stress gradient versus strain gradient constitutive models within elasticity abstract a stress gradient elasticity theory is developed which is based on the eringen method to address nonlocal elasticity by means of differential equations by suitable thermodynamics arguments involving the free enthalpy instead of the free internal energy the restrictions on the related constitutive equations are determined which include the well known eringen stress gradient constitutive equations as well as the associated so far uncertain boundary conditions the proposed theory exhibits complementary characters with respect to the analogous strain gradient elasticity theory the associated boundary value problem is shown to admit a unique solution characterized by a hellinger reissner type variational principle the main differences between the eringen stress gradient model and the concomitant aifantis strain gradient model are pointed out a rigorous formulation of the stress gradient euler bernoulli beam is provided the response of this beam model is discussed as for its sensitivity to the stress gradient effects and compared with the analogous strain gradient beam model

triangulations of subanalytic sets and locally subanalytic manifolds if two polyhedrons are locally subanalytically homeomorphic that is the graph is locally subanalytic they are pl homeomorphic a lo cally subanalytic manifold is one whose coordinate transformations are locally subanalytic it is proved that a locally subanalytic manifold has a unique pl manifold structure a semialgebraic manifold also is considered

efficient modeling of localized material failure by means of a variationally consistent embedded strong discontinuity approach this paper is concerned with a novel embedded strong discontinuity approach suitable for the analysis of material failure at finite strains focus is on localized plastic deformation particularly relevant for slip bands in contrast to already existing models the proposed implementation allows to consider several interacting discontinuities in each finite element based on a proper re formulation of the kinematics an efficient parameterization of the deformation gradient is derived it permits to compute the strains explicitly that improves the performance significantly however the most important novel contribution of the present paper is the advocated variational constitutive update within this framework every aspect is naturally driven by energy minimization i e all unknown variables are jointly computed by minimizing the stress power the proposed update relies strongly on an extended principle of maximum dissipation this framework provides enough flexibility for different failure types and for a broad class of non associative evolution equations by discretizing the aforementioned continuous variational principle an efficient numerical implementation is obtained it shows in addition to its physical and mathematical elegance several practical advantages for instance the physical minimization principle itself specifies automatically and naturally the set of active strong discontinuities copyright 2011 john wiley sons ltd

elliptic inhomogeneities and inclusions in anti plane couple stress elasticity with application to nano composites abstract it is well known that classical continuum theory has certain deficiencies in predicting material s behavior at the micro and nanoscales where the size effect is not negligible higher order continuum theories introduce new material constants into the formulation making the interpretation of the size effect possible one famous version of these theories is the couple stress theory invoked to study the anti plane problems of the elliptic inhomogeneities and inclusions in the present work the formulation in elliptic coordinates leads to an exact series solution involving mathieu functions subsequently the elastic fields of a single inhomogeneity in conjunction with the mori tanaka theory is employed to estimate the overall anti plane shear moduli of composites with uni directional elliptic cylindrical fibers the dependence of the anti plane elastic moduli on several important physical parameters such as size aspect ratio and rigidity of the fiber the characteristic length of the constituents and the orientation of the reinforcements is analyzed based on the available data in the literature certain nano composite models have been proposed and their overall behavior estimated using the present theory

scattering of an anti plane shear wave by an embedded cylindrical micro nano fiber within couple stress theory with micro inertia abstract the inadequacy of traditional theory of elasticity in describing such a phenomenon as dispersion associated to a propagating wave with wavelength comparable to the intrinsic length of the medium of interest is well known moreover under certain circumstances it is incapable of capturing all the propagating waves a remedy to such dilemmas is the employment of the more accurate higher order continuum theories which give rise to the appearance of at least one new characteristic length in the formulation the experimental evidences as well as lattice dynamic analysis suggest that although higher order continuum theories result in some improvements but cannot fully overcome the above mentioned dilemmas unless the micro inertia term is included in the formulations the current work addresses the elastodynamic fields of an anti plane shear wave scattered by a micro nano fiber embedded in an infinite matrix using couple stress theory with micro inertia term moreover the formulations pertinent to the cases where the incident wave strikes an embedded micro nano size circular cavity or a rigid immovable micro nano fiber are also obtained within this theory the appearance of a new length scale so called dynamic characteristic length stems from consideration of the micro inertia which gives rise to physically realistic dispersion relations with characteristic resembling those observed in experiments the effects of two different types of boundary conditions for the cases of elastic and rigid immovable fiber encountered within the present theory are discussed by using this theory the corresponding analytical expressions of the elastodynamic fields total and differential scattering cross sections and the dynamic stress concentration factor are presented and their dependence on the characteristic lengths and frequency are examined it has been shown that the effect of micro inertia term is more noticeable in higher frequencies

some basic contact problems in couple stress elasticity indentation tests have long been a standard method for material characterization due to the fact that they provide an easy inexpensive non destructive and objective method of evaluating basic properties from small volumes of materials as the contact scales in such experiments reduce progressively micro to nano scales the internal material lengths become important and their effect upon the macroscopic response cannot be ignored in the present study we derive general solutions for three basic two dimensional 2d plane strain contact problems within the framework of the generalized continuum theory of couple stress elasticity this theory introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying microstructure and has proved to be very effective for modeling microstructured materials by using this theory we initially study the problem of the indentation of a deformable elastic half plane by a flat punch then by a cylindrical indentor and finally by a shallow wedge indentor our approach is based on singular integral equations which have resulted from a treatment of the mixed boundary value problems via integral transforms and generalized functions the results show significant departure from the predictions of classical elasticity revealing that it is inadequate to analyze indentation problems in microstructured materials employing only classical contact mechanics

mori tanaka estimates of the effective elastic properties of stress gradient composites a stress gradient material model was recently proposed by forest and sab mech res comm 40 16 25 2012 as an alternative to the well known strain gradient model introduced in the mid 60s we propose a theoretical framework for the homogenization of stress gradient materials we derive suitable boundary conditions ensuring that hill mandel s lemma holds as a first result we show that stress gradient materials exhibit a softening size effect to be defined more precisely in this paper while strain gradient materials exhibit a stiffening size effect this demonstrates that the stress gradient and strain gradient models are not equivalent as intuition would have it but rather complementary using the solution to eshelby s spherical inhomogeneity problem that we derive in this paper we propose mori tanaka estimates of the effective properties of stress gradient composites with spherical inclusions thus opening the way to more advanced multi scale analyses of stress gradient materials

strain gradient theory in orthogonal curvilinear coordinates in this short note general formulations of the toupin mindlin strain gradient theory in orthogonal curvilinear coordinate systems are derived and are then specified for the cases of cylindrical coordinates and spherical coordinates expressions convenient for practical use are presented for the corresponding equilibrium equations boundary conditions and the physical components for strains and strain gradients in the two coordinate systems the results obtained in this paper are general and complete and can be useful for a wide range of applications such as asymptotic crack tip field analysis cylindrical and spherical cavity expansion problems and the interpretation of micro nano indentation tests and bending twisting tests on small scales

