uncertainty propagation in reduced order models based on crystal plasticity abstract in this work an uncertainty propagation study is performed based on simulated ensembles of statistical volume elements sve used to inform a reduced order internal state variable model focusing on model form and uncertainties in numerical simulations a rate dependent polycrystal plasticity finite element model cp fem of cartridge brass is calibrated to room temperature uniaxial tension testing data of an annealed sample model forms are considered with and without the inclusion of back stress in the cp model three sizes of sve are explored for simulation uncertainty effects effects are explored with regard to the parameters of a bammann chiesa johnson bcj macroscopic viscoplasticity model calibrated element wise to sves from an ensemble modeled using cp fem simulations exploring quasi static uniaxial tension variability in stress strain response at multiple defined length scales is measured the selection of model form is discussed the numerical simulation uncertainty of the model reduction process is quantified

elastic plastic analysis of arbitrary heterogeneous materials with the voronoi cell finite element method abstract in this paper a voronoi cell finite element method is developed to solve small deformation elastic plasticity problems for arbitrary heterogenous materials dirichlet tessellation of microstructural representative materials results in a network of arbitrary sided polygons called voronoi cells each voronoi cell encompasses one second phase heterogeneity at most these are natural elements for the microstructure representing the basic structural elements of the material in this paper formulations are developed for directly considering voronoi cells as elements in a finite element model without any further dissection furthermore a composite voronoi cell finite element method is developed to account for the presence of the second phase within each polygonal element various numerical elastic plastic examples are executed for validating the effectiveness of this formulation finally studies are conducted to understand the effect of size shape and distribution of second phase on the averaged and true local responses of representative material elements

a primal formulation for imposing periodic boundary conditions on conforming and nonconforming meshes abstract a variational multiscale discontinuous galerkin vmdg method is developed for microscale modeling of domains containing conforming and non conforming meshes essentially the product of the applied volume average strain or macro strain and the domain diameter acts as an imposed displacement jump within the vmdg terms hence the method is suitable for modeling deformation of both block and truly self periodic representative volume elements rves the primal displacement field and macro strain are the only unknowns because the method eliminates the lagrange multiplier lm enforcement of the kinematic constraint rigorous derivation of the method provides a framework to accommodate either the macro stress or macro strain as the driver of the microscale boundary value problem the method is developed first for finite deformations and then specialized to small deformation kinematics algorithmic modifications to the method are also studied for their effects on tangent symmetry and convergence rate the results from numerical studies for isotropic and anisotropic materials show that the proposed method is robust accurate stable and variationally consistent for modeling complicated conforming and nonconforming rves

an age structured sir epidemic model with fixed incubation period of infection this paper is devoted to the study of an age structured sir epidemic system on the basis of the model of polycyclic population dynamics of susceptible infected and recovered individuals this model was considered as a nonlinear competitive system of three initialboundary value problems for the nonlinear transport equations with non local integral boundary conditions and discrete time delay fixed incubation period of infection it was obtained the explicit recurrent formulae for computing the traveling wave solution of such system provided the model parameters coefficients of equations and initial values satisfy the restrictions that guarantee the existence and uniqueness of continuous solution using some insignificant simplifications the age structured sir model was reduced to the nonlinear autonomous system of delay ode it was studied the dimensionless indicators and conditions of existence of trivial disease free equilibrium two non trivial endemic equilibriums for the incurable and curable infection induced diseases respectively by carrying out an analysis of the local asymptotical stability of the solution of such system we obtain the restrictions for the time delay that guarantee the stability of solutions in the neighborhood of equilibriums the numerous simulations of dynamics of sir population illustrate the results of theoretical analysis

