equivalent spatial and material descriptions of finite deformation elastoplasticity in principal axes abstract a spatial description of the theory of rate independent finite deformation elastoplasticity in which the stress tensor is defined through the strain energy function is discussed the main assumption of isotropic elastic response and invariance requirements under superposed rigid body motion restrict the acceptable forms of the strain energy function to those given in terms of principal values of the strain measure of elastic distortion the formulation is developed on a manifold and the corresponding material description is obtained simply by pull back of the derived spatial form by appealing to the notion of covariance the method of principal axes is systematically exploited to derive the explicit expression for the stress tensor computation for an arbitrary form of the strain energy function and the explicit form of the evolution equation for an arbitrary form of the yield function a model problem of volume preserving plastic flow is discussed in the closure

numerical implementation of multiplicative elasto plasticity into assumed strain elements with application to shells at large strains alternative formulations of isotropic large strain elasto plasticity are presented which are especially well suited for the implementation into assumed strain elements based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts three distinct eigenvalue problems related to the reference intermediate and current configuration are investigated these eigenvalue problems are connected by similarity transformations which preserve the eigenvalues they play an important role in the subsequent development of alternative constitutive formulations and the corresponding finite element implementation the developed constitutive procedures rely on the right cauchy green tensor or equivalently on the green lagrangian strain tensor rather than the deformation gradient consequently they can be applied directly to assumed strain elements specifically we are concerned with efficient low order shell elements for which the assumed strain method has proven to be extremely powerful to overcome spurious locking effects

on free energy based formulations for kinematic hardening and the decomposition f fpfe within the framework of linear plasticity based on additive decomposition of the linear strain tensor kinematical hardening can be described by means of extended potentials the method is elegant and avoids the need for evolution equations the extension of small strain formulations to the finite strain case which is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts proved not straight forward specifically the symmetry of the resulting back stress remained elusive in this paper a free energy based formulation incorporating the effect of kinematic hardening is proposed the formulation is able to reproduce symmetric expressions for the back stress while incorporating the multiplicative decomposition of the deformation gradient kinematic hardening is combined with isotropic hardening where an associative flow rule and von mises yield criterion are applied it is shown that the symmetry of the back stress is strongly related to its treatment as a truly spatial tensor where contraction operations are to be conducted using the current metric the latter depends naturally on the deformation gradient itself various numerical examples are presented

joint mean covariance models with applications to longitudinal data unconstrained parameterisation summary we provide unconstrained parameterisation for and model a covariance using covariates the cholesky decomposition of the inverse of a covariance matrix is used to associate a unique unit lower triangular and a unique diagonal matrix with each covariance matrix the entries of the lower triangular and the log of the diagonal matrix are unconstrained and have meaning as regression coefficients and prediction variances when regressing a measurement on its predecessors an extended generalised linear model is introduced for joint modelling of the vectors of predictors for the mean and covariance subsuming the joint modelling strategy for mean and variance heterogeneity gabriel s antedependence models dempster s covariance selection models and the class of graphical models the likelihood function and maximum likelihood estimators of the covariance and the mean parameters are studied when the observations are normally distributed applications to modelling nonstationary dependence structures and multivariate data are discussed and illustrated using real data a graphical method similar to that based on the correlogram in time series is developed and used to identify parametric models for nonstationary covariances

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

nonparametric modeling of longitudinal covariance structure in functional mapping of quantitative trait loci estimation of the covariance structure of longitudinal processes is a fundamental prerequisite for the practical deployment of functional mapping designed to study the genetic regulation and network of quantitative variation in dynamic complex traits we present a nonparametric approach for estimating the covariance structure of a quantitative trait measured repeatedly at a series of time points specifically we adopt huang et al s 2006 biometrika 93 85 98 approach of invoking the modified cholesky decomposition and converting the problem into modeling a sequence of regressions of responses a regularized covariance estimator is obtained using a normal penalized likelihood with an l 2 penalty this approach embedded within a mixture likelihood framework leads to enhanced accuracy precision and flexibility of functional mapping while preserving its biological relevance simulation studies are performed to reveal the statistical properties and advantages of the proposed method a real example from a mouse genome project is analyzed to illustrate the utilization of the methodology the new method will provide a useful tool for genome wide scanning for the existence and distribution of quantitative trait loci underlying a dynamic trait important to agriculture biology and health sciences