three dimensional free vibration of arbitrarily shaped laminated micro plates with sliding interfaces within couple stress theory abstract free vibration of laminated micro plates with arbitrary geometry and boundary conditions consisting of several micro layers with free sliding frictional sliding perfect interfaces is of interest the inter layer bond in the direction normal to the interfaces is perfect and thus the corresponding displacement component is continuous across the interfaces the mentioned in plane interface conditions may be realized by varying the stiffness of the sliding inter layer spring of vanishing thickness for free sliding and perfect interface conditions the stiffness 0 and respectively couple stress theory as a useful higher order continuum theory is utilized to formulate the problem subsequently the corresponding hamiltonian is presented the three components of the displacement field in each layer are given by three distinct expressions each expression consists of the product of a base function and three dimensional polynomials with unknown coefficients the base functions are chosen according to the geometries of the system and the corresponding layer and to satisfy the homogeneous essential boundary conditions for the enforcement of the displacement continuity in the direction normal to the interfaces an appropriate series with unknown coefficients pertinent to each layer is added the influences of the level of inter layer imperfection and couple stress on the dynamical characteristics including the angular frequencies of free vibration and the corresponding mode shapes are addressed

attack detection in sensor network target localization systems with quantized data we consider a sensor network focused on target localization where sensors measure the signal strength emitted from the target each measurement is quantized to one bit and sent to the fusion center a general attack is considered at some sensors that attempts to cause the fusion center to produce an inaccurate estimation of the target location the attack is a combination of man in the middle hacking and spoofing attacks that can effectively change both signals going into and coming out of the sensor nodes in a realistic manner we show that the essential effect of attacks is to alter the naive estimate of the distance between the target and each attacked sensor which ignores the existence of attacks to a different extent giving rise to a geometric inconsistency among the attacked and unattacked sensors with the help of two secure sensors a class of detectors are proposed to detect the attacked sensors by scrutinizing the existence of the geometric inconsistency we show that the false alarm and miss probabilities of the proposed detectors decrease exponentially as the number of measurement samples increases which implies that with sufficient measurement samples the proposed detectors can identify the attacked and unattacked sensors with any required accuracy numerical results show that compared to the cases where all sensors are employed without detecting attacks or only the secure sensors are employed the localization performance can be significantly improved if we employ the secure sensors and the sensors which are declared as unattacked by the proposed detector

quantization for maximin are in distributed estimation we consider the design of optimal quantizers for the distributed estimation of a deterministic parameter in particular we design deterministic scalar quantizers to maximize the minimum asymptotic relative efficiency are between quantized and unquantized ml estimators we first design identical quantizers using the class of score function quantizers sfq we show that the structure of sfqs generally depend on the parameter value but can be expressed as thresholds on the sufficient statistic for a large class of distributions we provide a convergent iterative algorithm to obtain the best sfq that maximizes the minimum are for distributions of that class we compare the performance of the optimal sfq with a general quantizer designed without making any restrictions on the structure this general quantizer is hard to implement due to lack of structure but is optimal if the iterative design algorithm does not encounter local minima through numerical simulations we illustrate that the two quantizers designed are identical in other words the optimal quantizer structure is that of an sfq for a distributed estimation setup designing identical quantizers is shown to be suboptimal we therefore propose a joint multiple quantizer design algorithm based on a person by person optimization technique employing the sfq structure using numerical examples we illustrate the gain in performance due to designing nonidentical quantizers

a thermodynamically motivated implicit gradient damage framework and its application to brick masonry cracking a new gradient damage model is derived starting from thermodynamic statements nonstandard terms are added to the free energy potential for this purpose in contrast with existing approaches these terms are related to the kinematics of the problem and therefore come into play already in the elastic regime following the argument that the second law of thermodynamics need only be satisfied globally for a nonlocal continuum an energy balance equation is derived which must be solved together with the usual equilibrium equations numerical solutions of this coupled set of equations have been generated for a one dimensional problem in order to study the localisation behaviour of the new model in the limit where the elastic modulus related to the energy balance goes to 0 an earlier gradient damage model is retrieved this simplified model is used to study cracking of brick masonry under the influence of mechanical loading

uniqueness studies in boundary value problems involving some second gradient models abstract enhanced models such as second gradient models have been mainly theoretically developed during the sixties and the seventies new attention has been paid to these models recently when it has been recognized that classical inelastic constitutive equations especially the ones not obeying a normality rule induce ill posed boundary value problems however little work has been done to study the well posedness properties of boundary value problems involving these enhanced models the aim of this paper is a partial study of this point only uniqueness of solution of numerical discretization of boundary value problems involving second gradient models is considered we extend to second gradient models a numerical search method to find non uniqueness already established for classical media in the case of loss of uniqueness for the underlying model our numerical results show clearly that in some cases uniqueness is lost for second gradient model as well it seems that second gradient extensions of classical models do not restore the uniqueness properties but only the objectivity of the numerical computation finally our numerical experiments show once more that post peak behavior is a structural effect they also suggest that some constitutive equations often used in geomaterials modeling may be questionable and may not be complete because even adding second gradient enhancement to these models yields non unique solutions

subgrid interaction and micro randomness novel invariance requirements in infinitesimal gradient elasticity abstract we present a micromechanically motivated form of the curvature energy in infinitesimal isotropic gradient elasticity the basis is a homogenization averaging scheme using a micro randomness assumption imposed on a directional higher gradient interaction term these directional interaction terms are matrix valued allowing to apply the standard orthogonal cartan lie algebra decomposition averaging over all subgrid directions leads to three quadratic curvature terms which are conformally invariant when neglecting volumetric effects restricted to rotational inhomogeneities we motivate thereby a symmetric couple stress tensor in the infinitesimal indeterminate couple stress model of koiter mindlin toupin type relations are established to a novel conformally invariant linear cosserat model

a micropolar formulation of the desai hierarchical model for elastoplastic porous media in this contribution the desai hierarchical model is extended to the case of 3d elasto plastic two phase micropolar continuum an unconditionally stable implicit euler backward algorithm for integration of the constitutive relations is developed and presented in detail the regularizing effect of the introduction of a length parameter to the classical desai model is demonstrated by means of several case studies of single phase and two phase porous media

on thermoelastostatics of composites with nonlocal properties of constituents ii estimation of effective material and field parameters abstract one considers a linear thermoelastic composite medium which consists of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated heterogeneities it is assumed that the stress strain constitutive relations of constituents are described by the nonlocal integral operators whereas the equilibrium and compatibility equations remain unaltered as in classical local elasticity the general integral equations connecting the stress and strain fields in the point being considered and the surrounding points are obtained the method is based on a centering procedure of subtraction from both sides of a known initial integral equation their statistical averages obtained without any auxiliary assumptions such as e g effective field hypothesis implicitly exploited in the known centering methods in a simplified case of using of the effective field hypothesis for analyzing composites with one sort of heterogeneities one proves that the effective moduli explicitly depend on both the strain and stress concentrator factor for one heterogeneity inside the infinite matrix and does not directly depend on the elastic properties local or nonlocal of heterogeneities in such a case the levin s 1967 formula in micromechanics of composites with locally elastic constituents is generalized to their nonlocal counterpart a solution of a volume integral equation for one heterogeneity subjected to inhomogeneous remote loading inside an infinite matrix is proposed by the iteration method the operator representation of this solution is incorporated into the new general integral equation of micromechanics without exploiting of basic hypotheses of classical micromechanics such as both the effective field hypothesis and ellipsoidal symmetry assumption quantitative estimations of results obtained by the abandonment of the effective field hypothesis are presented

