numerical modelling of crack propagation automatic remeshing and comparison of different criteria modelling of a crack propagating through a finite element mesh under mixed mode conditions is of prime importance in fracture mechanics three different crack growth criteria and the respective crack paths prediction for several test cases are compared the maximal circumferential stress criterion the strain energy density fracture criterion and the criterion of the maximal strain energy release rate are implemented using advanced finite element techniques a fully automatic remesher enables to deal with multiple boundaries and multiple materials the propagation of the crack is calculated with both remeshing and nodal relaxation several examples are presented to check for the robustness of the numerical techniques and to study specific features of each criterion

three dimensional non planar crack growth by a coupled extended finite element and fast marching method a numerical technique for non planar three dimensional linear elastic crack growth simulations is proposed this technique couples the extended finite element method x fem and the fast marching method fmm in crack modeling using x fem the framework of partition of unity is used to enrich the standard finite element approximation by a discontinuous function and the two dimensional asymptotic crack tip displacement fields the initial crack geometry is represented by two level set functions and subsequently signed distance functions are used to maintain the location of the crack and to compute the enrichment functions that appear in the displacement approximation crack modeling is performed without the need to mesh the crack and crack propagation is simulated without remeshing crack growth is conducted using fmm unlike a level set formulation for interface capturing no iterations nor any time step restrictions are imposed in the fmm planar and non planar quasi static crack growth simulations are presented to demonstrate the robustness and versatility of the proposed technique copyright 2008 john wiley sons ltd

crack tip enrichment in the xfem using a cutoff function we consider a variant of the extended finite element method xfem in which a cutoff function is used to localize the singular enrichment surface the goal of this variant is to obtain numerically an optimal convergence rate while reducing the computational cost of the classical xfem with a fixed enrichment area we give a mathematical result of quasi optimal error estimate one of the key points of this paper is to prove the optimality of the coupling between the singular and the discontinuous enrichments finally we present some numerical computations validating the theoretical result these computations are compared with those of the classical xfem and a non enriched method copyright 2008 john wiley sons ltd

nonlinear analysis of river flow time sequences within the field of chaos theory several methods for the analysis of complex dynamical systems have recently been proposed in light of these ideas we study the dynamics which control the behavior over time of river flow investigating the existence of a low dimension deterministic component the present article follows the research undertaken in the work of porporato and ridolfi 1996a in which some clues as to the existence of chaos were collected particular emphasis is given here to the problem of noise and to nonlinear prediction with regard to the latter the benefits obtainable by means of the interpolation of the available time series are reported and the remarkable predictive results attained with this nonlinear method are shown

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

modeling three dimensional crack propagation a comparison of crack path tracking strategies the development of a new finite element technique for the simulation of discontinuous failure phenomena in three dimensions is the key objective of this study in contrast to the widely used extended finite element technique we apply a purely deformation based strategy based on an independent interpolation of the deformation field on both sides of the discontinuity this method has been applied successfully for two dimensional crack propagation problems in the past however when it comes to three dimensional failure phenomena it faces the same difficulties as the extended finite element method unlike in two dimensions the characterization for the three dimensional failure surface is non unique and the tracking of the discrete crack can be performed in several conceptually different ways in this work we review the four most common three dimensional crack tracking strategies we perform a systematic comparison in terms of standard algorithmic quality measures such as mesh independency efficiency robustness stability and computational cost moreover we discuss more specific issues such as crack path continuity and integratability in commercial finite element packages the features of the suggested crack tracking algorithms will be elaborated by means of characteristic benchmark problems in failure analysis copyright 2008 john wiley sons ltd

geometrically non linear and consistently linearized embedded strong discontinuity models for 3d problems with an application to the dissection analysis of soft biological tissues three different finite element formulations with embedded strong discontinuities are derived on the basis of the enhanced assumed strain method according to the work by jirasek and zimmermann int j numer methods engrg 50 2001 1269 they are referred to as statically optimal symmetric sos kinematically optimal symmetric kos and statically and kinematically optimal non symmetric skon formulations the effect of the discontinuities are characterized by additional degrees of freedom on the element level modifications to the standard kos and skon formulations are proposed in order to achieve consistency with the employed type of a three field hu washizu principle under mode i condition under this condition the formulation satisfies the internal compatibility at the discontinuity i e the relation between the stress in the bulk material and the traction across the discontinuity surface which is not the case for the classical kos formulation we propose a suitable explicit expression for a transversely isotropic traction law in form of a displacement energy function and assume that softening phenomena in the cohesive zone are modeled by a damage law which depends on the maximum gap displacement of the deformation path a linearization of all quantities which are related to the non linear problem leads to new closed form expressions in particular we focus attention on the linearization of the cohesive traction vector the associated element residua and stiffness matrices are provided standard static condensation of the internal degree of freedom leads to a generalized displacement model a comparative study of the modified formulations carried out by means of two numerical examples show the performance of the individual approach we employ constant strain tetrahedral elements with a single discontinuity embedded among the known stress locking phenomena associated with the sos formulation we recognized that the non symmetric skon formulation was not able to provide meaningful results for the dissection process of an arterial layer in three dimensions on distorted meshes for both numerical examples the symmetric kos formulation seems to be most suitable for representing the embedded discontinuities