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

on the spatial formulation of anisotropic multiplicative elasto plasticity abstract this contribution aims at a thermodynamically consistent and modular formulation of anisotropic multiplicative elasto plasticity embedded in the well established framework of non standard dissipative materials we adopt as a key ingredient the introduction of additional symmetric arguments typically structural tensors into the relevant scalar valued isotropic tensor functions on this basis the fundamental covariance relation leads us to a formulation which allows itself to be set up directly in terms of spatial arguments and thus guarantees a convenient implementation within a finite element setting

covariance matrix selection and estimation via penalised normal likelihood summary we propose a nonparametric method for identifying parsimony and for producing a statistically efficient estimator of a large covariance matrix we reparameterise a covariance matrix through the modified cholesky decomposition of its inverse or the one step ahead predictive representation of the vector of responses and reduce the nonintuitive task of modelling covariance matrices to the familiar task of model selection and estimation for a sequence of regression models the cholesky factor containing these regression coefficients is likely to have many off diagonal elements that are zero or close to zero penalised normal likelihoods in this situation with l1 and l2 penalities are shown to be closely related to tibshirani s 1996 lasso approach and to ridge regression adding either penalty to the likelihood helps to produce more stable estimators by introducing shrinkage to the elements in the cholesky factor while because of its singularity the l1 penalty will set some elements to zero and produce interpretable models an algorithm is developed for computing the estimator and selecting the tuning parameter the proposed maximum penalised likelihood estimator is illustrated using simulation and a real dataset involving estimation of a 102 x 102 covariance matrix

analysis of the anisotropic viscoplastic damage response of composite laminates continuum basis and computational algorithms the mathematical structure underlying the rate equations of a recently developed constitutive model for the coupled viscoplastic damage response of anisotropic composites is critically examined in this regard a number of tensor projection operators have been identified and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the euler fully implicit integration method in particular this facilitated i the derivation of explicit expressions of the consistent material tangent stiffnesses that are valid for both three dimensional as well as subspace e g plane stress formulations ii the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint and iii the development of an effective time step control strategy to ensure accuracy and convergence of the solution in addition the special limiting case of inviscid elastoplasticity is treated the results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed

a shell finite element for large strain elastoplasticity with anisotropies part i shell theory and variational principle a shell model for finite elastic and finite plastic strains is derived taking into account initial and induced anisotropies a corresponding eight node c 0 shell element with three displacement and three director degrees of freedom at each node is developed which combines the advantages of an isoparametric description of geometry and deformation with an effective plane stress formulation the element accounts for isochoric or approximately isochoric deformation due to finite plastic strains because of the three displacement and three director degrees of freedom at each node it is easily possible to link different parts of a composed irregular shell structure or to connect the derived shell element with solid brick elements this paper presents the shell theory based on the kinematics of finite elastoplasticity proposed in schieck and stumpf 1995 and the special geometric concept of the derived shell model the lagrange multiplier method is applied to introduce into the virtual work principle the transverse normality constraint and the condition of isochoric deformation where the lagrange multipliers can be condensed inside the element procedure various assumed strain techniques designed to avoid the membrane locking are compared with known methods in the literature according to the numerical experience so far the proposed shell finite element is free of locking effects and spurious modes part ii presents the constitutive equations for finite elastic plastic strains accounting for initial and induced anisotropies and the implementation of the model into the fe code a comprehensive set of numerical examples is provided involving the tension of a plane specimen with necking and shear band localization the elastic plastic response of a simply supported plate with a localization of the plastic bending strains in the four corner zones the elastic plastic deformation mode of the so called scordelis lo roof and the elastic plastic buckling of a cylindrical shell showing an essential influence of the anisotropic material behavior the results illustrate the performance of the proposed shell finite element for a wide range of engineering applications

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

on the implementation of inelastic constitutive equations with special reference to large deformation problems abstract methods for finite element analysis of inelastic problems are reviewed problems with currently popular methods based on rate principles of virtual work are pointed out a formulation is presented based on the exact incremental virtual work equation the procedure for integration of the constitutive rate equations to obtain incremental constitutive equations is based on the assumption of a constant strain rate or straight strain path during the increment full newton raphson iteration is used to solve the resulting set of nonlinear equations the treatment of the constitutive equations in this newton raphson scheme leads to a linearized form which is substantially different from the classical rate equations the procedure is implemented in a finite element program and its effectiveness is shown in a number of examples

an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

a formulation of finite elastoplasticity based on dual co and contra variant eigenvector triads normalized with respect to a plastic metric the article presents a new formulation of isotropic elastoplasticity at large strains in both the lagrangian and the eulerian geometric setting and addresses aspects of its numerical implementation the key ingredients on the theoretical side are the introduction of a plastic metric for the description of the local history dependent inelastic material response the definition of a convex elastic domain in the space of the local stress like variable conjugate to the plastic metric denoted as the plastic force and a fully equivalent lagrangian and eulerian representation of all constitutive functions in spectral form for general non cartesian coordinate charts in terms of dual co and contra variant eigenvector triads which are normalized with respect to the plastic metric on the numerical side we propose a stress update algorithm for general non associative isotropic elasto visco plastic response with an arbitrary number of scalar internal variables the algorithm is based on an exponential map integrator and is recast into a general return mapping scheme methodically organized with tensorial pre and postprocessing and a constitutive box in the eigenvalue space furthermore we propose a new perturbation stabilization technique which dramatically enhances the convergence of the general return algorithm the theoretical and numerical developments are applied to a constitutive model problem with large elastic and large plastic strains the von mises tresca type associative plastic flow in ogden type large strain elastic materials

consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part i theoretical formulation abstract a derivation of the projected algorithm for general isotropic three invariant plasticity models under plane stress conditions is presented it is obtained by consistently specializing the 3d formulation to the 2d subspace defined by the plane stress condition closed form intrinsic algorithm linearization and a novel expression of the consistent tangent tensor are provided these are also shown to directly emanate from the analogous quantities pertaining to the fully 3d case a detailed discussion of the proposed implementation along with a representative set of numerical examples is provided in the second part of this paper valoroso n rosati l 2008 consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part ii computational issues international journal of solids and structures 46 92 124

on a path following method for non linear solid mechanics with applications to structural and cardiac mechanics subject to arbitrary loading scenarios abstract in computational solid mechanics path following methods have been proven useful when dealing with non monotonously evolving loading magnitudes as encountered e g in instability or softening behaviour the present work derives from a displacement based method a cavity volume based path following method and considers its application specifically to cardiac mechanics problems both methods are able to account for an arbitrary number of simultaneously acting loading conditions when applied to the newton raphson method the corresponding loading increments are computed by means of volume increments or point wise prescribed displacement increments respectively no additional variables are required and the physics of the problem at hands is not altered both methods are implemented in an in house meshfree modelling software and successfully applied to non linear elastic and inelastic problems in structural mechanics the cavity volume control method in particular is demonstrated to accurately predict the highly non linear elastic and anisotropic material behaviour encountered when modelling the heart albeit the proposed methods can be equally used e g in finite element methods they are very well suited for meshfree methods where the kronecker delta property does not apply

parsimonious covariance matrix estimation for longitudinal data this article proposes a data driven method to identify parsimony in the covariance matrix of longitudinal data and to exploit any such parsimony to produce a statistically efficient estimator of the covariance matrix the approach parameterizes the covariance matrix through the cholesky decomposition of its inverse for longitudinal data this is a one step ahead predictive representation and the cholesky factor is likely to have off diagonal elements that are zero or close to zero a hierarchical bayesian model is used to identify any such zeros in the cholesky factor similar to approaches that have been successful in bayesian variable selection the model is estimated using a markov chain monte carlo sampling scheme that is computationally efficient and can be applied to covariance matrices of high dimension it is demonstrated through simulations that the proposed method compares favorably in terms of statistical efficiency with a highly regarded competing approach the estimator is applied to three

a shell finite element for large strain elastoplasticity with anisotropies part ii constitutive equations and numerical applications abstract an eight node c 0 shell element for finite elastic plastic deformations with anisotropies is developed it combines the advantages of an isoparametric description of geometry and deformation the application of tensors in cartesian components and a real and effective plane stress description with three displacement and three director degrees of freedom at each node in part i of the paper the shell theory including the kinematics the variational principle the application of lagrange multipliers with their condensation on the element level and a comparative study of various assumed strain techniques were presented and the results of convergence tests given in this paper we consider the constitutive equations for large elastic and large plastic strains accounting for initial and induced anisotropies and the corresponding thermodynamics then we investigate the return algorithm for finite strains and the implementation of the element procedure including stiffness matrix and residual force vector finally we present the results of extended numerical applications and a comparison with fe solutions published in the literature as far as such are available

on the formulation and numerical solution of problems in anisotropic finite plasticity abstract this article discusses an extension of the green naghdi finite plasticity theory to explicitly include anisotropic effects in the stress response yield condition flow rule and hardening rule constitutive models are developed within the context of the extended theory and used in formulating implicit integration algorithms which inherit the characteristics of the classical return mapping scheme of isotropic plasticity representative numerical simulations demonstrate the applicability and predictive capacity of the proposed model in the presence of large plastic deformations