attacks on sensor network parameter estimation with quantization performance and asymptotically optimum processing byzantine attacks on sensor systems estimating the value of an unknown deterministic parameter based on quantized observations are studied initially asymptotically optimum processing is investigated for the family of attacks that would pass bad data detectors at the sensors bad data detectors check that the sensor data fits the models employed by the estimation approach when it assumes no attack is present it is then shown that it is possible to identify the attacked sensors under stated assumptions with perfect accuracy as the number of observations k from each sensor tends to infinity if the number of sensors tends to infinity while having a finite k it is shown that the attacked sensors can be identified with a given accuracy that can be set by k allowing considerable design flexibility next the performance of any estimation approach employed by the sensor system under any general attack is described for cases where any number of observations and sensors are employed a classification for these general attacks which categorizes them according to the information available to the attacking entity is introduced solving optimization problems over these attack classes leads to expressions which describe the performance of any specific estimation algorithm under the most devastating attacks with full information and the generally less effective information free attacks constraints are considered to account for some attack detection performed by the sensor system

on thermoelastostatics of composites with nonlocal properties of constituents i general representations for effective material and field parameters abstract a theory of thermoelastic composites with nonlocal properties of constituents is analyzed for multiphase elastic solids of arbitrary geometry and material symmetry due to their generality one uses the nonlocal integral models because the gradient models are usually derived as approximations of corresponding integral models in the immediate infinitely closed vicinity of the point being considered one explores a simplified theory for linear macroscopically elasticity which differs from the classical local theory in the stress strain constitutive relation only whereas the equilibrium and compatibility equations remain unaltered one obtains the new representation of the effective modulus and compliance through the mechanical influence function which does not explicitly depend as opposed to its local counterpart on the elastic operators of constituents the representations for the effective eigenstrains and eigenstresses through either the mechanical influence functions or transformation influence functions are presented the effective strain energy and potential energy are expressed in terms of only average values of the state variables and the effective properties representations of both the first and second statistical moments of stress and strain fields in the constituents are also performed many of the results were obtained as the straightforward generalizations of their local counterparts because the methods used for obtaining the mentioned results widely exploit the hill s 1963 condition which holds for any compatible strain field and equilibrium stress field not necessarily related to each other by a specific stress strain relation

strain gradient solution for a finite domain eshelby type plane strain inclusion problem and eshelby s tensor for a cylindrical inclusion in a finite elastic matrix abstract a solution for the finite domain eshelby type inclusion problem of a finite elastic body containing a plane strain inclusion prescribed with a uniform eigenstrain and a uniform eigenstrain gradient is derived in a general form using a simplified strain gradient elasticity theory ssget the formulation is facilitated by an extended betti s reciprocal theorem and an extended somigliana s identity based on the ssget and suitable for plane strain problems the disturbed displacement field is obtained in terms of the ssget based green s function for an infinite plane strain elastic body which differs from that in earlier studies using the three dimensional green s function the solution reduces to that of the infinite domain inclusion problem when the boundary effect is suppressed the problem of a cylindrical inclusion embedded concentrically in a finite plane strain cylindrical elastic matrix of an enhanced continuum is analytically solved for the first time by applying the general solution with the eshelby tensor and its average over the circular cross section of the inclusion obtained in closed forms this eshelby tensor being dependent on the position inclusion size matrix size and a material length scale parameter captures the inclusion size and boundary effects unlike existing ones it reduces to the classical elasticity based eshelby tensor for the cylindrical inclusion in an infinite matrix if both the strain gradient and boundary effects are not considered numerical results quantitatively show that the inclusion size effect can be quite large when the inclusion is very small and that the boundary effect can dominate when the inclusion volume fraction is very high however the inclusion size effect is diminishing with the increase of the inclusion size and the boundary effect is vanishing as the inclusion volume fraction becomes sufficiently low

elastic field of a spherical inclusion with non uniform eigenfields in second strain gradient elasticity in this paper within the complete form of mindlin s second strain gradient theory the elastic field of an isolated spherical inclusion embedded in an infinitely extended homogeneous isotropic medium due to a non uniform distribution of eigenfields is determined these eigenfields in addition to eigenstrain comprise eigen double and eigen triple strains after the derivation of a closed form expression for green s function associated with the problem two different cases of non uniform distribution of the eigenfields are considered as follows i radial distribution i e the distributions of the eigenfields are functions of only the radial distance of points from the centre of inclusion and ii polynomial distribution i e the distributions of the eigenfields are polynomial functions in the cartesian coordinates of points while the obtained solution for the elastic field of the latter case takes the form of an infinite series the solution to the former case is represented in a closed form moreover eshelby s tensors associated with the two mentioned cases are obtained

numerical algorithms and mesh dependence in the disturbed state concept the disturbed state concept dsc provides a unified approach for constitutive modelling of engineering materials including such factors as elastic plastic and creep strains microcracking damage and softening and sti ening responses the interacting mechanisms in the material mixture composed of the relative intact and fully adjusted states provide implicitly for various factors such as microcrack interaction and character istic dimension the dsc model can allow for well posedness reduction or elimination of spurious mesh dependence and localization a number of problems are solved to illustrate convergence and uniqueness of the finite element procedures localization spurious mesh dependence and validation with respect to observed behavior of simulated and practical problems 1997 by john wiley sons ltd

hyperplane based vector quantization for distributed estimation in wireless sensor networks this paper considers distributed estimation of a vector parameter in the presence of zero mean additive multivariate gaussian noise in wireless sensor networks due to stringent power and bandwidth constraints vector quantization is performed at each sensor to convert its local noisy vector observation into one bit of information which is then forwarded to a fusion center where a final estimate of the vector parameter is obtained within such a context this paper focuses on a class of hyperplane based vector quantizers which linearly convert the observation vector into a scalar by using a compression vector and then carry out a scalar quantization it is shown that the key of the vector quantization design is to find a compression vector for each sensor under the framework of the cramer rao bound crb analysis the compression vector design problem is formulated as an optimization problem that minimizes the trace of the crb matrix such an optimization problem is extensively studied in particular an efficient iterative algorithm is developed for the general case along with optimal and near optimal solutions for some specific but important noise scenarios performance analysis and simulation results are carried out to illustrate the effectiveness of the proposed scheme

theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity the paper presents the theory and the numerics of a thermodynamically consistent formulation of gradient plasticity at small strains starting from the classical local continuum formulation which fails to produce physically meaningful and numerically converging results within localization computations a thermodynamically motivated gradient plasticity formulation is envisioned the model is based on an assumption for the helmholtz free energy incorporating the gradient of the internal history variable a yield condition and the postulate of maximum dissipation resulting in an associated structure as a result the driving force conjugated to the hardening evolution is identified as the quasi non local drag stress which incorporates besides the strictly local drag stress essentially the divergence of a vectorial hardening flux at the numerical side besides the balance of linear momentum the algorithmic consistency condition has to be solved in weak form thereby the crucial issue is the determination of the active constraints exhibiting plastic loading which is solved by an active set search algorithm borrowed from convex non linear programming moreover different discretization techniques are proposed in order to compare the fe performance in local plasticity with the advocated gradient formulation both for hardening and softening copyright 2001 john wiley sons ltd