a nurbs based generalized finite element scheme for 3d simulation of heterogeneous materials a 3d nurbs based interface enriched generalized finite element method nigfem is introduced to solve problems with complex discontinuous gradient fields observed in the analysis of heterogeneous materials the method utilizes simple structured meshes of hexahedral elements that do not necessarily conform to the material interfaces in heterogeneous materials by avoiding the creation of conforming meshes used in conventional fem the nigfem leads to significant simplification of the mesh generation process to achieve an accurate solution in elements that are crossed by material interfaces the nigfem utilizes non uniform rational b splines nurbs to enrich the solution field locally the accuracy and convergence of the nigfem are tested by solving a benchmark problem we observe that the nigfem preserves an optimal rate of convergence and provides additional advantages including the accurate capture of the solution fields in the vicinity of material interfaces and the built in capability for hierarchical mesh refinement finally the use of the nigfem in the computational analysis of heterogeneous materials is discussed development of generalized finite element method for 3d mesoscale modeling of materials with complex microstructures novel nurbs based enrichment functions built in capability to perform hierarchical local mesh refinement method is applicable to engineering problems characterized by discontinuous gradient and complex internal geometry

tame kernels of cubic cyclic fields there are many results describing the structure of the tame kernels of algebraic number fields and relating them to the class numbers of appropriate fields in the present paper we give some explicit results on tame kernels of cubic cyclic fields table 1 collects the results of computations of the structure of the tame kernel for all cubic fields with only one ramified prime p 7 p 5 000 in particular we investigate the structure of the 7 primary and 13 primary parts of the tame kernels the theoretical tools we develop based on reflection theorems and singular primary units enable the determination of the structure even of 7 primary and 13 primary parts of the tame kernels for all fields as above the results are given in tables 2 and 3

quality improvement of non manifold hexahedral meshes for critical feature determination of microstructure materials this paper describes a novel approach to improve the quality of non manifold hexahedral meshes with feature preservation for microstructure materials in earlier works we developed an octree based isocontouring method to construct unstructured hexahedral meshes for domains with multiple materials by introducing the notion of material change edge to identify the interface between two or more materials however quality improvement of non manifold hexahedral meshes is still a challenge in the present algorithm all the vertices are categorized into seven groups and then a comprehensive method based on pillowing geometric flow and optimization techniques is developed for mesh quality improvement the shrink set in the modified pillowing technique is defined automatically as the boundary of each material region with the exception of local non manifolds in the relaxation based smoothing process non manifold points are identified and fixed planar boundary curves and interior spatial curves are distinguished and then regularized using b spline interpolation and resampling grain boundary surface patches and interior vertices are improved as well finally the local optimization method eliminates negative jacobians of all the vertices we have applied our algorithms to two beta titanium datasets and the constructed meshes are validated via a statistics study finite element analysis of the 92 grain titanium is carried out based on the improved mesh and compared with the direct voxel to element technique

gradient elasticity in statics and dynamics an overview of formulations length scale identification procedures finite element implementations and new results in this paper we discuss various formats of gradient elasticity and their performance in static and dynamic applications gradient elasticity theories provide extensions of the classical equations of elasticity with additional higher order spatial derivatives of strains stresses and or accelerations we focus on the versatile class of gradient elasticity theories whereby the higher order terms are the laplacian of the corresponding lower order terms one of the challenges of formulating gradient elasticity theories is to keep the number of additional constitutive parameters to a minimum we start with discussing the general mindlin theory that in its most general form has 903 constitutive elastic parameters but which were reduced by mindlin to three independent material length scales further simplifications are often possible in particular the aifantis theory has only one additional parameter in statics and opens up a whole new field of analytical and numerical solution procedures we also address how this can be extended to dynamics an overview of length scale identification and quantification procedures is given finite element implementations of the most commonly used versions of gradient elasticity are discussed together with the variationally consistent boundary conditions details are provided for particular formats of gradient elasticity that can be implemented with simple linear finite element shape functions new numerical results show the removal of singularities in statics and dynamics as well as the size dependent mechanical response predicted by gradient elasticity