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

a hyperelastic based large strain elasto plastic constitutive formulation with combined isotropic kinematic hardening using the logarithmic stress and strain measures summary this paper addresses the formulation of a set of constitutive equations for finite deformation metal plasticity the combined isotropic kinematic hardening model of the infinitesimal theory of plasticity is extended to the large strain range on the basis of three main assumptions i the formulation is hyperelastic based ii the stress strain law preserves the elastic constants of the infinitesimal theory but is written in terms of the hencky strain tensor and its elastic work conjugate stress tensor and iii the multiplicative decomposition of the deformation gradient is adopted since no stress rates are present the formulation is of course numerically objective in the time integration it is shown that the model gives adequate physical behaviour and comparison is made with an equivalent constitutive model based on the additive decomposition of the strain tensor

a formulation of the mitc4 shell element for finite strain elasto plastic analysis abstract a finite strain elasto plastic formulation is developed for the mitc4 shell element the developed formulation is based on lee s multiplicative decomposition of the deformation gradient and on the hyperelastic expression of von mises flow rule expressed in terms of hencky s strain tensor the formulation incorporates thickness stretching degrees of freedom that are condensed at the element level by imposing the classical in layer plane stress condition a symmetric and consistent tangent stiffness matrix is also developed

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

on use of the em algorithm for penalized likelihood estimation summary the em algorithm is a popular approach to maximum likelihood estimation but has not been much used for penalized likelihood or maximum a posteriori estimation this paper discusses properties of the em algorithm in such contexts concentrating on rates of conver gence and presents an alternative that is usually more practical and converges at least as quickly the em algorithm is a general approach to maximum likelihood estimation rather than a specific algorithm dempster et al 1977 discussed the method and derived basic properties demonstrating that a variety of procedures previously developed rather informally could be unified the common strand to problems where the approach is applicable is a notion of incomplete data this includes the conventional sense of missing data but is much broader than that the em algorithm demon strates its strength in situations where some hypothetical experiment yields data from which estimation is particularly convenient and economical the incomplete data actually at hand are regarded as observable functions of these complete data the resulting algorithms while usually slow to converge are often extremely simple and remain practical in large problems where no other approaches may be feasible dempster et al 1977 briefly refer to the use of the same approach to the problem of finding the posterior mode maximum a posteriori estimate in a bayesian estima

a model of finite strain viscoplasticity based on unified constitutive equations theoretical and computational considerations with applications to shells abstract a model of multiplicative finite strain viscoplasticity is developed hereby the elastic internal potential is assumed to depend quadratically on the elastic strain measure ce by means of corresponding invariants hence possible extension of the model to take anisotropy into account is straightforward the evolution equation of the unified type due to bodner and partom asme j appl mech 42 1975 385 are modified so as to fit into the framework adopted the numerical treatment of the problem is fully developed specifically the algorithmic aspects of the resulting non additive structure are intensively discussed hereby the treatment of the exponential map of a non symmetric argument is of a central importance two consistent methods are developed various applications to shell problems are considered hereby a shell theory with seven degrees of freedom together with a 4 node enhanced strain finite element formulation are used a central feature of the shell formulation is its eligibility to the application of a three dimensional constitutive law

a computational model for elasto viscoplastic solids at finite strain with reference to thin shell applications this work extends a previously developed methodology for computational plasticity at finite strains that is based on the exponential map and logarithmic stretches to the context of isotropic elasto viscoplastic solids a particular form of the strain energy function given in terms of its principal values is employed it is noticeable that within the proposed framework the small strain integration algorithms and the corresponding consistent tangent operators automatically extend to the finite strain regime central to the effort of this formulation is the derivation of the closed form of a tangent modulus obtained by linearization of incremental non linear problem this ensures asymptotically quadratic rates of convergence of the newton raphson procedure in the implicit finite element solution to illustrate the performance of the presented formulation several numerical examples involving failure by strain localization and finite deformations are given 1998 john wiley sons ltd

on anisotropic flow rules in multiplicative elastoplasticity at finite strains abstract hill s anisotropic formulation of the flow rule is extended so as to fit in the realm of multiplicative finite strain plasticity the anisotropic hill type yield criterion is formulated in terms of purely material quantities the list of arguments of the flow function includes a non symmetric material eshelby like stress tensor as well as structural tensors that describe the anisotropy at hand the formulation is exemplified on orthotropy where three structural tensors are employed the fact that the stress tensor is not symmetric necessitates a special treatment of the flow function where representation theorems of tensor valued function with non symmetric arguments are invoked the consequences of such a definition on the resulting inelastic rate are discussed in full it is shown that the corresponding resulting rate as defined at the actual configuration is not symmetric any more accordingly the rate naturally includes a plastic material spin moreover we deal with the theoretically interesting question of how to define spin free rates it is also demonstrated that the flow function must depend not only on the stress tensor and on adequate structural tensors but also on the deformation itself in form of the right cauchy green tensor c however this surprising dependency which must obey a specific form can be justified as physically meaningful various numerical examples of large plastic deformations of structural components are presented that underpin the capabilities of the formulation