spectral analysis of localization in nonlocal and over nonlocal materials with softening plasticity or damage the paper shows that spectral wave propagation analysis reveals in a simple and clear manner the effectiveness of various regularization techniques for softening materials i e materials for which the yield limits soften as a function of the total strain both plasticity and damage models are considered it is verified analytically in a simple way that the nonlocal integral type model with degrading yield limit depending on the total strain works correctly if and only one adopts an unconventional nonlocal formulation introduced in 1994 by vermeer and brinkgreve and in 1996 by planas and by stromberg and ristinmaa which is here called for the sake of brevity over nonlocal because it uses a linear combination of local and nonlocal variables in which a negative weight imposed on the local variable is com pensated by assigning to the nonlocal variable weight greater than 1 this is equivalent to a nonlocal variable with a smooth positive weight function of total weight greater than 1 normalized by superposing a negative delta function spike at the center the spectral approach readily confirms that the nonlocal integral type generalization of softening plasticity with an additive format gives correct localization properties only if an over nonlocal formulation is adopted by contrast the nonlocal integral type generalization of softening plasticity with a multiplicative format provides real istic localization behavior just like the nonlocal integral type damage model and thus does not necessitate an over non local formulation the localization behavior of explicit and implicit gradient type models is also analyzed a simple analysis shows that plasticity and damage models with gradient type localization limiter whether explicit or implicit have very different localization behaviors 2005 elsevier ltd all rights reserved

a micromechanics based approach for the derivation of constitutive elastic coefficients of strain gradient media a micromechanics based approach for the derivation of the effective properties of periodic linear elastic composites which exhibit strain gradient effects at the macroscopic level is presented at the local scale all phases of the composite obey the classic equations of three dimensional elasticity but since the assumption of strict separation of scales is not verified the macroscopic behavior is described by the equations of strain gradient elasticity the methodology uses the series expansions at the local scale for which higher order terms which are generally neglected in standard homogenization framework are kept in order to take into account the microstructural effects an energy based micro macro transition is then proposed for upscaling and constitutes in fact a generalization of the hill mandel lemma to the case of higher order homogenization problems the constitutive relations and the definitions for higher order elasticity tensors are retrieved by means of the state law associated to the derived macroscopic potential as an illustration purpose we derive the closed form expressions for the components of the gradient elasticity tensors in the particular case of a stratified periodic composite for handling the problems with an arbitrary microstructure a fft based computational iterative scheme is proposed in the last part of the paper its efficiency is shown in the particular case of composites reinforced by long fibers

bandwidth constrained distributed estimation for wireless sensor networks part i gaussian case we study deterministic mean location parameter estimation when only quantized versions of the original observations are available due to bandwidth constraints when the dynamic range of the parameter is small or comparable with the noise variance we introduce a class of maximum likelihood estimators that require transmitting just one bit per sensor to achieve an estimation variance close to that of the clairvoyant sample mean estimator when the dynamic range is comparable or larger than the noise standard deviation we show that an optimum quantization step exists to achieve the best possible variance for a given bandwidth constraint we will also establish that in certain cases the sample mean estimator formed by quantized observations is preferable for complexity reasons we finally touch upon algorithm implementation issues and guarantee that all the numerical maximizations required by the proposed estimators are concave

atomistic viewpoint of the applicability of microcontinuum theories abstract microcontinuum field theories including micromorphic theory microstructure theory micropolar theory cosserat theory nonlocal theory and couple stress theory are the extensions of the classical field theories for the applications in microscopic space and time scales they have been expected to overlap atomic model at microscale and encompass classical continuum mechanics at macroscale this work provides an atomic viewpoint to examine the physical foundations of those well established microcontinuum theories and to justify their applicability through lattice dynamics and molecular dynamics

gradient plasticity theory with a variable length scale parameter the definition and magnitude of the intrinsic length scale are keys to the development of the gradient plasticity theory that incorporates size effects however a fixed value of the material length scale is not always realistic and different problems could require different values moreover a linear coupling between the local and nonlocal terms in the gradient plasticity theory is not always realistic and that different problems could require different couplings this work addresses the proper modifications required for the full utility of the current gradient plasticity theories in solving the size effect problem it is shown that the current gradient plasticity theories do not give sound interpretations of the size effects in micro bending and micro torsion tests if a definite and fixed length scale parameter is used a generalized gradient plasticity model with a non fixed length scale parameter is proposed based on dislocation mechanics this model assesses the sensitivity of predictions to the way in which the local and nonlocal parts are coupled or to the way in which the statically stored and geometrically necessary dislocations are coupled in addition a physically based relation for the length scale parameter as a function of the course of deformation and the material microstructural features is proposed the proposed model gives good predictions of the size effect in micro bending tests of thin films and micro torsion tests of thin wires

time and space adaptive methods applied to localization phenomena in empty and saturated micropolar and standard porous materials localization phenomena as e g shear bands occur as a result of local concentrations of plastic strains in small bands of finite width the reason for this behaviour lies in the basic properties of elasto plastic frictional materials where variations of the lode angle together with the non associated plastic dilatation result in local softening effects proceeding from non viscous empty porous materials it is well known that the computation of shear bands reveals an ill posed problem to overcome this behaviour two different regularization strategies are considered which are 1 the inclusion of independent rotational degrees of freedom micropolar formulation and 2 the inclusion of viscosity effects standard formulation by taking into consideration viscoplastic properties of the solid matrix or a viscous pore fluid respectively the numerical treatment furthermore proceeds from time and space adaptive strategies to refine and to coarsen both the time step and the mesh size considering quasi static problems the space discretization yields a dae system of index 1 in the time domain which can be successfully treated by sdirk methods thus allowing for an efficient estimation of the time error and as a consequence for an adaptive time step control in the space domain the present investigation proceeds from an error indicator of zienkiewicz zhu type where smoothened values of the l2 norms of characteristic quantities are compared to the respective discrete values the efficiency of this procedure is demonstrated by the computation of the biaxial experiment on an empty and a liquid saturated porous soil material and of the slope failure problem of a fluid saturated soil copyright 2001 john wiley sons ltd

asymptotically optimum distributed estimation in the presence of attacks distributed estimation of a deterministic mean shift parameter in additive zero mean noise is studied when using quantized data in the presence of byzantine attacks several subsets of sensors are assumed to be tampered with by adversaries using different attacks such that the compromised sensors transmit fictitious data first we consider the task of identifying and categorizing the attacked sensors into different groups according to distinct types of attacks it is shown that increasing the number k of time samples at each sensor and enlarging the size n of the sensor network can both ameliorate the identification and categorization but to different extents as k rightarrow infty the attacked sensors can be perfectly identified and categorized while with finite but sufficiently large k as n rightarrow infty it can be shown that the fusion center can also ascertain the number of attacks and obtain an approximate categorization with a sufficiently small percentage of sensors that are misclassified next in order to improve the estimation performance by utilizing the attacked observations we consider joint estimation of the statistical description of the attacks and the parameter to be estimated after the sensors have been well categorized when using the same quantization approach successfully employed without attacks it can be shown that the corresponding fisher information matrix fim is singular to overcome this a time variant quantization approach is proposed which will provide a nonsingular fim provided that k geq 2 furthermore the fim is employed to provide necessary and sufficient conditions under which utilizing the compromised sensors in the proposed fashion will lead to better estimation performance when compared to approaches where the compromised sensors are ignored