determination of constitutive equations for human arteries from clinical data stress strain analyses of vessel walls require appropriate constitutive equations determination of constitutive equations is based on experimental data of i diameter and length of a vessel segment subject to internal pressure and external axial force and ii the load free reference geometry typical clinical data however provide only pressure diameter relations in the diastolic systolic pressure range in order to overcome this problem an approach is proposed allowing the determination of constitutive equations from clinical data by means of reasonable assumptions regarding in situ configurations and stress states of arterial walls the approach is based on a two dimensional fung type stored energy function capturing the characteristic nonlinear and anisotropic responses of arteries examples concerning human aortas from a normotensive and a hypertensive subject illustrate the potential of the approach

vector level sets for description of propagating cracks in finite elements a new level set method is developed for describing surfaces that are frozen behind a moving front such as cracks in this formulation the level set is described in two dimensions by a three tuple the sign of the level set function and the components of the closest point projection to the surface the update of the level set is constructed by geometric formulas which are easily implemented results are given for growth of lines in two dimensions that show the method is very accurate the method combines very naturally with the extended finite element method xfem where the discontinuous enrichment for cracks is best described in terms of level set functions examples of crack growth simulations obtained by combining this level set method with the extended finite element method are given copyright 2003 john wiley sons ltd

computation of the gamma digamma and trigamma functions this paper gives an approximation for the gamma function that while different has the same form as one by lanczos siam j numer anal b1 1964 pp 86 96 both approximations correct stirlin

an analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids abstract this paper presents an analysis of strong discontinuities in inelastic solids at finite strains solutions exhibiting this type of discontinuities characterized by a discontinuous displacement field are shown to make physical and mathematical sense in a classical multiplicative plasticity continuum model if the softening modulus is reinterpreted as a singular distribution physically the strainsoftening is localized along the discontinuity conditions for the appearance of strong discontinuities in the geometrically nonlinear range are characterized as it is the response of the material during localization in addition these analytical results are exploited in the design of a new class of finite element methods the proposed methods fall within the class of enhanced strain methods and lead to solutions independent of the mesh size and insensitive to mesh alignment without requiring any regularization of the solutions by numerical parameters like a characteristic length

hp generalized fem and crack surface representation for non planar 3 d cracks a high order generalized finite element method gfem for non planar three dimensional crack surfaces is presented discontinuous p hierarchical enrichment functions are applied to strongly graded tetrahedral meshes automatically created around crack fronts the gfem is able to model a crack arbitrarily located within a finite element fe mesh and thus the proposed method allows fully automated fracture analysis using an existing fe discretization without cracks we also propose a crack surface representation that is independent of the underlying gfem discretization and controlled only by the physics of the problem the representation preserves continuity of the crack surface while being able to represent non planar non smooth crack surfaces inside of elements of any size the proposed representation also provides support for the implementation of accurate robust and computationally efficient numerical integration of the weak form over elements cut by the crack surface numerical simulations using the proposed gfem show high convergence rates of extracted stress intensity factors along non planar curved crack fronts and the robustness of the method copyright 2008 john wiley sons ltd

a note on some alternating series involving zeta and multiple zeta values in this article we consider various generalizations of euler s famous relation gamma sum n geq 2 1 n frac zeta n n linking euler s constant gamma to special values of the riemann zeta function at positive integers among other things we highlight the existence of a very similar relation for the apostol vu harmonic zeta function which have never been noticed before

nonparametric density estimation prediction and regression for markov sequences abstract let xi be a stationary markov sequence having a transition probability density function f y x giving the pdf of x i 1 xi x in this study nonparametric density and regression techniques are employed to infer f y x and m x e x i 1 xi x it is seen that under certain regularity and markovian assumptions the asymptotic convergence rate of the nonparametric estimator mn x to the predictor m x is the same as it would have been had the xi s been independently and identically distributed and this rate is optimal in a certain sense consistency can be maintained after differentiability and even the markovian assumptions are abandoned computational and modeling ramifications are explored i claim that my methodology offers an interesting alternative to the popular arma approach

subdivision schemes for smooth contact surfaces of arbitrary mesh topology in 3d this paper presents a strategy to parameterize contact surfaces of arbitrary mesh topology in 3d with at least c1 continuity for both quadrilateral and triangular meshes in the regular mesh domain four quadrilaterals or six triangles meet in one node even c2 continuity is attained therefore we use subdivision surfaces for which non physical pressure jumps are avoided for contact interactions they are usually present when the contact kinematics is based on facet elements discretizing the interacting bodies the properties of subdivision surfaces give rise to basically four different implementation strategies each strategy has specific features and requires more or less efforts for an implementation in a finite element program one strategy is superior with respect to the others in the sense that it does not use nodal degrees of freedom of the finite element mesh at the contact surface instead it directly uses the degrees of freedom of the smooth surface thereby remarkably it does not require an interpolation we show how the proposed method can be used to parameterize adaptively refined meshes with hanging nodes this is essential when dealing with finite element models whose geometry is generated by means of subdivision techniques three numerical 3d problems demonstrate the improved accuracy robustness and performance of the proposed method over facet based contact surfaces in particular the third problem adopted from biomechanics shows the advantages when designing complex contact surfaces by means of subdivision techniques copyright 2004 john wiley sons ltd