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

a continuum based shell theory for non linear applications the paper introduces a non linear shell theory which provides a complete three dimensional state of stress since the theory is derived from simple three dimensional continuum mechanics it is very easy to understand as an example the theory is applied to quadrilateral shell elements which provide only displacement degrees of freedom located at nodes on the outer surfaces and one degree of freedom at the middle surface it is proposed to eliminate this degree of freedom on element level so that the elements have the same layout as the equivalent brick elements but have a better behaviour in bending have stress resultants and are cheaper with respect to computational effort the advantages with respect to implementation in a finite element program as well as in special applications are obvious however well known conditioning problems in thin shell applications must be expected therefore emphasis is put on this issue in the example problems it is shown that the elements can give acceptable answers in engineering applications and offer a potential for material non linear applications which will be considered in a forthcoming paper

on the mathematical foundation of the 1 1 2 platemodel abstract the plate problem of three dimensional 3 d linearized elastostatics is considered inthe framework of the hierarchical modelling with the help of the energy projection method it isshown that the 1 1 2 bending model is the simplest asymptotically correct model in thehierarchical family i e the distance between the solution of the 3 d problem and themodel solution in the energy norm tends to zero for vanishing plate thickness h whileusing unmodified 3 d material laws the formulation of the 1 1 2 bending model and the mechanical significance of itsingredients are discussed we present error estimates for the deviation of the 1 1 2 solutionfrom the kirchhoff solution as well as from the 3 d solution by using the 1 1 2 energy normand the 3 d energy norm respectively the analysis leads to h as order of convergence the results are illustrated by a numerical example

functional mapping of quantitative trait loci underlying growth trajectories using a transform both sides logistic model the incorporation of developmental control mechanisms of growth has proven to be a powerful tool in mapping quantitative trait loci qtl underlying growth trajectories a theoretical framework for implementing a qtl mapping strategy with growth laws has been established this framework can be generalized to an arbitrary number of time points where growth is measured and becomes computationally more tractable when the assumption of variance stationarity is made in practice however this assumption is likely to be violated for age specific growth traits due to a scale effect in this article we present a new statistical model for mapping growth qtl which also addresses the problem of variance stationarity by using a transform both sides tbs model advocated by carroll and ruppert 1984 journal of the american statistical association 79 321 328 the tbs based model for mapping growth qtl cannot only maintain the original biological properties of a growth model but also can increase the accuracy and precision of parameter estimation and the power to detect a qtl responsible for growth differentiation using the tbs based model we successfully map a qtl governing growth trajectories to a linkage group in an example of forest trees the statistical and biological properties of the estimates of this growth qtl position and effect are investigated using monte carlo simulation studies the implications of our model for understanding the genetic architecture of growth are discussed

formulation of implicit finite element methods for multiplicative finite deformation plasticity some constitutive and computational aspects of finite deformation plasticity are discussed attention is restricted to multiplicative theories of plasticity in which the deformation gradients are assumed to be decomposable into elastic and plastic terms it is shown by way of consistent linearization of momentum balance that geometric terms arise which are associated with the motion of the intermediate configuration and which in general render the tangent operator non symmetric even for associated plastic flow both explicit i e no equilibrium iteration and implicit finite element formulations are considered an assumed strain formulation is used to accommodate the near incompressibility associated with fully developed isochoric plastic flow as an example of explicit integration the rate tangent modulus method is reviewed in some detail an implicit scheme is derived for which the consistent tangents resulting in quadratic convergence of the equilibrium iterations can be written out in closed form for arbitrary material models all the geometrical terms associated with the motion of the intermediate configuration and the treatment of incompressibility are given explicitly examples of application to void growth and coalescence and to crack tip blunting are developed which illustrate the performance of the implicit method

on the numerical implications of multiplicative inelasticity with an anisotropic elastic constitutive law the statement that theories of inelasticity at finite strains have arrived at a high level of development is only true in conjunction with isotropic material behaviour from both points of view theoretical and computational the extension to anisotropic material behaviour seems to be a complicated task the statement is especially true when the multiplicative decomposition of the deformation gradient is considered a basis for the formulation of special interest are questions related to the mathematical form of the stored energy function or equivalently of the constitutive relation for the material stress tensor as the thermodynamical force this paper deals with the above issues the anisotropic formulation is accomplished using the notion of structural tensors here we suggest that the privileged directions of the material should be transformed in a specific way under the action of the inelastic part of the deformation gradient the inelastic behaviour is assumed to be governed by evolution equations of the unified type numerically we deal with the full multiplicative structure of the theory the numerical treatment is developed in full detail expressions concerning the local iteration as well as the tangent operator are derived various numerical examples with applications to shells are presented which demonstrate the influence of anisotropy and the applicability of the theory

maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix the positive definiteness constraint is the most awkward stumbling block in modelling the covariance matrix pourahmadi s 1999 unconstrained parameterisation models covariance using covariates in a similar manner to mean modelling in generalised linear models the new covariance parameters have statistical interpretation as the regression coefficients and logarithms of prediction error variances corresponding to regressing a response on its predecessors in this paper the maximum likelihood estimators of the parameters of a generalised linear model for the covariance matrix their consistency and their asymptotic normality are studied when the observations are normally distributed these results along with the likelihood ratio test and penalised likelihood criteria such as bic for model and variable selection are illustrated using a real dataset

generalized likelihood ratio statistics and wilks phenomenon likelihood ratio theory has had tremendous success in parametric inference due to the fundamental theory of wilks yet there is no general applicable approach for nonparametric inferences based on function estimation maximum likelihood ratio test statistics in general may not exist in nonparametric function estimation setting even if they exist they are hard to find and can not be optimal as shown in this paper we introduce the generalized likelihood statistics to overcome the drawbacks of nonparametric maximum likelihood ratio statistics a new s wilks phenomenon is unveiled we demonstrate that a class of the generalized likelihood statistics based on some appropriate nonparametric estimators are asymptotically distribution free and follow chi 2 distributions under null hypotheses for a number of useful hypotheses and a variety of useful models including gaussian white noise models nonparametric regression models varying coefficient models and generalized varying coefficient models we further demonstrate that generalized likelihood ratio statistics are asymptotically optimal in the sense that they achieve optimal rates of convergence given by ingster they can even be adaptively optimal in the sense of spokoiny by using a simple choice of adaptive smoothing parameter our work indicates that the generalized likelihood ratio statistics are indeed general and powerful for nonparametric testing problems based on function estimation

on theory and numerics of large viscoplastic deformation abstract a multiplicative theory and corresponding computations of finite elastic viscoplastic deformations based on unified constitutive equations are presented basic features of theory are 1 the inelastic part of the deformation gradient is understood as a material stretch type tensor no need arises for the notion of the intermediate configuration 2 in the isotropic case the use of an elastic logarithmic strain tensor is shown to lead to the identification that the elastic strains are given by the quantity c 1 p c with c p being an inelastic cauchy green type tensor 3 in spite of the fact that the logarithmic strain measure is used closed forms of the tangent operator within an implicit time integration scheme are given circumventing very involved elaborations when the spectral decomposition is used 4 evolution equations of the bodner and partom type are employed a general formalism is developed for the application of the evolution laws of the unified type within the theoretical framework the formalism can be used to generalize any unified evolution equations formulated for infinetismal strains to the range of finite strains 5 for the axisymmetric case in addition to the displacement based 4 node and 9 node finite elements an enhanced strain 4 node element is presented it is shown anyhow that in the highly nonlinear regime the enhanced strain formulation may exhibit numerical instabilities different numerical examples of finite strain deformations are presented

generalized midpoint finite element dynamic analysis of elastoplastic systems the application of a four parameter generalized midpoint integration method to small displacement elastoplastic dynamic problems is considered the integration of the governing relations over a time step is formulated as a non linear algebraic problem finite step problem by making use of generalized variables finite element modelling uniqueness and an extremum characterization of the solution of the finite step problem are discussed sufficient conditions for convergence of various iterative algorithms including newton raphson are given the b stability of the proposed procedure is assessed

on the numerical integration of a class of pressure dependent plasticity models with mixed hardening radial return algorithms for both three dimensional and plane stress situations are developed for a class of pressure dependent plasticity models formulated in state variables with mixed hardening the consistent tangent matrix has been developed which among other advantages does not require numerical inversion the algorithms for gurson s mixed hardening model are incorporated in a finite element program to solve several simple uniaxial tension problems when compared with numerically integrated solutions the results from the finite element analysis show excellent agreement finally results of the axisymmetric necking problem using gurson s mixed hardening model are presented as an example of application

sparsistency and rates of convergence in large covariance matrix estimation this paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions here sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one depending on the case of applications sparsity priori may occur on the covariance matrix its inverse or its cholesky decomposition we study these three sparsity exploration problems under a unified framework with a general penalty function we show that the rates of convergence for these problems under the frobenius norm are of order s n log p n n 1 2 where s n is the number of nonzero elements p n is the size of the covariance matrix and n is the sample size this explicitly spells out the contribution of high dimensionality is merely of a logarithmic factor the conditions on the rate with which the tuning parameter n goes to 0 have been made explicit and compared under different penalties as a result for the l 1 penalty to guarantee the sparsistency and optimal rate of convergence the number of nonzero elements should be small sn o pn at most among o pn2 parameters for estimating sparse covariance or correlation matrix sparse precision or inverse correlation matrix or sparse cholesky factor where sn is the number of the nonzero elements on the off diagonal entries on the other hand using the scad or hard thresholding penalty functions there is no such a restriction