a fundamental limitation on maximum parameter dimension for accurate estimation with quantized data it is revealed that there is a link between the quantization approach employed and the dimension of the vector parameter which can be accurately estimated by a quantized estimation system a critical quantity called inestimable dimension for quantized data idqd is introduced which does not depend on the quantization regions and the statistical models of the observations but instead depends only on the number of sensors and on the precision of the vector quantizers employed by the system it is shown that the idqd describes a quantization induced fundamental limitation on the estimation capabilities of the system to be specific if the dimension of the desired vector parameter is larger than the idqd of the quantized estimation system then the fisher information matrix for estimating the desired vector parameter is singular and moreover there exist infinitely many nonidentifiable vector parameter points in the vector parameter space furthermore it is shown that under some common assumptions on the statistical models of the observations and the quantization system a smaller idqd can be obtained which can specify an even more limiting quantization induced fundamental limitation on the estimation capabilities of the system

functional forms of optimum spoofing attacks for vector parameter estimation in quantized sensor networks estimation of an unknown deterministic vector from quantized sensor data is considered in the presence of spoofing attacks which alter the data presented to several sensors contrary to the previous work a generalized attack model is employed which manipulates the data using transformations with arbitrary functional forms determined by some attack parameters whose values are unknown to the attacked system for the first time necessary and sufficient conditions are provided under which the transformations provide a guaranteed attack performance in terms of cramer rao bound crb regardless of the processing the estimation system employs thus defining a highly desirable attack interestingly these conditions imply that for any such attack when the attacked sensors can be perfectly identified by the estimation system either the fisher information matrix fim for jointly estimating the desired and attack parameters is singular or that the attacked system is unable to improve the crb for the desired vector parameter through this joint estimation even though the joint fim is nonsingular it is shown that it is always possible to construct such a highly desirable attack by properly employing a sufficiently large dimension attack vector parameter relative to the number of quantization levels employed which was not observed previously to illustrate the theory in a concrete way we also provide some numerical results which corroborate that under the highly desirable attack attacked data are not useful in reducing the crb

variational principles for softening gradient dependent plasticity abstract a gradient dependent plasticity model is analysed in which the yield function not only depends on the stress tensor and an invariant plastic strain measure but also on the spatial derivatives of the latter quantity a minimum variational principle is obtained by analysing the structure discretized into sufficiently small plastic elements and thus the uniqueness of fe solutions can be ensured for softening plasticity the positive definiteness of the variational functional is determined only by the sign of the diffuse coefficient associated with the highest order derivative of the plastic multiplier in the yield function in order to adopt mix hybrid elements several general variational principles are obtained by relaxing the associated constraints on the displacement strain stress and or plastic multiplier gradient radiation fields

couple stress based strain gradient theory for elasticity the deformation behavior of materials in the micron scale has been experimentally shown to be size dependent in the absence of stretch and dilatation gradients the size dependence can be explained using classical couple stress theory in which the full curvature tensor is used as deformation measures in addition to the conventional strain measures in the couple stress theory formulation only conventional equilibrium relations of forces and moments of forces are used the couple s association with position is arbitrary in this paper an additional equilibrium relation is developed to govern the behavior of the couples the relation constrained the couple stress tensor to be symmetric and the symmetric curvature tensor became the only properly conjugated high order strain measures in the theory to have a real contribution to the total strain energy of the system on the basis of this modification a linear elastic model for isotropic materials is developed the torsion of a cylindrical bar and the pure bending of a flat plate of infinite width are analyzed to illustrate the effect of the modification

an algorithm and a method to search bifurcation points in non linear problems this paper is devoted to a numerical method able to help the determination of the bifurcation threshold in non linear time independent continuum mechanic problems first some theoretical results about uniqueness are recalled in the framework of the large strain assumption the differences between the classical finite step problem and the rate problem are presented an iterative algorithm able to solve the rate problem is given using different initializations it is seen in some numerical experiments that it is possible with this algorithm to get different solutions when the underlying mathematical problem solved does not enjoy a uniqueness property the constitutive equations used have been chosen to be simple enough to deduce some theoretical knowledge about the corresponding uniqueness problems finally a method is given which is able in some case to give an upper bound of the bifurcation threshold copyright 2001 john wiley sons ltd

non local yield limit degradation presented is a new type of a non local continuum model which avoids problems of convergence at mesh refinement and spurious mesh sensitivity in a softening continuum characterized by degradation of the yield limit the key idea which has recently been proposed in a general context and has already been applied to softening damage due to stiffness degradation is to apply the non local concept only to those parameters which cause the degradation while keeping the definition of the strains local compared to the previously advanced fully non local continuum formulation the new approach has the advantage that the stresses are subjected to the standard differential equations of equilibrium and standard boundary or interface conditions the new formulation exhibits no zero energy periodic modes imbrication of finite elements is unnecessary and finite elements with standard continuity requirements are sufficient two dimensional finite element solutions with up to 3248 degrees of freedom are presented to document convergence and efficacy the formulation is applied to tunnel excavation in a soil stabilized by cement grouting with the objective of preventing cave in burst of the tunnel sides due to compression softening

a new formulation and 0 implementation of dynamically consistent gradient elasticity in his article a special form of gradient elasticity is presented that can be used to describe wave dispersion this new format of gradient elasticity is an appropriate dynamic extension of the earlier static counterpart of the gradient elasticity theory advocated in the early 1990s by aifantis and co workers in order to capture dispersion of propagating waves both higher order inertia and higher order stiffness contributions are included a fact which implies and is denoted as dynamic consistency the two higher order terms are accompanied by two associated length scales to facilitate finite element implementations the model is rewritten such that 0 continuity of the interpolation is sufficient an auxiliary displacement field is introduced which allows the original fourth order equations to be split into two coupled sets of second order equations positive definiteness of the kinetic energy requires that the inertia length scale is larger than the stiffness length scale the governing equations boundary conditions and the discretized system of equations are presented finally dispersive wave propagation in a one dimensional bar is considered in a numerical example copyright 2007 john wiley sons ltd

inclusions and inhomogeneities in strain gradient elasticity with couple stresses and related problems abstract at small length scales and or in presence of large field gradients the implicit long wavelength assumption of classical elasticity breaks down postulating a form of second gradient elasticity with couple stresses as a suitable phenomenological model for small scale elastic phenomena we herein extend eshelby s classical formulation for inclusions and inhomogeneities while the modified size dependent eshelby s tensor and hence the complete elastic state of inclusions containing transformation strains or eigenstrains is explicitly derived the corresponding inhomogeneity problem leads to integrals equations which do not appear to have closed form solutions to that end eshelby s equivalent inclusion method is extended to the present framework in form of a perturbation series that then can be used to approximate the elastic state of inhomogeneities the approximate scheme for inhomogeneities also serves as the basis for establishing expressions for the effective properties of composites in second gradient elasticity with couple stresses the present work is expected to find application towards nano inclusions and certain types of composites in addition to being the basis for subsequent non linear homogenization schemes

gradient elastic stress analysis near cylindrical holes in a plane under bi axial tension fields abstract this paper is devoted to a gradient elastic stress analysis of an infinite plate weakened by a cylindrical hole and subjected to two perpendicular and independent uni axial tensions at infinity the problem setting can be considered as an extension and generalization of the well known kirsch problem of the classical elasticity theory which is here extended with respect to the external loadings and generalized with respect to the continuum framework a closed form solution in terms of displacements is derived for the problem within the strain gradient elasticity theory on plane stress strain assumptions the main characters of the total and cauchy stress fields are analyzed near the circumference of the hole for different combinations of bi axial tensions and for different parameter values for the original kirsch problem concerning a uni axially stretched plate the analytical solution fields for stresses and strains are compared to numerical results these results are shown to be in a full agreement with each other and in particular they reveal a set of new qualitative findings about the scale dependence of the stresses and strains provided by the gradient theory not common to the classical theory based on these findings we finally consider the physicalness of the concepts total and cauchy stress appearing in the strain gradient model