an extended finite element method with analytical enrichment for cohesive crack modeling a recent approach to fracture modeling has combined the extended finite element method xfem with cohesive zone models most studies have used simplified enrichment functions to represent the strong discontinuity but have lacked an analytical basis to represent the displacement gradients in the vicinity of the cohesive crack in this study enrichment functions based upon an existing analytical investigation of the cohesive crack problem are proposed these functions have the potential of representing displacement gradients in the vicinity of the cohesive crack and allow the crack to incrementally advance across each element key aspects of the corresponding numerical formulation and enrichment functions are discussed a parameter study for a simple mode i model problem is presented to evaluate if quasi static crack propagation can be accurately followed with the proposed formulation the effects of mesh refinement and mesh orientation are considered propagation of the cohesive zone tip and crack tip time variation of the cohesive zone length and crack profiles are examined the analysis results indicate that the analytically based enrichment functions can accurately track the cohesive crack propagation of a mode i crack independent of mesh orientation a mixed mode example further demonstrates the potential of the formulation copyright 2008 john wiley sons ltd

modelling of cohesive crack growth in concrete structures with the extended finite element method in this paper the extended finite element method xfem is used for a discrete crack simulation of concrete using an adaptive crack growth algorithm different criteria for predicting the direction of the extension of a cohesive crack are investigated in the context of the xfem the robustness of these criteria is analyzed with reference to three examples and the results are compared to experiments furthermore the efficient application of the quadtree data structure for an iterative mesh refinement in combination with the xfem is shown considerably to reduce the computational effort

remarks on some integrals and series involving the stirling numbers and from the perspective of the well known identity 2f a b c 1 rc cc a b we clarify the connections between the stirling numbers sk and the riemann zeta function c n as a consequence certain series and integrals can be evaluated in terms of c n and sn

on the discrete constitutive models induced by strong discontinuity kinematics and continuum constitutive equations on the basis of continuum constitutive models stress vs strain the introduction of strong discontinuity kinematics considering jumps in the displacement fields across a discontinuity interface induces projected discrete constitutive models traction displacement jumps in a consistent manner therefore this projection provides possible links between the classical continuum strain localization analysis and the non linear decohesive fracture mechanics techniques the strong discontinuity analysis shows that bandwidth based regularization of the hardening softening parameter is the crucial modification to be done on the continuum model to achieve such a projection and it also provides the strong discontinuity conditions that set restrictions on the stress state compatible with bifurcations in a strong discontinuity format the methodology is illustrated on the basis of two classical families of non linear constitutive models scalar continuum damage and elasto plasticity for which the corresponding discrete constitutive models and the strong discontinuity conditions are derived

a multiscale extended finite element method for crack propagation in this paper we propose a multiscale strategy for crack propagation which enables one to use a refined mesh only in the crack s vicinity where it is required two techniques are used in synergy a multiscale strategy based on a domain decomposition method to account for the crack s global and local effects efficiently and a local enrichment technique the x fem to describe the geometry of the crack independently of the mesh the focus of this study is the avoidance of meshing difficulties and the choice of an appropriate scale separation to make the strategy efficient we show that the introduction of the crack s discontinuity both on the microscale and on the macroscale is essential for the numerical scalability of the domain decomposition method to remain unaffected by the presence of a crack thus the convergence rate of the iterative solver is the same throughout the crack s propagation

a computational framework of three dimensional configurational force driven brittle crack propagation abstract we consider a variational formulation of quasi static brittle fracture and develop a new finite element based computational framework for propagation of cracks in three dimensional bodies we outline a consistent thermodynamical framework for crack propagation in elastic solids and show that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global clausius planck inequality in the sense of coleman s method consequently the crack propagation direction associated with the classical griffith criterion is identified by the material configurational force which maximizes the local dissipation at the crack front the variational formulation is realized numerically by a standard spatial discretization with finite elements which yields a discrete formulation of the global dissipation in terms configurational nodal forces therefore the constitutive setting of crack propagation in the space discretized finite element context is naturally related to discrete nodes of a typical finite element mesh in a consistent way with the node based setting the discretization of the evolving crack discontinuity is performed by the doubling of critical nodes and interface facets of the mesh the crucial step for the success of this procedure is its embedding into an r adaptive crack facet reorientation procedure based on configurational force based indicators in conjunction with crack front constraints we propose a staggered solution procedure that results in a sequence of positive definite discrete subproblems with successively decreasing overall stiffness providing a robust algorithmic setting in the postcritical range the predictive capabilitiy of the proposed formulation is demonstrated by means of representative numerical simulations

