merits of the two methods are compared and several examples are discussed both methods give very comparable results on test examples and their domains of applications appear to be complementary

on a class of left continuous t norms in this paper we study the subclass of left continuous t norms n which are definable by an arbitrary continuous t norm and a weak i e non necessarily involutive negation n by putting x n y 0 if x n y x n y x y otherwise thus generalizing the construction of the so called nilpotent minimum t norms we provide the characterization of weak negations compatible with a given continuous t norm and conversely which are the continuous t norms compatible with a given weak negation function

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

strain driven homogenization of inelastic microstructures and composites based on an incremental variational formulation the paper investigates computational procedures for the treatment of a homogenized macro continuum with locally attached micro structures of inelastic constituents undergoing small strains the point of departure is a general internal variable formulation that determines the inelastic response of the constituents of a typical micro structure as a generalized standard medium in terms of an energy storage and a dissipation function consistent with this type of inelasticity we develop a new incremental variational formulation of the local constitutive response where a quasi hyperelastic micro stress potential is obtained from a local minimization problem with respect to the internal variables it is shown that this local minimization problem determines the internal state of the material for finite increments of time we specify the local variational formulation for a setting of smooth single surface inelasticity and discuss its numerical solution based on a time discretization of the internal variables the existence of the quasi hyperelastic stress potential allows the extension of homogenization approaches of elasticity to the incremental setting of inelasticity focusing on macro strain driven micro structures we develop a new incremental variational formulation of the global homogenization problem where a quasi hyperelastic macro stress potential is obtained from a global minimization problem with respect to the fine scale displacement fluctuation field it is shown that this global minimization problem determines the state of the micro structure for finite increments of time we consider three different settings of the global variational problem for prescribed linear displacements periodic fluctuations and constant stresses on the boundary of the micro structure and discuss their numerical solutions based on a spatial discretization of the fine scale displacement fluctuation field the performance of the proposed methods is demonstrated for the model problem of von mises type elasto visco plasticity of the constituents and applied to a comparative study of micro to macro transitions of inelastic composites copyright 2002 john wiley sons ltd

a regularized phenomenological multiscale damage model summary we present a regularized phenomenological multiscale model where elastic properties are computed using direct homogenization and subsequently evolved using a simple three parameter orthotropic continuum damage model the salient feature of the model is a unified regularization framework based on the concept of effective softening strain the unified regularization scheme has been employed in the context of constitutive law rescaling and the staggered nonlocal approach we show that an element erosion technique for crack propagation when exercised with one of the two regularization schemes 1 possesses a characteristic length 2 is consistent with fracture mechanics approach and 3 does not suffer from pathological mesh sensitivity copyright 2014 john wiley sons ltd

effects of level and frequency on the detection of decrements and increments in sinusoids thresholds for the detection of decrements in level of sinusoidal signals were measured as a function of decrement duration level 25 40 55 and 70 db spl and frequency 250 1000 and 4000 hz in eleven normally hearing subjects thresholds for detecting a brief increment in level were also measured the sinusoids were presented in a background noise intended to mask spectral splatter associated with the decrement or increment performance tended to worsen with decreasing frequency for all decrement durations and for increment detection performance also worsened with decreasing level the results were analyzed using a model consisting of a compressive nonlinearity a sliding temporal integrator and a decision device the analysis indicated that the worsening in performance with decreasing frequency and decreasing level can be attributed partly to increases in the equivalent rectangular duration erd of the temporal integrator but mainly to changes in the efficiency of the detection process following the temporal integrator at lower frequencies and levels a larger change is required at the output of the integrator for threshold to be reached at each frequency the erd was relatively invariant with level for levels more than about 20 db above the absolute threshold

the triple rotation method for constructing t norms given an involutive negator n and a left continuous t norm t that either has no zero divisors or is rotation invariant we build a rotation invariant t norm from a rescaled version of t and its left right and front rotation depending on the involutive negator n and the set of zero divisors of t some reshaping of the rescaled version of t may occur during the rotation process the rescaled version of t itself can be understood as the b zoom of the newly constructed rotation invariant t norm with b the unique fixpoint of n starting with a rotation invariant t norm t there is however one important restriction the triple rotation method based on the involutive negator n will yield a t norm if and only if the companion q of t is commutative on 0 1 2 when q is not commutative on 0 1 2 there even does not exist a rotation invariant t norm with b zoom equal to t