determination of the size of the representative volume element for random composites statistical and numerical approach the representative volume element rve plays a central role in the mechanics and physics of random heterogeneous materials with a view to predicting their effective properties a quantitative definition of its size is proposed in this work a rve size can be associated with a given precision of the estimation of the wanted overall property and the number of realizations of a given volume v of microstructure that one is able to consider it is shown to depend on the investigated morphological or physical property the contrast in the properties of the constituents and their volume fractions the methodology is applied to a specific random microstructure namely a two phase three dimensional voronoi mosaic finite element simulations of volumes of different sizes are performed in the case of linear elasticity and thermal conductivity the volumes are subjected to homogeneous strain stress or periodic boundary conditions the effective properties can be determined for large volumes and a small number of realizations conversely smaller volumes can be used providing that a sufficient number of realizations are considered a bias in the estimation of the effective properties is observed for too small volumes for all types of boundary conditions the variance of computed apparent properties for each volume size is used to define the precision of the estimation the key notion of integral range is introduced to relate this error estimation and the definition of the rve size for given wanted precision and number of realizations one is able to provide a minimal volume size for the computation of effective properties the results can also be used to predict the minimal number of realizations that must be considered for a given volume size in order to estimate the effective property for a given precision the rve sizes found for elastic and thermal properties but also for a geometrical property like volume fraction are compared

the formula of 8 ranks of tame kernels abstract in this paper we always assume that f q d and e q d d a squarefree integer are quadratic number fields with d u 2 2 w 2 u w n this paper is mainly to give the formula 8 rank of k 2 o f 8 rank of c e a f where c e is the narrow class group of e a f 1 0 1 and 0 1 moreover 8 rank of k 2 o f 8 rank of c e 1 this paper is also to show the relations among 1 u d k 2 o f 4 the dyadic ideal class of c e and the dyadic ideal class of c e for e q 2 d

the mathematics of infectious diseases many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases threshold theorems involving the basic reproduction number r 0 the contact number sigma and the replacement number r are reviewed for the classic sir epidemic and endemic models similar results with new expressions for r 0 are obtained for mseir and seir endemic models with either continuous age or age groups values of r 0 and sigma are estimated for various diseases including measles in niger and pertussis in the united states previous models with age structure heterogeneity and spatial structure are surveyed

relating cellular structure of open solid food foams to their young s modulus finite element calculation abstract this paper investigates the role of structure on young s modulus of open cell materials of relative densities between 0 1 and 0 3 the cellular solid is obtained by generating mixture size of spherical voids using the random sequential addition rsa algorithm the relative density of the material is controlled by increasing void number and overlap structural effects consider mainly a gaussian distribution of spherical void size of varying width distribution centre and void overlap distance finite element method is used to calculate effective young s modulus using a regular meshing scheme of 3d typical cellular solids and conjugate gradient solver it is found that sphere overlap has the largest effect compared to sphere distribution width for a given density a large scatter in the wall thickness distribution is predicted when overlapping is increased or when the width of sphere size distribution is decreased increased rigidity is found to be correlated to particular arrangement of mixture size spheres which is pointed out using the pair correlation function experimental evidence of the role of void overlapping is treated in the case of bread crumbs structures determined using x ray tomography the scatter of effective young s modulus for a given relative density is sensitive to void overlapping

fourier based schemes with modified green operator for computing the electrical response of heterogeneous media with accurate local fields a modified green operator is proposed as an improvement of fou rier based numerical schemes commonly used for computing the electrical or thermal response of heterogeneous media contrary to other methods the number of iterations necessary to achieve convergence tends to a finite value when the contrast of properties between the phases becomes infinite furtherm ore it is shown that the method produces much more accurate local field s inside highly conducting and quasi insulating phases as well as in the vicinity of the phases interfaces these good propert ies stem from the discretization of green s function which is consistent with the pixel grid while retaining the local nature of the op erator that acts on the polarization field finally a fast im plementation of the direct scheme of moulinec et al 1994 that allows for parcimonious memory use is proposed