fast and robust level set update for 3d non planar x fem crack propagation modelling abstract in the x fem framework the need to represent a discontinuity independently of the structural mesh relies on the level set technique hence crack propagation can be simulated by an update of two distinct level sets the evolution of which is described by differential equations the aim of this paper is to analyse the resolution of these equations in order to formulate a robust and fast numerical process allowing 3d crack propagation simulations even in presence of high kink angles occurring in mixed mode propagation the numerical integration is accomplished by means of a robust finite difference upwind scheme applied to an auxiliary regular grid an alternative level set update equation and a fast localisation of the integration domain specifically developed for crack propagation problems are formulated and proposed in the paper in order to gain in stability robustness and performance

a nearest neighbor bootstrap for resampling hydrologic time series a nonparametric method for resampling scalar or vector valued time series is introduced multivariate nearest neighbor probability density estimation provides the basis for the resampling scheme developed the motivation for this work comes from a desire to preserve the dependence structure of the time series while bootstrapping resampling it with replacement the method is data driven and is preferred where the investigator is uncomfortable with prior assumptions as to the form e g linear or nonlinear of dependence and the form of the probability density function e g gaussian such prior assumptions are often made in an ad hoc manner for analyzing hydrologic data connections of the nearest neighbor bootstrap to markov processes as well as its utility in a general monte carlo setting are discussed applications to resampling monthly streamflow and some synthetic data are presented the method is shown to be effective with time series generated by linear and nonlinear autoregressive models the utility of the method for resampling monthly streamflow sequences with asymmetric and bimodal marginal probability densities is also demonstrated

a meshless method with enriched weight functions for three dimensional crack propagation the propagation of cracks in three dimensions is analysed by a meshless method the cracks are modelled by a set of triangles that are added when the propagation occurs since the method is meshless no remeshing of the domain is necessary during the propagation to avoid using a large number of degrees of freedom the stress singularity along the front of the cracks is taken into account by an enrichment of the shape functions of the meshless method by means of appropriate weight functions this enrichment technique is an extension of the technique that proved to be successful in two dimensions in a previous paper several algorithms for efficiently implementing the meshless method in three dimensions are detailed the accuracy of the enrichment is first assessed on simple examples and some results of non planar propagation of multiple cracks are then presented copyright 2005 john wiley sons ltd

modeling holes and inclusions by level sets in the extended finite element method a methodology to model arbitrary holes and material interfaces inclusions without meshing the internal boundaries is proposed the numerical method couples the level set method s osher j a sethian j comput phys 79 1 1988 12 to the extended finite element method x fem n moes j dolbow t belytschko int j numer methods engrg 46 1 1999 131 in the x fem the finite element approximation is enriched by additional functions through the notion of partition of unity the level set method is used for representing the location of holes and material interfaces and in addition the level set function is used to develop the local enrichment for material interfaces numerical examples in two dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique

on stirling numbers and euler sums abstract in this paper we propose another yet generalization of stirling numbers of the first kind for noninteger values of their arguments we discuss the analytic representations of stirling numbers through harmonic numbers the generalized hypergeometric function and the logarithmic beta integral we present then infinite series involving stirling numbers and demonstrate how they are related to euler sums finally we derive the closed form for the multiple zeta function p 1 1 for re p 1

two series expansions for the logarithm of the gamma function involving stirling numbers and containing only rational coefficients for certain arguments related to π 1 abstract in this paper two new series for the logarithm of the function are presented and studied their polygamma analogs are also obtained and discussed these series involve the stirling numbers of the first kind and have the property to contain only rational coefficients for certain arguments related to 1 in particular for any value of the form ln 1 2 n 1 and k 1 2 n 1 where k stands for the kth polygamma function is positive rational greater than 1 6 n is integer and k is non negative integer these series have rational terms only in the specified zones of convergence derived series converge uniformly at the same rate as n ln m n 2 where m 1 2 3 depending on the order of the polygamma function explicit expansions into the series with rational coefficients are given for the most attracting values such as ln 1 ln 2 1 ln 1 2 1 1 1 2 1 and k 1 besides in this article the reader will also find a number of other series involving stirling numbers gregory s coefficients logarithmic numbers also known as bernoulli numbers of the second kind cauchy numbers and generalized bernoulli numbers finally several estimations and full asymptotics for gregory s coefficients for cauchy numbers for certain generalized bernoulli numbers and for certain sums with the stirling numbers are obtained in particular these include sharp bounds for gregory s coefficients and for the cauchy numbers of the second kind

towards a generalization of a discrete strong discontinuity approach a generalized discrete strong discontinuity approach gsda is presented in which non homogeneous jumps are embedded in parent finite elements the new formulation presents similar kinematics as for interface elements accurately simulating both rigid body motion and stretching induced by the opening of a discontinuity this generalized discrete strong discontinuity approach is built within the framework of strong embedded discontinuity formulations as a consequence it is mesh independent and avoids the progressive remeshing needed with interface elements the gsda can be viewed as a generalization of other embedded formulations for which particular assumptions are adopted regarding both the jump transmission and the variational principle structural examples including mode i mode ii and mixed mode fracture are computed and compared with other embedded formulations and experimental results