sparse covariance matrix estimation by dca based algorithms this letter proposes a novel approach using the formula see text norm regularization for the sparse covariance matrix estimation scme problem the objective function of scme problem is composed of a nonconvex part and the formula see text term which is discontinuous and difficult to tackle appropriate dc difference of convex functions approximations of formula see text norm are used that result in approximation scme problems that are still nonconvex dc programming and dca dc algorithm powerful tools in nonconvex programming framework are investigated two dc formulations are proposed and corresponding dca schemes developed two applications of the scme problem that are considered are classification via sparse quadratic discriminant analysis and portfolio optimization a careful empirical experiment is performed through simulated and real data sets to study the performance of the proposed algorithms numerical results showed their efficiency and their superiority compared with seven state of the art methods

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

on the computational significance of the strain space formulation of plasticity theory the strain space and traditional stress space formulations of plasticity theory are compared we show how plasticity theory has been implemented numerically to solve static and dynamic problems and conclude that the numerical loading criteria that have been used for two decades are identical to the strain space loading criteria proposed by naghdi and co workers

on the numerical integration of three invariant elastoplastic constitutive models abstract we investigate the performance of a numerical algorithm for the integration of isotropically hardening three invariant elastoplastic constitutive models with convex yield surfaces the algorithm is based on a spectral representation of stresses and strains for infinitesimal and finite deformation plasticity and a return mapping in principal stress directions smooth three invariant representations of the mohr coulomb model such as the lade duncan and matsuoka nakai models are implemented within the framework of the proposed algorithm among the specific features incorporated into the formulation are the hardening softening responses and the tapering of the yield surfaces toward the hydrostatic axis with increasing confining pressure isoerror maps are generated to study the local accuracy of the numerical integration algorithm finally a boundary value problem involving loading of a strip foundation on a soil is analyzed with and without finite deformation effects to investigate the performance of the integration algorithm in a full scale non linear finite element simulation

on a numerical implementation of a formulation of anisotropic continuum elastoplasticity at finite strains in a recent theoretical study see c sansour i karsaj j soric a formulation of anisotropic continuum elastoplasticity at finite strains part i modelling international journal of plasticity 22 2006 2346 2365 a constitutive model for anisotropic elastoplasticity at finite strains has been developed the model is based on the multiplicative decomposition of the deformation gradient the stored energy function as well as the flow rule has been considered as quadratic functions of their arguments in both cases the list of arguments is extended to include structural tensors which describe the anisotropy of the material response at hand non linear isotropic hardening is considered as well in this paper the integration of the constitutive law is presented the associative flow rule is integrated using the exponential map which preserves the plastic incompressibility condition the numerical treatment of the problem is fully developed and expressions related to the local iteration and the consistent tangent operator are considered in detail it is shown that while the consistent linearisation of the model is quite complicated it still can be achieved if various intriguing implicit dependencies are identified and correctly dealt with various numerical examples of three dimensional deformations of whole structural components are presented the examples clearly illustrate the influence of anisotropy on finite elastoplastic deformations

an element by element solution algorithm for problems of structural and solid mechanics abstract it is proposed to solve large scale finite element equation systems arising in structural and solid mechanics by way of an element by element approximate factorization technique which obviates the need for a global coefficient matrix the procedure has considerable operation count and i o advantages over direct elimination schemes and it is easily implemented numerical results demonstrate the effectiveness of the method and suggest its potential for the analysis of large scale systems

a consistent formulation for the integration of combined plasticity and creep within the context of the consistent tangent update this paper outlines a stress update algorithm for combined creep and plasticity the algorithm is implicit providing unconditional stability and utilizes local newton iteration to solve scalar forms of the coupled constitutive equations for the creep and plastic strain increments the tangent for the local iteration is obtained accurately providing quadratic convergence at the gauss point level quadratic convergence of the global iteration procedure is also maintained using an explicitly derived consistent tangent for combined plasticity and creep further combination with an automatic time stepping scheme provides an efficient stable accurate and robust computational algorithm the algorithm has been implemented in the general purpose fe package lusas1