mixed types of waves in a discrete diffusive epidemic model with nonlinear incidence and time delay abstract in this paper we investigate the traveling wave solutions of a discrete diffusive epidemic model with nonlinear incidence and time delay employing the method of upper and lower solutions schauder s fixed point theorem and a limiting approach we prove the existence of bounded super critical and critical traveling wave solutions moreover we obtain the positiveness and asymptotic boundary of the traveling wave solutions which guarantee that the traveling wave solutions are non trivial the existence results show that the traveling waves are mixed of front type and pulse type by way of contradiction and two sided laplace transform we derive the non existence of non trivial positive and bounded traveling wave solutions it is the first time to apply the method of upper and lower solutions together with schauder s fixed point theorem and two sided laplace transform to investigate the existence and non existence of traveling wave solutions for discrete diffusive epidemic models respectively

comparison of full field and single pore approaches to homogenization of linearly elastic materials with pores of regular and irregular shapes abstract two approaches to predict the overall elastic properties of solids with regularly and irregularly shaped pores are compared the first approach involves direct finite element simulations of periodic representative volume elements containing arrangements of pores a simplified algorithm of collective rearrangement type is developed for generating microstructures with the desired density of randomly distributed pores of regular and irregular shapes homogeneity and isotropy where appropriate of the microstructures are confirmed by generating two point statistics functions the second approach utilizes mori tanaka and maxwell micromechanical models implemented via the cavity compliance contribution tensor h tensor formalism the effects of pore shape and matrix poisson s ratio on compliance contribution parameters of different shapes are discussed h tensors of cubical octahedral and tetrahedral pores for several values of matrix poisson s ratio are published in explicit form for the first time good correspondence between the direct finite element simulations and micromechanical homogenization is observed for randomly oriented and parallel pores of the same shape as well as mixtures of pores of various shapes up to 0 25 pore volume fractions

characterization of the mechanical behaviors of solid fluid mixture by the homogenization method the mechanical behaviors of a solid fluid mixture are characterized by using the homogenization method which is based on the method of asymptotic expansions according to the choice of the so called effective parameters the formal derivation yields two distinct systems of well known macromechanical governing equations one for poroelasticity and the other for viscoelasticity the homogenized equations representing the asymptotic behaviors entail the locally defined field equations and the geometry of a repeating unit in addition to the identities of both formulations with ones in classical mechanics the formulation enables the evaluation of actual mechanical responses of microstructures this distinctive feature of the homogenization method is called the localization which must be a key capability that provides a bridge between micromechanics and macromechanics thus the present developments and several numerical simulations will provide insight into a variety of engineering problems in regard to solid fluid coupled systems

the 2 sylow subgroup of k2of for number fields f abstract let f be a quadratic number field we give a criterion via hilbert symbols for an element of order two in the tame kernel of f to be a fourth power in the tame kernel of f the result can be applied to compute the 8 rank of the tame kernel of f and the tate kernel of an imaginary quadratic number field we list the 8 ranks of k 2 o f for all quadratic number fields whose discriminants have exactly two odd prime divisors in the case when f is an imaginary quadratic number field with the 8 rank of k 2 o f 0 the tate kernel of f is given too an application of our method to the maximal real subfield of a cyclotomic field is discussed numerical examples in particular the examples of quadratic number fields f with 4 rank of k 2 o f 8 rank of k 2 o f 2 illustrate our results

the coherent potential approximation is a realizable effective medium scheme the effective electrical conductivity of an aggregate composed of grains of various conductivities is frequently estimated by the coherent potential approximation which embodies a local effective medium concept it is proved rigorously that this approximation is exact for a wide class of hierarchical model composites made of spherical grains the starting material 0 in the hierarchy is chosen arbitrarily otherwise materialj 1 2 consists of equisized spheres sayj spheres of arbitrary conductivities embedded in materialj 1 the spatial distribution of thej spheres must satisfy a mild homogeneity condition and their radiusr j must asymptotically increase faster than exponentially withj furthermore the minimum spacing 2s j between thej spheres is such that the ratios j r j diverges on the basis of these and some further ancillary conditions it is established that the coherent potential approximation becomes asymptotically exact for the effective conductivity of materialj the results extend to other effective parameters of the composites including the thermal conductivity dielectric constant and magnetic permeability in addition the model composites and the proof of realizability may be generalized to allow non spherical grains