a note on the ordinal sum theorem and its consequence for the construction of triangular norms in this paper the well known ordinal sum theorem of semigroups is generalized and applied to construct new families of triangular subnorms and triangular norms t norms among them one can find several new families of left continuous t norms too

solution of a system of linear equations with fuzzy numbers in this paper the interval nature of fuzzy numbers is revealed by showing that many interesting results from classical interval analysis transfer also into the fuzzy case the paper deals with a solution of a fuzzy interval system of linear equations i e a system in which fuzzy intervals numbers appear instead of crisp numbers

hierarchical modeling of heterogeneous solids in this paper a methodology is introduced for the development of adaptive methods for hierarchical modeling of elastic heterogeneous bodies the approach is based on the idea of computing an estimate of the modeling error introduced by replacing the actual fine scale material tensor with that of a homogenized material and to adaptively refine the material description until a prespecified error tolerance is met this process generates a family of coarse scale solutions in which the solution corresponding to the fine scale model of the body which embodies the exact microstructure loading and boundary conditions represents the highest level of sophistication in a family of continuum models the adaptive strategy developed can lead to a new non uniform description of material properties which reflects the loading and boundary conditions a post processing technique is also introduced which endows the coarse scale solutions with fine scale information through a local solution process convergence of the adaptive algorithm is proven and modeling error estimates as a function of scale of material description are presented preliminary results of several numerical experiments are given to confirm estimates and to illustrate the promise of the approach in practical applications

a mathematical homogenization perspective of virial stress a continuum stress measure is derived from molecular dynamics equations using a generalized mathematical homogenization gmh theory gmh consists of solving a coupled fine scale atomistic unit cell problem and a coarse scale continuum problem the fine scale problem derived can be interpreted as a molecular statics at 0 k problem where the coarse scale problem derived is a constitutive law free continuum equation which calculates the cauchy stress directly from atomistics the continuum stress derived is compared to various versions of the virial stress formula copyright 2005 john wiley sons ltd

generalizations to the constructions of t norms rotation annihilation construction in this paper the constructions of triangular norms are investigated specially based on weak negations which are not necessarily involutive the rotation and the rotation annihilation constructions are extended by means of these methods we can get new families of left continuous t norms compatible with weak negations given however not all weak negations are suitable for those generalized constructions to highlight it some counterexamples are given

hierarchical model reduction at multiple scales a hierarchical model reduction approach aimed at reducing computational complexity of non linear homogenization at multiple scales is developed the method consists of the following salient features 1 formulation of non linear unit cell problems at multiple scales in terms of eigendeformation modes that a priori satisfy equilibrium equations at multiple scales and thus eliminating the need for costly solution of discretized non linear equilibrium 2 the ability to control the discretization of the eigendeformation modes at multiple scales to maintain desired accuracy and 3 hierarchical solution strategy that requires sequential solution of single scale problems a two scale formulation is verified against an one dimensional model problem for which an analytical solution can be obtained and a three scale formulation is validated against tube crash experiments copyright 2009 john wiley sons ltd

rotation invariant t norms where triple rotation and rotation annihilation meet generalizing the notion of a zoom of a t norm not only allows to extend the triple rotation method and its corresponding decomposition but also allows to describe the interface between the triple rotation method and the rotation annihilation method an alternative view on the partition behind the rotation annihilation method is required to make both methods compatible besides zooms we also use contour lines and the companion of a t norm to concisely formulate the results