finite element concepts for finite elastoplastic strains and isotropic stress response in shells theoretical and computational analysis this paper presents appropriate finite element concepts accounting for finite elastoplastic strains and isotropic stress response in arbitrary shells three parameterization strategies for the calculation of thin and thick smooth shells as well as shell intersections are discussed in detail in this context the importance of the deformation gradient for an efficient implementation is especially emphasized according to the parameterizations the computational plasticity algorithms are derived in general three dimensional 3 d form for thick shell structures and a restricted 2 d form satisfying the plane stress state underlying thin shells in order to describe arbitrary shell geometries the isoparametric concept is applied to all proposed finite element formulations these are based on quadrilateral 4 node mixed finite shell elements the variational approaches of the enhanced assumed strain method the assumed natural strain concept and the reduced integration technique are accurately considered by means of representative numerical examples the performance of the three different finite element concepts is demonstrated furthermore their individual properties are addressed with respect to efficiency and numerical accuracy thus crucial consequences for an optimal modelling of finite plastic strains in shells can be outlined

integrated structural analysis and design using three dimensional finite elements a design approach that combines iterative structural analysis with a traditional iterative optimization algorithm is applied to the optimum design of the shape of a hole in a plate in tension the plate is modeled by threedimensional finite elements and an element by el ement preconditioned conjugate gradient iterative algorithm is used for solving the equations of equilibrium several parameterizations of the optimum shape are considered and it is shown that a sine series can describe the optimum shape with only three design variables whereas other series require seven variables for similar results the optimum shape compares well with an experimental optimum obtained by a j durelli an investigation is performed to determine the best way of obtaining finite difference derivatives of the stresses with respect to design variables it is shown that a method based on modifying the equations of equilibrium for the perturbed problem performs best the benefit of the integrated approach is determined by comparing convergence with different initial iterates for the displacement field it is shown that using the final iterate of the previous solution can reduce the number of analysis iterations by about 40 compared to starting with a zero initial iterate

a theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains the article presents new aspects of large strain isotropic elastoplastic analysis of shells on the shell theory side we consider several possible continuum based parametrizations of the shell deformation and investigate their applicability with respect to the implementation of general three dimensional local constitutive models as an aspect of computational shell analysis we then discuss in detail the numerical implementation of a shell based on the parametrization of the top and bottom surface in terms of a new 8 node brick type mixed finite shell element on the basis of assumed strain and enhanced strain variational approaches on the side of plasticity theory we adopt a recently proposed intermediate configuration free formulation of large strain plasticity based on the notion of a plastic metric and consider its representation with respect to the parameter manifold of the shell this frame is formulated in terms of principal strains and principal stresses with respect to dual co and contra variant eigenvector triads associated with a mixed variant elastic strain tensor the new aspect of computational plasticity is the development of a stress update algorithm for the plasticity model mentioned above which includes a general return mapping in the eigenvalue space the algorithm can be applied to general coordinate charts and is particularly convenient when formulated with respect to the space of the curvilinear coordinates of the shell parametrization we demonstrate the performance of the finite element formulation and constitutive algorithms by means of several numerical examples

nonparametric estimation of large covariance matrices of longitudinal data summary estimation of an unstructured covariance matrix is difficult because of its positivedefiniteness constraint this obstacle is removed by regressing each variable on its predecessors so that estimation of a covariance matrix is shown to be equivalent to that of estimating a sequence of varying coefficient and varying order regression models our framework is similar to the use of increasing order autoregressive models in approximating the covariance matrix or the spectrum of a stationary time series as an illustration we adopt fan zhang s 2000 two step estimation of functional linear models and propose nonparametric estimators of covariance matrices which are guaranteed to be positive definite for parsimony a suitable order for the sequence of auto regression models is found using penalised likelihood criteria like aic and bic some asymptotic results for the local polynomial estimators of components of a covariance matrix are established two longitudinal datasets are analysed to illustrate the methodology a simulation study reveals the advantage of the nonparametric covariance estimator over the sample covariance matrix for large covariance matrices

sensitivity calculations for iteratively solved problems the calculation of sensitivity derivatives of solutions of iteratively solved systems of algebraic equations is investigated a modified finite difference procedure is presented which improves the accuracy of the calculated derivatives the procedure is demonstrated for a simple algebraic example as well as an element by element preconditioned conjugate gradient iterative solution technique applied to truss examples

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

three dimensional extension of non linear shell formulation based on the enhanced assumed strain concept conventional shell formulations such as 3 or 5 parameter theories or even 6 parameter theories including the thickness change as extra parameter require a condensation of the constitutive law in order to avoid a significant error due to the assumption of a linear displacement field across the thickness this means that the normal stress in thickness direction has to either vanish or be constant in general these extra constraints cannot be satisfied explicitly or they lead to elaborate strain expressions the main objective of the present study is to introduce directly a complete 3 d constitutive law without modification therefore a 7 parameter theory is utilized which includes a linear varying thickness stretch as extra variable allowing also large strain effects