stochastic finite element analysis of composite structures based on mesoscale random fields of material properties abstract the linking of microstructure uncertainty with the random variation of material properties at higher scales is of paramount importance in the framework of the stochastic finite element method sfem an efficient computational scheme has been recently proposed by the authors for the determination of mesoscale random fields for the apparent properties and of the rve size of particle reinforced composites based on computer simulated images of their microstructure the proposed approach exploits the excellent synergy of the extended finite element method xfem and monte carlo simulation in order to analyze the microstructure models and obtain statistical information probability distribution correlation structure for the apparent properties of the composite in each mesoscale size in this paper sample functions of the statistically homogeneous mesoscale random fields are generated using the spectral representation method in conjunction with translation field theory moreover micro mechanically consistent lower and upper bounds on the macroscopic response of composite structures are computed in the framework of sfem useful conclusions are derived regarding the effect of particle matrix stiffness ratio on the probabilistic characteristics of the mesoscale random fields as well as the influence of mesoscale size on the response variability

large scale 3d random polycrystals for the finite element method generation meshing and remeshing abstract a methodology is presented for the generation and meshing of large scale three dimensional random polycrystals voronoi tessellations are used and are shown to include morphological properties that make them particularly challenging to mesh with high element quality original approaches are presented to solve these problems i geometry regularization which consists in removing the geometrical details of the polycrystal morphology ii multimeshing which consists in using simultaneously several meshing algorithms to optimize mesh quality and iii remeshing by which a new mesh is constructed over a deformed mesh and the state variables are transported for large strain applications detailed statistical analyses are conducted on the polycrystal morphology and mesh quality the results are mainly illustrated by the high quality meshing of polycrystals with large number of grains up to 10 5 and the finite element method simulation of a plane strain compression of e 1 4 of a 3000 grain polycrystal the presented algorithms are implemented and distributed in a free open source software package neper

a multiple level set approach to prevent numerical artefacts in complex microstructures with nearby inclusions within xfem in this paper we highlight that when the extended finite element method xfem is employed to model a microstructure in which inclusions are involved and the distance between two inclusions is small enough to be comparable with the mesh size three numerical artefacts are induced significantly affecting the convergence and accuracy of the numerical solution to the problem with such a microstructure these artefacts are a an artificial percolation of nearby inclusions b an artificial distortion of phase domains c an enrichment deficiency we propose to improve the xfem levelset method so as to avoid these artefacts the new technique leading to this improvement uses one level set function for each inclusion and adds additional enrichment in an element whose support is cut by several interfaces a local description of the multiple level sets is provided to avoid the storage of all level set functions a simple integration rule is employed for numerical quadrature in elements cut by several interfaces we show that the artefacts mentioned hereinbefore are circumvented in this framework the performances of the method are demonstrated through benchmarks and examples applied to the homogenization of concrete materials in 2d and 3d cases

random field models of heterogeneous materials abstract one of the main challenges in solid mechanics lies in the passage from a heterogeneous microstructure to an approximating continuum model in many cases e g stochastic finite elements statistical fracture mechanics the interest lies in resolution of stress and other dependent fields over scales not infinitely larger than the typical microscale this may be accomplished with the help of a meso scale window which becomes the classical representative volume element rve in the infinite limit it turns out that the material properties at such a mesoscale cannot be uniquely approximated by a random field of stiffness compliance with locally isotropic realizations but rather two random continuum fields with locally anisotropic realizations corresponding respectively to essential and natural boundary conditions on the meso scale need to be introduced to bound the material response from above and from below we study the first and second order characteristics of these two meso scale random fields for anti plane elastic response of random matrix inclusion composites over a wide range of contrasts and aspect ratios special attention is given to the convergence of effective responses obtained from the essential and natural boundary conditions which sheds light on the minimum size of an rve additionally the spatial correlation structure of the crack density tensor with the meso scale moduli is studied