a new two point deformation tensor and its relation to the classical kinematical framework and the stress concept abstract starting from the issue of what is the correct form for a legendre transformation of the strain energy in terms of eulerian and two point tensor variables we introduce a new two point deformation tensor namely h f f t 2 as a possible deformation measure involving points in two distinct configurations the lie derivative of h is work conjugate to the first piola kirchhoff stress tensor p the deformation measure h leads to straightforward manipulations within a two point setting such as the derivation of the virtual work equation and its linearization required for finite element implementation the manipulations are analogous to those used for the lagrangian and eulerian frameworks it is also shown that the legendre transformation in terms of two point tensors and spatial tensors require lie derivatives as an illustrative example we propose a simple saint venant kirchhoff type of a strain energy function in terms of h the constitutive model leads to physically meaningful results also for the large compressive strain domain which is not the case for the classical saint venant kirchhoff material

cn continuous modelling of smooth contact surfaces using nurbs and application to 2d problems this paper presents a strategy for the finite element implementation of cn continuous contact surfaces for deformable bodies undergoing finite deformations whereby n represents an arbitrary level of continuity the proposed novel approach avoids the non physical oscillations of contact forces which are induced by the traditional enforcement of kinematic contact constraints via faceted surfaces discretizing the interacting boundaries in particular for certain problems the level of continuity may influence the rate of convergence significantly within a non linear solution scheme a hierarchical tree data structure is proposed for an efficient search algorithm to find the neighbour elements on adaptively refined meshes which are involved in the smoothing process of a particular finite element the same data structure is used for the automatic detection of the contact surfaces of a body three representative numerical examples demonstrate the increased rate of convergence the ability to trace the actual surface more accurately and the prevention of pressure jumps of the proposed method copyright 2003 john wiley sons ltd

a generalized finite element method for the simulation of three dimensional dynamic crack propagation this paper is aimed at presenting a partition of unity method for the simulation of three dimensional dynamic crack propagation the method is a variation of the partition of unity finite element method and hp cloud method in the context of crack simulation this method allows for modeling of arbitrary dynamic crack propagation without any remeshing of the domain in the proposed method the approximation spaces are constructed using a partition of unity pu and local enrichment functions the pu is provided by a combination of shepard and finite element partitions of unity this combination of pus allows the inclusion of arbitrary crack geometry in a model without any modification of the initial discretization it also avoids the problems associated with the integration of moving least squares or conventional shepard partitions of unity used in several meshless methods the local enrichment functions can be polynomials or customized functions these functions can efficiently approximate the singular fields around crack fronts the crack propagation is modeled by modifying the partition of unity along the crack surface and does not require continuous remeshings or mappings of solutions between consecutive meshes as the crack propagates in contrast with the boundary element method the proposed method can be applied to any class of problems solvable by the classical finite element method in addition the proposed method can be implemented into most finite element data bases several numerical examples demonstrating the main features and computational efficiency of the proposed method for dynamic crack propagation are presented

long lead probabilistic forecasting of streamflow using ocean atmospheric and hydrological predictors 1 a geostatistically based approach with a local regression method is used to predict the magnitude of seasonal streamflow using ocean atmospheric signals and the hydrological condition of a basin as predictors the model characterizes the stochastic behavior of a forecast variable by generating a conditional distribution of the predicted value for different hydroclimatic conditions the correlation structure between dependent and independent variables is represented by the variography of the predicted values in which the distance variable in the variogram is determined by measuring the distance between the predictors this variogram in a virtual field constructed from the predictors makes it possible to predict variables as unmeasured points while considering historic information as measurement points of the field different types of kriging as well as a generalized linear model regression are used to predict data in interpolation and extrapolation modes the forecast skill is evaluated using a linear error in probability space score for different combinations of predictors and different kriging methods the method is applied to a case study of the zayandeh rud river in isfahan iran the utility of the method is demonstrated for forecasting autumn winter and spring streamflow using the southern oscillation index the north atlantic oscillation serial correlation between seasonal streamflow series and the snow budget the study analyzes the application of the proposed method in comparison with a k nearest neighbor regression method the results of this study show that the proposed method can significantly improve the long lead probabilistic forecast skill for a nonlinear relationship between hydroclimatic predictors and streamflow in a region

a study of the representation of cracks with level sets the level set method has been used for a few years to represent cracks in fracture mechanics simulations instead of an explicit description of the cracks faces geometry this paper studies in detail the shape of the level set functions around a crack in two dimensions that is propagating with a sharp kink obtained both with level set update methods found in the literature and with several innovative update methods developed by the author a criterion based on the computation of a j integral of a virtual displacement field obtained with the values of the level set functions is proposed in order to assess the quality of these update methods with the help of this criterion two optimal approaches are identified which predict an accurate evolution of the crack with smooth and consistent level set functions these methods are then applied in three dimensions to the case of an initially penny shaped crack that propagates out of its plane copyright 2006 john wiley sons ltd

element local level set method for three dimensional dynamic crack growth summary an approximate level set method for three dimensional crack propagation is presented in this method the discontinuity surface in each cracked element is defined by element local level sets ellss the local level sets are generated by a fitting procedure that meets the fracture directionality and its continuity with the adjacent element crack surfaces in a least square sense a simple iterative procedure is introduced to improve the consistency of the generated element crack surface with those of the adjacent cracked elements the discrete discontinuity is treated by the phantom node method which is a simplified version of the extended finite element method xfem the ells method and the phantom node technology are combined for the solution of dynamic fracture problems numerical examples for three dimensional dynamic crack propagation are provided to demonstrate the effectiveness and robustness of the proposed method copyright q 2009 john wiley sons ltd