hybrid impotent incompatible eigenstrain based homogenization summary we present a constitutive framework for a periodic heterogeneous medium with minimal number of internal variables the method is based on a variant of the transformation field analysis tfa where eigenstrains are discretized using c 0 continuous approximation in matrix dominated mode of deformation hereafter referred to as impotent eigenstrain mode whereas in multiphase mode of deformation the eigenstrains are approximated using the usual c 1 approximation the delay in the onset of inelastic response and the eigenstrain induced anisotropy in a microphase both characteristic to averaging methods are alleviated by introducing an eigenstrain upwinding scheme and by enhancing constitutive laws of microphases the proposed formulation has been verified against a direct numerical simulation the method has been found to be very accurate in predicting an overall material response at a computational cost comparable with the phenomenological modeling of a periodic heterogeneous medium copyright 2013 john wiley sons ltd

a staggered nonlocal multiscale model for a heterogeneous medium summary a staggered nonlocal multiscale model for a heterogeneous medium is developed and validated the model is termed as staggered nonlocal in the sense that it employs current information for the point under consideration and past information from its local neighborhood for heterogeneous materials the concept of phase nonlocality is introduced by which nonlocal phase eigenstrains are computed using different nonlocal phase kernels the staggered nonlocal multiscale model has been found to be insensitive to finite element mesh size and load increment size furthermore the computational overhead in dealing with nonlocal information is mitigated by superior convergence of the newton method copyright 2012 john wiley sons ltd

a class of general algorithms for multi scale analyses of heterogeneous media abstract a class of computational algorithms for multi scale analyses is developed in this paper the two scale modeling scheme for the analysis of heterogeneous media with fine periodic microstructures is generalized by using relevant variational statements instead of the method of two scale asymptotic expansion the mathematical results on the generalized convergence are utilized in the two scale variational descriptions accordingly the global local type computational schemes can be unified in association with the homogenization procedure for general nonlinear problems after formulating the problem in linear elastostatics that with local contact condition and the elastoplastic problem we present representative numerical examples along with the computational algorithm consistent with our two scale modeling strategy as well as some direct approaches

topology on bl algebras in this paper by using a special family of filters on a bl algebra l we construct a topology on l show that l is a topological bl algebra find the closure of any subsets of l and obtain some conditions under which that l is a hausdorff space also we prove some theorems about connected components of this topological space and use them to construct a quotient semitopological bl algebras finally we introduce the concept of complete bl algebra and attempt to construct a complete bl algebra from l

psychoacoustic and phonetic temporal processing in normal and hearing impaired listeners four measures of auditory temporal processing were obtained from 16 normals and 16 individuals with a hearing loss of heterogeneous origin these measures were 1 temporal integration the difference in detection thresholds between signals of 10 and 1000 ms duration which was determined to provide an estimate of the ability to integrate energy over time 2 gap detection the shortest duration of silence between two noise bursts that can be discriminated from an uninterrupted noise 3 temporal difference limen the increment in duration necessary to detect a difference in the duration of a noise burst 4 gap difference limen the increment in duration necessary to detect a difference in the duration of a silent interval between two noise bursts each measure was obtained for stimuli centered both at 500 and at 4000 hz using a three alternative forced choice procedure in addition measures of identification and discrimination were obtained for two sets of synthetic speech syllables varying chiefly in a temporal parameter voice onset time from ba to pa and from bi to pi finally speech identification in noise was measured with the faaf test most of the hearing impaired listeners displayed poorer temporal analysis than the normals on all of the psychoacoustical tasks regardless of whether the two groups were compared at similar sound pressure levels or at similar sensation levels although the hearing impaired listeners displayed a reduction in the ability to discriminate subphonemic cues for the voiced voiceless distinction their identification of that distinction in stop consonants appeared to be normal the hearing impaired group made about twice as many errors as did the normals on each of the consonant features of place manner and voicing when identifying speech in noise increased temporal difference limen and longer gap detection thresholds were found to correlate significantly with reduced speech intelligibility in noise even when the effects of the pure tone threshold loss were partialed out