analysis of nonlinear integro differential equations arising in age dependent epidemic models basically there are two modes for directly transmitting an infectious disease within a single population vertical transmission and horizontal transmission vertical transmission is defined as the direct transfer of infection from a parent organism to its offsprings horizontal transmission is any transfer of infection except that which is vertically transmitted for example aids is both vertically and horizontally transmitted while malaria is horizontally transmitted vertically transmitted diseases have seldom been considered in mathematical models of epidemics examples of previous such models are found in anderson and may i cooke and busenberg 7 busenberg and cooke 3 busenberg cooke and pozio 4 fine lo and re gniere 171 likewise age dependent diseases has been presented by cooke and busenberg 7 and dietz 8 age dependence introduces a coupling of age structure and vertical transmission which can produce novel dynamic behavior in this paper a system of nonlinear integro differential equations which model an agedependent epidemic of a disease with vertical transmission is investigated this model treats the simple s i type of epidemic in this new setting existence and uniqueness are proved under suitable hypotheses and the asymptotic behavior of the system is determined a renewal theorem is used to study the behavior of the model equations in various pertinent parameter ranges a numerical method for integrating this system of equations is developed and is used to obtain approximations of its solutions for some special cases which illustrate the results obtained via analytical means moreover numerical integrations of the equations are used to study some phenomena that were not treated analytically

regularized virtual fields method for mechanical properties identification of composite materials abstract this paper presents a new material parameters identification method based on the virtual fields method vfm where a regularization term coming from a micromechanical model has been added in this regularized virtual fields method rvfm the system of equations associated to the vfm is solved within a constrained optimization framework the method was applied to virtual scanning electron microscope in situ tests aiming at determining the local properties of uni directional composites loaded in the transverse direction and for which the strain fields were obtained through digital image correlation dic the method was tested for composites with various volume fractions and properties contrasts and under different boundary conditions the potentials and limitations of the algorithm in the presence of noisy images were investigated and compared to that of the vfm and the other finite element based methods the corresponding results indicate that the proposed rvfm is more efficient than the other identification techniques in terms of both accuracy and computational time an optimum size of region of interest was also determined by taking into account dic magnification requirements and based on the accuracy of the identified parameters this kind of study can be very useful for determining a priori the level of resolution in the imaging system required for a favorable accuracy of the identified parameters

alleviating mesh constraints model reduction parallel time integration and high resolution homogenization industrial processes involving composite materials need for efficient numerical simulations in order to optimize the process parameters even if the thermo mechanical models are nowadays well established efficient simulations need for further developments in this work we are addressing some of these issues in particular the one related to fast solutions combining model reduction and parallel time integration a separated representation will be also proposed in the context of material homogenization allowing to alleviate the usual mesh constraints

a multiscale stochastic finite element method on elliptic problems involving uncertainties in this study a multiscale stochastic finite element method mssfem is developed to resolve scale coupling stochastic elliptic problems based on formulations of a stochastic variational approach and scale bridging multiscale shape functions by employing polynomial chaos expansions and lagrange polynomials stochastic galerkin method and stochastic collocation method are introduced and combined with deterministic multiscale methods i e variational multiscale method and multiscale finite element method the resulting spectral and pseudo spectral stochastic finite element methods are incorporated into the fine and coarse mesh computation of the mssfem a benchmark multiscale model and the numerical experiment based on the formulated mssfem are provided for illustration it is expected that the proposed mssfem can act as a paradigm for solving of general stochastic partial differential equations involving multiscale stochastic data

strong convergence of the partially truncated euler maruyama scheme for a stochastic age structured sir epidemic model abstract we study in this paper strong convergence of the partially truncated euler maruyama scheme for an age structured susceptible infected removed sir epidemic model with environmental noise using the semigroup theory the existence and uniqueness of global positive solution for the model is first proved we then define a truncated function and develop a partially truncated em numerical solutions to the stochastic age structured sir epidemic model we present the pth moment boundedness of the partially truncated em numerical approximate solutions under appropriate conditions furthermore the strong lq convergence is established for the condition of 2 q