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

post necking behaviour modelled by a gradient dependent plasticity theory abstract the delay of the onset of localization and the post necking behaviour for stretched thin sheets are determined by three dimensional effects thus a 2 d finite element analysis based on a local plasticity theory will give a physically unrealistic mesh dependent solution this in spite of the fact that the stress state is essentially two dimensional by incorporating a length scale with relation to the thickness of the sheet it is demonstrated how a 2 d finite element analysis based on a gradient dependent plasticity theory can give a good approximation of the post necking behaviour this is illustrated by numerical comparison of results from a full 3 d finite element analysis with results from a 2 d finite element model based on a finite strain version of a gradient dependent j 2 flow theory some numerical problems in the modeling will be discussed briefly

infinitesimal elastic plastic cosserat micropolar theory modelling and global existence in the rate independent case in this article we investigate the regularizing properties of generalized continua of cosserat micropolar type in the elasto plastic case we propose an extension of classical infinitesimal elasto plasticity to include consistently non dissipative micropolar effects it is shown that the new model is thermodynamically admissible and allows for a unique global in time solution of the corresponding rate independent initial boundary value problem the method of choice is the yosida approximation and a passage to the limit

theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage this paper presents the theory and the numerics of an isotropic gradient damage formulation within a thermodynamical background the main motivation is provided by localization computations whereby classical local continuum formulations fail to produce physically meaningful and numerically converging results we propose a formulation in terms of the helmholtz free energy incorporating the gradient of the damage field a dissipation potential and the postulate of maximum dissipation as a result the driving force conjugated to damage evolution is identified as the quasi nonlocal energy release rate which essentially incorporates the divergence of a vectorial damage flux besides the strictly local energy release rate on the numerical side besides balance of linear momentum the algorithmic consistency condition must be solved in weak form thereby the crucial issue is the selection of active constraints which is solved by an active set search algorithm borrowed from convex nonlinear programming in the examples we compare the behavior in local damage with the performance of the gradient formulation

solution of general integral equations of micromechanics of heterogeneous materials one considers a linear composite materials cm which consists of a homogeneous matrix containing a random set of heterogeneities an operator form of solution of the general integral equation gie for the general cases of local and nonlocal problems static and wave motion phenomena for composite materials with random statistically homogeneous and inhomogeneous so called graded structures containing coated or uncoated inclusions of any shape and orientation with perfect and imperfect interfaces and subjected to any number of coupled or uncoupled homogeneous or inhomogeneous external fields of different physical nature the gie connecting the driving fields and fluxes in a point being considered and the fields in the surrounding points are obtained for the random fields of heterogeneities in the infinite media estimations of the effective properties and both the first and second statistical moments of fields in the constituents of cms are presented in a general form of perturbations introduced by the heterogeneities and taking into account a possible imperfection of interface conditions the solution methods of gies are obtained without any auxiliary assumptions such as the effective field hypothesis efh which is implicitly exploited in the known methods of micromechanics some particular cases asymptotic representations and simplifications of proposed methods are presented for the particular constitutive equations such as linear thermoelastic cases with the perfect and imperfect interfaces conductivity problem problems for piezoelectric and other coupled phenomena composites with nonlocal elastic properties of constituents and the wave propagation in composites with electromagnetic optic and mechanical responses

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

meshfree analysis of softening elastoplastic solids using variational multiscale method a meshfree multiscale method is presented for efficient analysis of elastoplastic solids in the analysis of softening elastoplastic solids standard finite element methods or meshfree methods typically yield mesh dependent results the reason for this well known effect is the loss of ellipticity of the boundary value problem in this work the scale decomposition is carried out based on a variational form of the problem a coarse scale is designed to represent global behavior and a fine scale to represent local behavior a fine scale region is detected from the local failure analysis of an acoustic tensor to indicate a region where deformation changes abruptly each scale variable is approximated using a meshfree method meshfree approximation is well suited for adaptivity as a method of increasing the resolution a partition of unity based extrinsic enrichment is used in particular fine scale approximations are designed to appropriately represent local behavior by using a localization angle moreover the regularization effect through the convexification of non convex potential is embedded to represent fine scale behavior each scale problem is solved iteratively the proposed method is applied to shear band problems in the results of analysis about pure shear and compression problems straight shear bands can be captured and mesh insensitive results are obtained curved shear bands can also be captured without mesh dependency in the analysis of indentation problem

the mechanically based approach to 3d non local linear elasticity theory long range central interactions abstract this paper presents the generalization to a three dimensional 3d case of a mechanically based approach to non local elasticity theory recently proposed by the authors in a one dimensional 1d case the proposed model assumes that the equilibrium of a volume element is attained by contact forces between adjacent elements and by long range forces exerted by non adjacent elements specifically the long range forces are modelled as central body forces depending on the relative displacement between the centroids of the volume elements measured along the line connecting the centroids further the long range forces are assumed to be proportional to a proper material dependent distance decaying function and to the products of the interacting volumes consistently with the modelling of the long range forces as central body forces the static boundary conditions enforced on the free surface of the solid involve only local stress due to contact forces the proposed 3d formulation is developed both in a mechanical and in a variational context for this the elastic energy functionals of the solid with long range interactions are introduced based on the principle of virtual work to set the proper correspondence between the mechanical and the kinematic variables of the model numerical applications are reported for 2d solids under plane stress conditions

global existence results for viscoplasticity at finite strain we study a model for rate dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor and investigate the existence of global in time solutions to the related pde system we reveal its underlying structure as a generalized gradient system where the driving energy functional is highly nonconvex and features the geometric nonlinearities related to finite strain elasticity as well as the multiplicative decomposition of finite strain plasticity moreover the dissipation potential depends on the left invariant plastic rate and thus depends on the plastic state variable the existence theory is developed for a class of abstract nonsmooth and nonconvex gradient systems for which we introduce suitable notions of solutions namely energy dissipation balance and energy dissipation inequality solutions hence we resort to the toolbox of the direct method of the calculus of variations to check that the specific energy and dissipation functionals for our viscoplastic models comply with the conditions of the general theory

a formulation for the micromorphic continuum at finite inelastic strains the paper presents a generalized theory of deformation which can capture scale effects also in a homogenously deforming body scale effects are relevant when the dimensions of the specimen or structure themselves are in the micron and submicron scale but also when it comes to high strain concentrations as in the case of localised shear bands or at crack tips etc in this context so called generalized continuum formulations have been proven to provide remedy as they allow for the incorporation of internal length scale parameters which reflect the micro structural influence on the macroscopic material response here we want to adopt a generalized continuum framework which is based on the mathematical description of a combined macro and micro space sansour 1998b the approach introduces additional degrees of freedom which constitute a so called micromorphic deformation first the treatment presented is general in nature but will be specified for the sake of an example and the number of extra degrees of freedom will be reduced to four based on the generalized deformation description new strain and stress measures are defined which lead to the formulation of a corresponding generalized variational principle the theory is completed by dirichlet boundary conditions for the displacement field of great advantage is the fact that the constitutive law is defined in the generalized space but can be classical otherwise this limits the number of the extra material parameters necessary to those needed for the specification of the micro space in the example presented to only one an example of scale effects in a homogenously deforming specimen and a further example of shearband formation are presented where the constitutive law is a classical viscoplastic one

energy relaxation of non convex incremental stress potentials in a strain softening elastic plastic bar abstract we propose a fundamentally new concept to the treatment of material instabilities and localization phenomena based on energy minimization principles in a strain softening elastic plastic bar the basis is a recently developed incremental variational formulation of the local constitutive response for generalized standard media it provides a quasi hyperelastic stress potential that is obtained from a local minimization of the incremental energy density with respect to the internal variables the existence of this variational formulation induces the definition of the material stability of inelastic solids based on convexity properties in analogy to treatments in elasticity furthermore localization phenomena are understood as micro structure development associated with a non convex incremental stress potential in analogy to phase decomposition problems in elasticity for the one dimensional bar considered the two phase micro structure can analytically be resolved by the construction of a sequentially weakly lower semicontinuous energy functional that envelops the not well posed original problem this relaxation procedure requires the solution of a local energy minimization problem with two variables which define the one dimensional micro structure developing the volume fraction and the intensity of the micro bifurcation the relaxation analysis yields a well posed boundary value problem for an objective post critical localization analysis the performance of the proposed method is demonstrated for different discretizations of the elastic plastic bar which document on the mesh independence of the results

gradient dependent plasticity formulation and algorithmic aspects a plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure hardening parameter but also on the laplacian thereof the consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity to properly solve the set of non linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements for appropriate boundary conditions this formulation can also be derived from a variational principle accordingly the theory is complete

gradient damage models toward full scale computations abstract the description of localisation and structural failure through local damage constitutive laws leads to ill posed problems to retrieve a well posed problem the material state is described through the gradients of damage in addition to the strain and the damage under some assumptions it is shown that these gradient laws can be cast into a variational formulation its numerical treatment is reduced to the design of a mixed finite element so that algorithms such as newton s method and path following techniques are still available possible convergence difficulties related to the reduction of the damage band width and the appearance of micro instabilities are removed thanks to the design of a new class of brittle laws finally numerical applications show the convergence with mesh refinement the compatibility with coarser approaches such as griffith s theory and cohesive crack models the robustness in case of unstable multi cracking the applicability to full scale 3d situations and the physical relevance compared to experimental data

limit theorems for gradient dependent elastoplastic geomaterials in this paper the limit theorems proposed by drucker and co workers are reformulated to address a class of gradientdependent elastoplastic geomaterials the gradient effects are accounted for by incorporating strain gradients and their conjugate higher order stresses into the constitutive descriptions gradient dependent equilibrium equations and higher order boundary conditions are defined for both statically admissible and kinematically admissible states and the associated lower bound and upper bound theories are recast for the gradient enhanced limit theorems a generalised drucker prager yield criterion that includes the gradient influence on the deviatoric stress is proposed and then employed to investigate the collapse loads for soil layers under conditions of generalised plane strain simple shear and uniaxial compression the corresponding lower and upper bounds are found for these problems it is demonstrated that the predicted collapse bounds are generally dependent on both the conventional and gradient properties with normalised length scale s being present in the results this feature enables us to give physically reasonable interpretations for size effects and shear banding during material collapse comparisons are also made between the gradient dependent bounds and those obtained through conventional plasticity theories influences of model parameters and sample dimensions on the predictions are also discussed it is shown that the proposed gradient dependent limit theorems can be used to provide physically meaningful predictions for general geotechnical applications 2006 elsevier ltd all rights reserved

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

modeling strong discontinuities at finite strains a novel numerical implementation abstract in this paper a finite element formulation suitable for the modeling of locally embedded strong discontinuities at finite strains is presented following the enhanced assumed strain concept eas the proposed numerical model is based on an additive decomposition of the displacement gradient into a conforming and an enhanced part the enhanced part is associated with the final failure kinematics of solids which are approximated by means of a discontinuous displacement field strong discontinuities referring to the displacement jump no special assumption such as purely mode i or mode ii failure is made the same holds for the class of interface laws considered which govern the evolution of the displacement discontinuity in terms of the traction vector acting at the surface of strong discontinuities consequently the suggested numerical framework can be applied to a broad range of different interface laws including damage based models in contrast to previous works the presented finite element formulation does not require the static condensation technique to be employed more precisely instead of computing the conforming part of deformation and the displacement jump simultaneously from the weak form of equilibrium and the weak form of traction continuity the different parts of the local deformation are decomposed according to a predictor corrector algorithm the proposed predictor and the corrector step are formally identical to that of classical computational plasticity models hence subroutines designed for standard models continuous deformation can be applied with only minor modifications necessary the applicability as well as the performance of the resulting finite element formulation are demonstrated by means of a fully three dimensional analysis of shear band formation in a bar made of a ductile material

variational formulation of a simplified strain gradient elasticity theory and its application to a pressurized thick walled cylinder problem abstract a detailed variational formulation is provided for a simplified strain gradient elasticity theory by using the principle of minimum total potential energy this leads to the simultaneous determination of the equilibrium equations and the complete boundary conditions of the theory for the first time to supplement the stress based formulation the coordinate invariant displacement form of the simplified strain gradient elasticity theory is also derived anew in view of the lack of a consistent and complete formulation derivation details are included for the tutorial purpose it is shown that both the stress and displacement forms of the simplified strain gradient elasticity theory obtained reduce to their counterparts in classical elasticity when the strain gradient effect a measure of the underlying material microstructure is not considered as a direct application of the newly obtained displacement form of the theory the problem of a pressurized thick walled cylinder is analytically solved the solution contains a material length scale parameter and can account for microstructural effects which is qualitatively different from lame s solution in classical elasticity in the absence of the strain gradient effect this strain gradient elasticity solution reduces to lame s solution the numerical results reveal that microstructural effects can be large and lame s solution may not be accurate for materials exhibiting significant microstructure dependence

target location estimation in sensor networks with quantized data a signal intensity based maximum likelihood ml target location estimator that uses quantized data is proposed for wireless sensor networks wsns the signal intensity received at local sensors is assumed to be inversely proportional to the square of the distance from the target the ml estimator and its corresponding crameacuter rao lower bound crlb are derived simulation results show that this estimator is much more accurate than the heuristic weighted average methods and it can reach the crlb even with a relatively small amount of data in addition the optimal design method for quantization thresholds as well as two heuristic design methods are presented the heuristic design methods which require minimum prior information about the system prove to be very robust under various situations

strain gradient theory of chiral cosserat thermoelasticity without energy dissipation in this paper we use the green naghdi theory of thermomechanics of continua to derive a linear strain gradient theory of cosserat thermoelastic bodies the theory is capable of predicting a finite speed of heat propagation and leads to a symmetric conductivity tensor the constitutive equations for isotropic chiral thermoelastic materials are presented in this case in contrast with the classical cosserat thermoelasticity a thermal field produces a microrotation of the particles the thermal field is influenced by the displacement and microrotation fields even in the equilibrium theory existence and uniqueness results are established the theory is used to study the effects of a concentrated heat source in an unbounded homogeneous and isotropic chiral solid

numerical approximation of incremental infinitesimal gradient plasticity we investigate a representative model of continuum infinitesimal gradient plasticity the formulation is an extension of classical rate independent infinitesimal plasticity based on the additive decomposition of the symmetric strain tensor into elastic and plastic parts it is assumed that dislocation processes contribute to the storage of energy in the material whereby the curl of the plastic distortion appears in the thermodynamic potential and leads to an additional nonlocal backstress tensor the formulation is cast into a numerical framework by a saddle point approximation of the corresponding minimization problem in each incremental loading step this allows one to reformulate the nonlocal dissipation inequality to a point wise flow rule and yields a solution scheme which is a direct extension of the standard approach in classical plasticity our numerical results show the regularizing effects of the additional physically motivated terms copyright 2008 john wiley sons ltd

noncoherent mimo radar for location and velocity estimation more antennas means better performance this paper presents an analysis of the joint estimation of target location and velocity using a multiple input multiple output mimo radar employing noncoherent processing for a complex gaussian extended target a mimo radar with m transmit and n receive antennas is considered to provide insight we focus on a simplified case first assuming orthogonal waveforms temporally and spatially white noise plus clutter and independent reflection coefficients under these simplifying assumptions the maximum likelihood ml estimate is analyzed and a theorem demonstrating the asymptotic consistency large mn of the ml estimate is provided numerical investigations given later indicate similar behavior for some reasonable cases violating the simplifying assumptions in these initial investigations we study unconstrained systems in terms of complexity and energy where each added transmit antenna employs a fixed energy so that the total transmitted energy is allowed to increase as we increase the number of transmit antennas following this we also look at constrained systems where the total system energy and complexity are fixed to approximate systems of fixed complexity in an abstract way we restrict the total number of antennas employed to be fixed here we show numerical examples which indicate a preference for receive antennas similar to mimo communications but where systems with multiple transmit antennas yield the smallest possible mean square error mse the joint cramer rao bound crb is calculated and the mse of the ml estimate is analyzed it is shown for some specific numerical examples that the signal to clutter plus noise ratio scnr threshold indicating the scnrs above which the mse of the ml estimate is reasonably close to the crb can be lowered by increasing mn the noncoherent mimo radar ambiguity function af is developed in two different ways and illustrated by examples it is shown for some specific examples that the size of the product mn controls the levels of the sidelobes of the af

stiefel whitney classes and the conormal cycle of a singular variety a geometric construction of sullivan s stiefel whitney homology classes of a real analytic variety x is given by means of the conormal cycle of an embedding of x in a smooth variety we prove that the stiefel whitney classes define additive natural transformations from certain constructible functions to homology we also show that for a complex analytic variety these classes are the mod 2 reductions of the chern macpherson classes we present a new definition of the stiefel whitney homology classes of a possibly singular real analytic variety x the original definition due to sullivan s involves a triangulation of x its geometric meaning is unclear our definition uses the conormal cycle of an embedding of x in a smooth variety the conormal cycle of a subanalytic subset x of an analytic manifold m was defined by the first author f4 using geometric measure theory the conormal cycle is an integral current representing up to sign kashiwara s characteristic cycle of the sheaf dmrx f4 4 7 our construction of the stiefel whitney classes is based on the fundamental observation that the conormal cycle of a real analytic variety is antipodally symmetric mod 2 we use this observation to give a definition of stiefel whitney classes which is parallel to the first author s definition of the chern schwartz macpherson classes of a complex analytic variety f5 this definition of chern classes is related to earlier work of brylinski dubson kashiwara bdk and sabbah sa in fact we show that the stiefel whitney homology classes of a complex analytic variety are the mod 2 reductions of the chern classes we prove that our stiefel whitney classes satisfy axioms similar to the deligne grothendieck axioms for chern classes and we prove a specialization formula for the stiefel whitney classes of a family of varieties we show that the stiefel whitney classes of an affine real analytic variety x are represented by the polar cycles of x introduced for simplicial spaces by banchoff b and mccrory mc and we give a new proof of the combinatorial formula for stiefel whitney classes of manifolds our central result is a specialization formula for the conormal cycle theorem 3 7 we use this formula to prove the basic results of kashiwara and schapira s calculus of subanalytically constructible functions sc ks 9 7 as well as the pushforward and specialization formulas for stiefel whitney classes received by the editors october 2 1995 1991 mathematics subject classification primary 14p25 57r20 secondary 14p15 49q15

disturbed state constitutive modeling based on stress strain and nondestructive behavior the proposed disturbed state concept dsc is based on the idea that a deforming material element can be treated as a mixture of two constituent parts in the relative intact ri and fully adjusted fa states referred to as reference states during external loading the material experiences internal changes in its microstructure due to a process of self adjustment and as a consequence the initial ri state transforms continuously to the fa state the self adjustment process which may involve relative motions of material particles that can lead to microcracking and damage or strengthening can cause disturbances in the observed response with respect to the responses under the two reference states then the observed response is expressed in terms of the responses for the ri and fa states that are determined from laboratory tests on material specimens the dsc permits development of unified constitutive models that include hierarchically other previous continuum and damage models as special cases various aspects of the dsc are verified here with respect to laboratory behavior of two materials a cemented sand and a ceramic composite some of the unique features of this study are that 1 the constitutive behavior and parameters can be obtained from the stress strain volume change behavior and from the measurements of ultrasonic p wave velocities 2 correlations between mechanical and ultrasonic response can be established 3 the concept can provide a description of the crack density and 4 it can be simplified for predicting the remaining life of materials through definition of constitutive models and evaluation of design moduli affected by mechanical and environmental loading

an algorithm for gradient regularized plasticity coupled to damage based on a dual mixed fe formulation abstract a thermodynamically consistent theory of gradient regularized plasticity with coupling to isotropic damage was presented by svedberg and runesson 23 its main purpose was to describe the successive development of the localization zone that is pertinent to the softening regime due to excessive damage close to failure explicit constitutive relations were established for a model problem based on von mises plasticity with isotropic hardening of two types local and gradient enhanced the main purpose of this paper is to describe a new numerical algorithm for the gradient enhanced formulation using the backward euler rule leads to a gradient enhanced format of the classical closest point projection method the plastic multiplier increment is solved via a dual mixed method which is a convenient feature in the present context this leads to an unambiguous representation of the constitutive relations in the equilibrium equation moreover the classical local algebraic kuhn tucker conditions are obtained in a straightforward fashion in the limit case of local theory the developed algorithm was implemented in the educational finite element package 5 numerical results are shown for the extension of a plate in plane stress these results demonstrate the convergence characteristics with mesh refinement as well as the salient features of the adopted damage based constitutive model