psychometric functions for gap detection in a yes no procedure to examine models of temporal resolution and to investigate the decision processes underlying the detection of a brief pause in a bandpass noise psychometric functions for gap detection were measured at octave frequencies from 0 25 to 8 khz three normal listeners were tested using a constant stimulus procedure with a cued yes no paradigm the minimum detectable gap mdg estimated from the midpoint of the psychometric functions decreased systematically with increasing frequency the slopes of the psychometric functions generally increased as the test frequency increased up to 2 khz but remained constant at the higher frequencies two models were investigated an energy detector model and a loudness detector model both consisted of auditory filtering a nonlinearity and short term integration in the energy detector model the nonlinearity was a square law in the loudness detector model it was a compressive power law using the usual gaussian approximations the energy detector model fails at low fr

a generalized space time mathematical homogenization theory for bridging atomistic and continuum scales a generalized space time mathematical homogenization theory which constructs an equivalent continuum description directly from molecular dynamics md equations is developed the noteworthy theoretical findings of this work are i the coarse scale continuum equations pdes obtained from the homogenization of md equations are identical to those obtained from the classical homogenization of the fine scale continuum ii the lower order effective continuum properties such as the fourth order elasticity tensor have similar characteristics to those resulting from the homogenization of fine scale continuum iii the higher order effective properties such as polarization and dispersion tensors substantially differ from those of continuum due to the discreteness effect both the heterogeneous continuum and discrete media possess the size effect but only atomistic medium has the discreteness effect some demonstrative numerical examples are presented to verify the formulation copyright 2005 john wiley sons ltd

on the scope of some formulas defining additive connectives in fuzzy logics in fuzzy sets and systems 149 2005 297 wang et al defined a new fuzzy logic called nmg they also introduced new formulas to define the additive connectives from multiplicative conjunction residuated implication and bottom in nmg however they did not study the scope of these formulas in the general framework of fuzzy logics this is the aim of this paper therefore we add the definability formulas to known fuzzy logics as new axioms following the method used in beyond two theory and applications of multiple valued logic 2003 251 and we obtain some families of logics presented in a simpler language finally we discuss the standard completeness of these new logics

generalized mathematical homogenization of atomistic media at finite temperatures in three dimensions we derive thermo mechanical continuum equations from molecular dynamics md equations using the generalized mathematical homogenization gmh theory developed by the authors for 0 k applications gmh constructs an array of atomistic unit cell problems coupled with a thermo mechanical continuum problem the unit cell problem derived is a molecular dynamics problem defined for the perturbation from the average atomistic displacements subjected to the deformation gradient and temperature extracted from the continuum problem the coarse scale problem derived is a constitutive law free continuum thermo mechanical equation attention is restricted to heat transfer by lattice vibration phonons the method is verified on several model problems against the reference molecular dynamics solution 2006 elsevier b v all rights reserved

multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method abstract this paper deals with the development of a multiple scale finite element method by combining the asymptotic homogenization theory with voronoi cell vcfem for microstructural modeling the voronoi cell finite element model originates from dirichlet tessellation of a representative material element or a base cell in the microstructure homogenized material coefficients for a global displacement finite element model are generated by vcfem analysis using periodic boundary conditions on the base cell following the macroscopic analysis the local vcfem analysis is implemented to depict the true evolution of microstructural stresses and strains various numerical examples are executed for validating the effectiveness of vcfem macro micro modeling of elastic materials the effect of size shape orientation and distribution of heterogeneities on the local and global response are examined

reduced order computational continua abstract we present a new multiscale approach hereafter referred to as reduced order computational continua rc 2 that possesses computational efficiency of phenomenological models for heterogeneous media with accuracy inherent to generalized and nonlocal continua models the rc 2 approach introduces no scale separation makes no assumption about infinitesimality of the fine scale structure does not require higher order continuity introduces no new degrees of freedom is free of higher order boundary conditions and exploits a pre computed material database to effectively solve a unit cell representative volume problem it features three building blocks i the nonlocal quadrature scheme ii the coarse scale stress function and iii the residual free fields the nonlocal quadrature scheme permits nonlocal interactions to extend over finite neighborhoods and thus introduces nonlocality into the two scale integrals employed in the multiple scale asymptotic expansion methods or alternatively into the hill mandel macrohomogeneity condition the coarse scale stress function which replaces the classical notion of coarse scale stress being the average of fine scale stresses is constructed to express the governing equations in terms of coarse scale fields only finally the residual free fields are constructed to avoid costly discrete equilibrium solution of the unit cell problems which is known to be the bottleneck of multiscale computations