strict and effective bounds in goal oriented error estimation applied to fracture mechanics problems solved with xfem in this work we analyze a method that leads to strict and high quality local error bounds in the context of fracture mechanics we investigate in particular the capability of this method to evaluate the discretization error for quantities of interest computed using the extended finite element method xfem the goal oriented error estimation method we are focusing on uses the concept of constitutive relation error along with classical extraction techniques the main innovation in this paper resides in the methodology employed to construct admissible fields in the xfem framework which involves enrichments with singular and level set basis functions we show that this construction can be performed through a generalization of the classical procedure used for the standard finite element method thus the resulting goal oriented error estimation method leads to relevant and very accurate information on quantities of interest that are specific to fracture mechanics such as mixed mode stress intensity factors the technical aspects and the effectiveness of the method are illustrated through two dimensional numerical examples

3d crack propagation in unreinforced concrete a two step algorithm for tracking 3d crack paths tensile failure of unreinforced concrete involves progressive micro cracking and the related strain softening can coalesce into geometrical discontinuities which separate the material advanced mechanical theories and numerical schemes are required to efficiently and adequately represent crack propagation in 3d in this paper we use the concept of strong discontinuities to model concrete failure we introduce a cohesive fracture process zone which is characterized by a transversely isotropic traction separation law we combine the cohesive crack concept with the partition of unity finite element method where the finite element space is enhanced by the heaviside function the concept is implemented for tetrahedral elements and the failure initialization is based on the simple non local rankine criterion for each element we assume the embedded discontinuity to be flat in the reference configuration which leads to a non smooth crack surfaces approximation in 3d in general different concepts for tracking non planar cracks in 3d are reviewed in addition we propose a two step algorithm for tracking the crack path where a predictor step defines discontinuities according to the non local failure criterion and a corrector step draws in non local information of the existing discontinuities in order to predict a closed 3d crack surface implementation details are provided the proposed framework is used to analyze the predictability of concrete failure by two benchmark examples i e the nooru moharned test and the brokenshire test we compare our numerical results which are mesh independent with experimental data and numerical results adopted from the literature

on the localization properties of multiplicative hyperelasto plastic continua with strong discontinuities abstract the objective of this work is to examine the large strain localization properties of hyperelasto plastic materials which are based on the multiplicative decomposition of the deformation gradient thereby the case of strong discontinuities is investigated to this end first an explicit expression for the spatial tangent operator is given taking into account anisotropic as well as nonassociated material behaviour then the structure of a regularized discontinuous velocity gradient is elaborated and discussed in detail based on these two results the localization condition is derived with special emphasis on the loading conditions inside and outside an anticipated localization band thereby the intriguingly simple structure of the tangent operator which resembles the structure of the geometrically linear theory is extensively exploited this similarity carries over to the general representation for the critical hardening modulus which is exemplified for isotropic materials as a result analytical solutions are available under the assumption of small elastic strains which is justified for metals finally examples are given for the special case of the associated von mises flow rule to this end the critical localization direction and the critical hardening modulus are investigated with respect to the amount of finite elastic strain within different modes of homogeneous elasto plastic deformations

the heat equation shrinks embedded plane curves to round points soit c 0 s 1 r 2 une courbe lisse plongee dans le plan alors c s 1 0 t r 2 existe en satisfaisant c t k n ou k est la courbure de c et n est son vecteur unite normal entrant c t est lisse pour tout t il converge vers un point quand t t et sa forme limite quand t t est un cercle rond avec convergence dans norme c

a simple method for crack growth in mixed mode with x fem abstract in this paper a new method for level set update is proposed in the context of crack propagation modeling with the extended finite element method x fem and level sets compared with the existing methods such as the resolution of the hamilton jacobi equations this new method is much simpler because it does not required complex manipulations of the level sets this method called the projection method uses both a classical discretization of the surface of the crack segments for 2d cracks and triangles for 3d cracks and a level set representation of the crack this discretization is updated with respect to the position of the new crack front then the level sets are re computed using the true distance to the new crack by an orthogonal projection of each node of the structure onto the new crack surface then numerical illustrations are given on 2d and 3d academic examples finally three illustrations are given on 3d industrial applications

non planar 3d crack growth by the extended finite element and level sets part i mechanical model a methodology for solving three dimensional crack problems with geometries that are independent of the mesh is described the method is based on the extended finite element method in which the crack discontinuity is introduced as a heaviside step function via a partition of unity in addition branch functions are introduced for all elements containing the crack front the branch functions include asymptotic near tip fields that improve the accuracy of the method the crack geometry is described by two signed distance functions which in turn can be defined by nodal values consequently no explicit representation of the crack is needed examples for three dimensional elastostatic problems are given and compared to analytic and benchmark solutions the method is readily extendable to inelastic fracture problems copyright 2002 john wiley sons ltd

finite deformation formulation for embedded frictional crack with the extended finite element method we reformulate an extended finite element fe framework for embedded frictional cracks in elastoplastic solids to accommodate finite deformation including finite stretching and rotation for the fe representation we consider a galerkin approximation in which both the trial and weighting functions adapt to the current contact configuration contact and frictional constraints employ two kuhn tucker conditions a contact separation constraint nesting over a stick slip constraint for the case when the crack faces are in frictional sliding mode we integrate finite deformation bulk plasticity into the formulation using the multiplicative decomposition technique of nonlinear continuum mechanics we then present plane strain simulations demonstrating various aspects of the extended fe solutions the mechanisms considered include combined opening and frictional sliding in initially straight curved and s shaped cracks with and without bulk plasticity to gain further insight into the extended fe solutions we perform mesh convergence studies focusing on both the global and the local responses of structures with cracks including the distribution of the normal component of traction on the crack faces copyright 2009 john wiley sons ltd

a mixed interface finite element for cohesive zone models abstract the phenomena of crack initiation propagation and ultimate fracture are studied here under the following assumptions i the crack law is modelled by means of a cohesive zone model and ii the crack paths are postulated a priori in this context a variational formulation is proposed which relies on an augmented lagrangian a mixed interface finite element is introduced to discretise the crack paths the degrees of freedom of which consist in the displacement on both crack lips and the density of cohesive forces this enables an exact treatment of multi valued cohesive laws e g initial adhesion contact conditions possible rigid unloading etc without penalty regularisation a special attention is paid to the convergence with mesh refinement i e the well posedness of the problem on the basis of theoretical results of contact mechanics and some complementary numerical investigations fulfilment of the lbb condition is the key factor to gain the desired properties moreover it is shown that the integration of the constitutive law admits a unique solution as soon as some condition on the augmented lagrangian is enforced finally a 3d simulation shows the applicability to practical engineer problems including in particular the robustness of the formulation and its compatibility with classical solution algorithms newton method line search path following techniques

nearest neighbor methods for nonparametric rainfall runoff forecasting this paper introduces a nonparametric regression method for time series to the stochastic hydrology literature the technique known as the nearest neighbor nn method is motivated by the classical rainfall runoff forecasting problem we have shown in a companion paper yakowitz 1987 that in the time series setting it has attractive large sample properties as summarized herein these include asymptotic convergence to the optimal forecaster under many circumstances in which the forecaster is not a linear function of the data the technique is applied to a sequence of about 3000 seasonalized rainfall runoff pairs from the coshocton watershed we compare the nn forecasting performance on a split sample with those of autoregressive maximum and instantaneous unit hydrograph forecasters

an automatic nonrigid registration for stained histological sections automatic computer based analyses of histological sections which are differently stained require that they are related to each other most registration methods are only able to perform rigid body motion and are sensitive to noise and artifacts histological images however are accompanied by several artifacts and different contrasts which require a nonrigid registration in this paper we present a hierarchical nonrigid registration algorithm able to align images which contain minor image artifacts the algorithm requires no a priori knowledge of the true image the hierarchical design of the algorithm enhances robustness and accuracy and saves computational costs the proposed algorithm is decomposed into a fast coarse rigid registration step and a slower but finer nonrigid step for the coarse registration we use image pyramids while for the second step we combine a point based registration with an elastic thin plate spline interpolation accuracy tests performed for 20 histological images obtained from human arteries have shown that the error measure is acceptable and that the image noise does not cause a problem the associated convergence rate of the mean pixel displacement error during the rigid and nonrigid registrations is satisfying the algorithm can be applied to various multicontrast elastic registration problems in medical imaging and may be extended to three dimensions

numerical analysis of growing crack problems using particle discretization scheme this paper presents the particle discretization scheme pds to analyze brittle failure of solids the scheme uses characteristic functions of voronoi and delaunay tessellations to discretize a function and its derivatives respectively a discretized function has numerous discontinuities so that these discontinuities are utilized as a candidate of crack path segment in modeling propagating cracks without making any extra computation to accommodate new displacement discontinuities when the scheme is implemented to a finite element method fem the resulting stiffness matrix coincides with the one that is obtained by using linear elements the accuracy of computing a stress intensity factor at a crack tip is examined it is shown that the accuracy is better than that of a fem with linear elements when the rotational degree of freedom is included in discretizing displacement functions three three dimensional growing crack problems are solved by means of the pds and the results are presented copyright 2009 john wiley sons ltd

new development in extended finite element modeling of large elasto plastic deformations this paper presents new achievements in the extended finite element modeling of large elasto plastic deformation in solid problems the computational technique is presented based on the extended finite element method x fem coupled with the lagrangian formulation in order to model arbitrary interfaces in large deformations in x fem the material interfaces are represented independently of element boundaries and the process is accomplished by partitioning the domain with some triangular sub elements whose gauss points are used for integration of the domain of elements the large elasto plastic deformation formulation is employed within the x fem framework to simulate the non linear behavior of materials the interface between two bodies is modeled by using the x fem technique and applying the heaviside and level set based enrichment functions finally several numerical examples are analyzed including arbitrary material interfaces to demonstrate the efficiency of the x fem technique in large plasticity deformations copyright 2008 john wiley sons ltd