gap detection in normal and hearing impaired listeners temporal resolution estimated by measuring the minimum detectable gap t msec separating two successive signals was assessed in five normal hearing and five cochlear impaired listeners the signals were octave band noises 400 800 hz 800 1600 hz and 2000 4000 hz presented in a background of continuous broadband notched noise that was applied to eliminate unwanted spectral cues temporal resolution in all listeners showed systematic improvement with an increase in octave band center frequency resolution in the hearing impaired subjects was significantly poorer than normal regardless of whether the comparisons were made at equal sound pressure level or at equal sensation level

micro inertia effects in nonlinear heterogeneous media summary the manuscript presents a dispersive nonlinear continuum theory for the case where the shortest wavelength is several times larger than the characteristic size of the microstructure and the observation window is large we develop a general purpose computational framework which is valid for nonlinear problems and requires standard c 0 continuous formalism the fine scale inertia effect is accounted for by formulating a quasidynamic unit cell problem where the fine scale inertia effect is represented by so called inertia induced eigenstrain the solution of the nonlinear quasi dynamic unit cell problem gives rise to the modification of either coarse scale mass matrix in the implicit solvers or internal force in the explicit solvers similarly to the classical homogenization theory scale separation is assumed but higher order homogenization is not pursued to avoid higher order coarse scale gradients higher order continuity and higher order boundary conditions numerical examples for both the one dimensional model problem and three dimensional heterogeneous medium with layered and fibrous composite microstructure are used to validate the computational framework proposed copyright 2012 john wiley sons ltd

mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading we present a generalization of the classical mathematical homogenization theory aimed at accounting for finite unit cell distortions which gives rise to a nonperiodic asymptotic expansion we introduce an auxiliary macro deformed configuration where the overall cauchy stress is defined and nonperiodic boundary conditions verification studies against a direct numerical simulation demonstrate the versatility of the proposed method

eigendeformation based reduced order homogenization for failure analysis of heterogeneous materials the manuscript presents a novel model reduction approach for periodic heterogeneous media which combines the multiple scale asymptotic msa expansion method with the transformation field analysis tfa to reduce the computational cost of a direct homogenization approach without significantly compromising on solution accuracy the evolution of failure in micro phases and interfaces is modeled using eigendeformation adaptive model improvement strategy incorporating a hierarchical sequence of computational homogenization models is employed to control the accuracy of the model we present the model formulation and the computational details along with verification with respect to direct homogenization and validation with respect to physical experiments studies

finite deformation plasticity for composite structures computational models and adaptive strategies abstract we develop computational models and adaptive modeling strategies for obtaining an approximate solution to a boundary value problem describing the finite deformation plasticity of heterogeneous structures a nearly optimal mathematical model consists of an averaging scheme based on approximating eigenstrains and elastic concentration factors in each micro phase by a constant in the portion of the macro domain where modeling errors are small whereas elsewhere a more detailed mathematical model based on a piecewise constant approximation of eigenstrains and elastic concentration factors is utilized the methodology is developed within the framework of statistically homogeneous composite material and local periodicity assumptions

a triangular norm based propositional fuzzy logic in 1997 wang introduced the formal system l for a type of fuzzy propositional calculus given by a particular t norm different from the three famous ones lukasiewicz godel product recently pei proved the completeness theorem for l with respect to w semantic by developing a theory of algebraic systems in this paper we aim to prove it by essentially metamathematical method furthermore we discussed originally the completeness for the schematic extension l n of l with respect to w n semantic

undefinability of min conjunction in mtl firstly a sufficient and necessary condition is given to decide whether the lattice operations of a wnm chain can be definable from its other operations secondly we show that it is indeed necessary to introduce the min conjunction into mtl as a primitive connective by constructing a left continuous t norm such that in the propositional calculus defined by this t norm the min conjunction and max disjunction are not definable from the strong conjunction implication and truth constant email protected

generalized mathematical homogenization from theory to practice a generalized mathematical homogenization gmh theory for coupling atomistic and continuum descriptions at finite temperature has been extended to account for many body potentials gmh gives rise to the constitutive law free coarse scale equations where coupled continuum thermo mechanical equations are directly derived from molecular dynamics equations an integrated computational approach which seamlessly integrates abaqus for coarse scale finite element method computations with a molecular dynamics code has been developed the accuracy and efficiency of the method has been studied for crystal silicon structures including failure predictions of nanowires

a characterization theorem on the rotation construction for triangular norms the rotation construction for t norms is introduced in j appl non classical logics 10 2000 83 92 in the present paper we characterize the widest class of operators with which the rotation construction results in left continuous t norms with involutive associated negations

parameterizing the semantics of fuzzy attribute implications by systems of isotone galois connections we study the semantics of fuzzy if then rules called fuzzy attribute implications parameterized by systems of isotone galois connections the rules express dependences between fuzzy attributes in object attribute incidence data the proposed parameterizations are general and include as special cases the parameterizations by linguistic hedges used in earlier approaches we formalize the general parameterizations propose bivalent and graded notions of semantic entailment of fuzzy attribute implications show their characterization in terms of least models and complete axiomatization and provide characterization of bases of fuzzy attribute implications derived from data

a fuzzy logic for an ordinal sum t norm among the class of residuated fuzzy logics a few of them have been shown to have standard completeness both for propositional and predicate calculus like godel nm and monoidal t norm based logic systems in this paper a new residuated logic nmg which aims at capturing the tautologies of a class of ordinal sum t norms and their residua is introduced and its standard completeness both for propositional calculus and for predicate calculus are proved

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

rotation invariant t norm solutions of a system of functional equations the generalization of the disjunctive and conjunctive boolean normal forms to fuzzy set theory obtained by interpreting as a t norm as a t conorm and as a negator often provides a kind of standard fuzzification procedure a system of functional equations turns up if some functional independence of the difference between both generalizations is demanded in this paper we explore which de morgan triplets based on a left continuous t norm t solve this system imposing some extra continuity conditions on t these t norm solutions can be obtained by the rotation construction of jenei the cauchy equation plays a key role in the reasoning process

prediction of the mechanical behavior of nonlinear heterogeneous systems by multi level finite element modeling an accurate homogenization method that accounts for large deformations and viscoelastic material behavior on microscopic and macroscopic levels is presented this method is based on the classical homogenization theory assuming local spatial periodicity of the microstructure consequently the microstructure is identified by a representative volume element rve with conformity of opposite boundaries at any stage of the deformation process the local macroscopic stress is obtained by applying the local macroscopic deformation represented by the deformation tensor on a unique rve through imposing appropriate boundary conditions and averaging the resulting rve stress field if the assumption of local periodicity of the morphology is valid this homogenization procedure supplies a consistent objective relationship between the local macroscopic deformation and the microstructural deformation the homogenization method was implemented in a multi level finite element program with meshes on macroscopic level mesh of entire structure and microscopic level meshes of rves the performance was successfully verified by the comparison of the deformation of a perforated macroscopic sheet to the response of a homogenized sheet

multiscale aggregating discontinuities a method for circumventing loss of material stability new methods for the analysis of failure by multiscale methods that invoke unit cells to obtain the subscale response are described these methods called multiscale aggregating discontinuities are based on the concept of perforated unit cells which exclude subdomains that are unstable i e exhibit loss of material stability using this concept it is possible to compute an equivalent discontinuity at the coarser scale including both the direction of the discontinuity and the magnitude of the jump these variables are then passed to the coarse scale model along with the stress in the unit cell the discontinuity is injected at the coarser scale by the extended finite element method analysis of the procedure shows that the method is consistent in power and yields a bulk stress strain response that is stable applications of this procedure to crack growth in heterogeneous materials are given copyright 2007 john wiley sons ltd