a marching cubes based failure surface propagation concept for three dimensional finite elements with non planar embedded strong discontinuities of higher order kinematics summary this paper presents an advanced failure surface propagation concept based on the marching cubes algorithm initially proposed in the field of computer graphics and applies it to the embedded finite element method when modeling three dimensional 3d solids at failure the propagation of the failure surface representing a crack or shear band should not exhibit a strong sensitivity to the details of the finite element discretization this results in the need for a propagation of the discrete failure zone through the individual finite elements which is possible for finite elements with embedded strong discontinuities whereas for two dimensional calculations the failure zone propagation location is easily predicted by the maximal principal stress direction more advanced strategies are needed to achieve a smooth failure surface in 3d simulations an example for such method is the global tracking algorithm which predicts the crack path by a scalar level set function computed on the basis of the solution of a simplified heat conduction like problem its prediction may though lead to various scenarios on how the failure surface may propagate through the individual finite elements in particular for a hexahedral eight node finite element 256 such cases exist to capture all those possibilities the marching cubes algorithm is combined with the global tracking algorithm and the finite elements with embedded strong discontinuities in this work in addition because many of the possible cases result in non planar failure surfaces within a single finite element and because the local quantities used to describe the kinematics of the embedded strong discontinuities are physically meaningful in a strict sense only for planar failure surfaces a remedy for such scenarios is proposed various 3d failure propagation simulations outline the performance of the proposed concept copyright 2013 john wiley sons ltd

non planar 3d crack growth by the extended finite element and level sets part ii level set update we present a level set method for treating the growth of non planar three dimensional cracks the crack is defined by two almost orthogonal level sets signed distance functions one of them describes the crack as a two dimensional surface in a three dimensional space and the second is used to describe the one dimensional crack front which is the intersection of the two level sets a hamilton jacobi equation is used to update the level sets a velocity extension is developed that preserves the old crack surface and can accurately generate the growing surface the technique is coupled with the extended finite element method which approximates the displacement field with a discontinuous partition of unity this displacement field is constructed directly in terms of the level sets so the discretization by finite elements requires no explicit representation of the crack surface numerical experiments show the robustness of the method both in accuracy and in treating cracks with significant changes in topology copyright 2002 john wiley sons ltd

conditional parametric models for storm sewer runoff 1 the method of conditional parametric modeling is introduced for flow prediction in a sewage system it is a well known fact that in hydrological modeling the response runoff to input precipitation varies depending on soil moisture and several other factors consequently nonlinear input output models are needed the model formulation described in this paper is similar to the traditional linear models like final impulse response fir and autoregressive exogenous arx except that the parameters vary as a function of some external variables the parameter variation is modeled by local lines using kernels for local linear regression as such the method might be referred to as a nearest neighbor method the results achieved in this study were compared to results from the conventional linear methods fir and arx the increase in the coefficient of determination is substantial furthermore the new approach conserves the mass balance better hence this new approach looks promising for various hydrological models and analysis

a partition of unity based finite element method for level sets level set methods have recently gained much popularity to capture discontinuities including their possible propagation typically the partial differential equations that arise in level set methods in particular the hamilton jacobi equation are solved by finite difference methods however finite difference methods are less suited for irregular domains moreover it seems slightly awkward to use finite differences for the capturing of a discontinuity while in a subsequent stress analysis finite elements are normally used for this reason we here present a finite element approach to solving the governing equations of level set methods after a review of the governing equations the initialization of the level sets the discretization on a finite domain and the stabilization of the resulting finite element method will be discussed special attention will be given to the proper treatment of the internal boundary condition which is achieved by exploiting the partition of unity property of finite element shape functions finally a quantitative analysis including accuracy analysis is given for a one dimensional example and a qualitative example is given for a two dimensional case with a curved discontinuity

numerical schemes for the hamilton jacobi and level set equations on triangulated domains borrowing from techniques developed for conservation law equations numerical schemes which discretize the hamilton jacobi h j level set and eikonal equations on triangulated domains are presented the first scheme is a provably monotone discretization for the h j equations unfortunately the basic scheme lacks lipschitz continuity of the numerical hamiltonian by employing a virtual edge flipping technique local lipschitz continuity of the numerical flux is restored on acute triangulations next schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous hamiltonians these schemes possess a discrete maximum principle on arbitrary triangulations and exhibit local lipschitz continuity of the numerical hamiltonian finally a class of petrov galerkin approximations is considered these schemes are stabilized via a least squares bilinear form the petrov galerkin schemes do not possess a discrete maximum principle but generalize to high order accuracy discretization of the level set equation also requires the numerical approximation of a mean curvature term a simple mass lumped galerkin approximation is presented in section 6 and analyzed using maximum principle analysis the use of unstructured meshes permits several forms of mesh adaptation which have been incorporated into numerical examples these numerical examples include discretizations of convex and nonconvex forms of the h j equation the eikonal equation and the level set equation

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis