linear systems and normality this paper is concerned with responses of linear systems to non gaussian random excitation and with the measurement of the departure of the responses from gaussian behavior first we show the classical rosenblatt result and its nonapplicability to the most popular practical systems described by differential equations of first and second order then using a simple measure of departure from normality the asymmetry and excess coefficients and performing numerical calculations we give quantitative information about the effect of system parameters and the radius of correlation of the excitation process on the distance from normality

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

universal anisotropic yield criterion based on superquadric functional representation part 1 algorithmic issues and accuracy analysis abstract a robust and efficient stress update algorithm for the anisotropic yield criterion represented in the form of superquadric function introduced by barlat et al is presented it relies on a discrete variational formulation of the lagrangian functional which results from the principle of maximum plastic dissipation numerical solution of the discretized equations of evolution is based on the operator split methodology and the newton raphson method a line search algorithm is implemented to overcome numerical instabilities and to expand the convergence region of the basic newton raphson solution procedure the consistent tangent modulus is expressed in a closed form as a result of the exact linearization of the discrete kuhn tucker condition numerical testing of the integration algorithm based on iso error maps is provided for several variants of the yield function

non smooth multisurface plasticity and viscoplasticity loading unloading conditions and numerical algorithms rate independent plasticity and viscoplasticity in which the boundary of the elastic domain is defined by an arbitrary number of yield surfaces intersecting in a non smooth fashion are considered in detail it is shown that the standard kuhn tucker optimality conditions lead to the only computationally useful characterization of plastic loading on the computational side an unconditionally convergent return mapping algorithm is developed which places no restrictions aside from convexity on the functional forms of the yield condition flow rule and hardening law the proposed general purpose procedure is amenable to exact linearization leading to a closed form expression of the so called consistent algorithmic tangent moduli for viscoplasticity a closed form algorithm is developed based on the rate independent solution the methodology is applied to structural elements in which the elastic domain possesses a non smooth boundary numerical simulations are presented that illustrate the excellent performance of the algorithm

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

definition of a general implicit orthotropic yield criterion abstract the definition of an orthotropic yield criterion presents a serious challenge in the formulation of constitutive models based on such theories as elastoplasticity viscoplasticity damage etc the need to model the behavior of a real orthotropic material requires the formulation of orthotropic yield criteria and these may be difficult to obtain for metals orthotropic yield functions have been formulated by hill proc roy soc lon ser a 193 1948 281 j mech phys solids 38 3 1990 200 barlat int j plasticity 5 1989 51 7 1991 693 chu numisheet 93 1993 199 and dutko et al comput methods appl mech engrg 109 1993 73 but in many cases these functions do not describe the true behavior of the metal the situation is worse when one attempts to represent a nonmetal such as a polymer ceramic or composite in this paper we present a general definition of an explicit orthotropic yield criterion together with a general method for defining implicit orthotropic yield functions the latter formulation is based on the transformed tensor method whose principal advantage lies in the possibility of adjusting an arbitrary isotropic yield criterion to the behavior of an anisotropic material as example we choose the adjustment to the hill hoffman j comp materials 1 1967 200 and tsai wu j comp materials 5 1971 58 criteria but these particular cases serve to establish the methodology for achieving the desired function adjustment for any other well known criterion or experimental set of data obtained from laboratory

numerical computation of a certain dirichlet series attached to siegel modular forms of degree two the rankin convolution type dirichlet series df g s of siegel modular forms f and g of degree two which was introduced by kohnen and the second author is computed numerically for various f and g in particular we prove that the series df g s which share the same functional equation and analytic behavior with the spinor l functions of eigenforms of the same weight are not linear combinations of those in order to conduct these experiments a numerical method to compute the petersson scalar products of jacobi forms is developed and discussed in detail

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

time integration scheme for elastoplastic models based on anisotropic strain rate potentials modelling of plastic anisotropy requires the definition of stress potentials coinciding with the yield criteria in case of the associated flow rules or alternatively plastic strain rate potentials the latter approach has several advantages whenever material parameters are determined by means of texture measurements and crystal plasticity simulations this paper deals with a phenomenological description of anisotropy in elastoplastic rate insensitive models by using strain rate potentials a fully implicit time integration algorithm is developed in this framework and implemented in a static implicit finite element code algorithmic details are discussed including the derivation of the consistent algorithmic tangent modulus and the numerical treatment of the yield condition typical sheet forming applications are simulated with the proposed implementation using the recent non quadratic strain rate potential srp2004 18p numerical simulations are carried out for materials that exhibit strong plastic anisotropy the numerical results confirm that the presented algorithm exhibits the same generality robustness accuracy and time efficiency as state of the art yield criterion based algorithms

weil representations associated with finite quadratic modules to any finite quadratic module that is a finite abelian group together with a non degenerate quadratic form it is possible to associate a representation of mathrm mp 2 mathbb z the metaplectic cover of the modular group this representation is usually referred to as a weil representation and our main result is a general explicit formula for its matrix coefficients this result completes earlier work by scheithauer in the case when the representation factors through mathrm sl 2 mathbb z furthermore our formula is given in a such a way that it is easy to implement efficiently on a computer

elasto plastic finite element method based on incremental deformation theory and continuum based shell elements for planar anisotropic sheet materials abstract an implicit approach for the incremental analysis of planar anisotropic sheet forming processes is developed based on the incremental deformation theory the incremental deformation theory based on the minimum plastic work path enables convenient decoupling of deformation and rotation by the polar decomposition the mathematical description of a constitutive law for the incremental deformation theory is obtained from the flow theory along the minimum plastic work path the resulting constitutive law is then incorporated in an elasto plastic finite element analysis code in the elasto plastic formulation continuum based resultant cbr shell element is employed the cbr shell allows large rotation and large membrane bending strain the laminar coordinate system is taken to coincide with planar anisotropic material axes then planar anisotropic axes during deformation are updated using a newly developed algorithm based on the polar decomposition an iterative solving method based on the incremental deformation theory is also developed for an accurate and stable stress integration the planar anisotropy is incorporated into the formulation for sheet forming by introducing non quadratic barlat s yield function for verification purposes two examples have been simulated and compared with experimental results the good verification results show that the present elasto plastic formulation for planar anisotropic sheet materials can provide a good theoretical basis for more extended analyses of sheet forming processes

effects of parameter uncertainty on the response of vibratory systems to random excitation abstract vibratory systems subjected to a stationary random external excitation and having random uncertainties in parameters are analyzed some quantities characterizing the quality of such systems quality measures are defined and evaluated they are for example the average number of level crossings the average number of maxima and the departure from normality the effects of random uncertainty in system parameters on the quality measures are investigated analytically and numerically via conditioning this means that first the conditional quantities obtained for fixed parameters are used and then integration with respect to the appropriate distribution is performed the analysis includes also a discussion of the quality predictions for systems subjected to a random excitation with an exponential correlation by considering a system with an equivalent white noise excitation

symmetry preserving return mapping algorithms and incrementally extremal paths a unification of concepts in this work we seek to characterize the conditions under which an elastic plastic stress update algorithm preserves the symmetries inherent to the material response from a numerical standpoint the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality for the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving for hardening plasticity symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations we show that these restrictions amount to the existence of a pseudo internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli in view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and hence in symmetric tangents we address the question of whether any connections exist between the two approaches we show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence

computations of siegel modular forms of genus two we explain the basic notions and theorems for doing computations in the theory of siegel modular forms of degree two on the full modular group and of even weight this synopsis concludes with a handy and computationally realistic algorithm for tabulating the fourier coefficients of such forms and the euler factors of their spinor zeta functions in the second part of this paper we present and discuss some of the results of actual computations which we performed following this algorithm we point out two theoretically striking phenomena that are implied by the results of these computations

studies in anisotropic plasticity with reference to the hill criterion algorithms based upon the notion of return mapping have been developed for the hill yield function of anisotropic plasticity the relative accuracy of two algorithms is assessed by means of iso error maps the choice of the algorithm turns out to be much more critical for the orthotropic hill criterion than for the underlying isotropic von mises plasticity model a tangent operator that is consistent with the developed integration algorithm is formulated and its efficiency is assessed compared with the classical continuum tangent operator the model has been applied to three shell plate structures

on the formulation of closest point projection algorithms in elastoplasticity part i the variational structure we present in this paper the characterization of the variational structure behind the discrete equations defining the closest point projection approximation in elastoplasticity rate independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range the later in the context of isotropic finite strain multiplicative plasticity primal variational principles in terms of the stresses and stress like hardening variables are presented first followed by the formulation of dual principles incorporating explicitly the plastic multiplier augmented lagrangian extensions are also presented allowing a complete regularization of the problem in the constrained rate independent limit the variational structure identified in this paper leads to the proper framework for the development of new improved numerical algorithms for the integration of the local constitutive equations of plasticity as it is undertaken in part ii of this work

characteristics functionals of randomly excited physical systems abstract this paper deals with charateristics functionals of the solutions of a wide class of stochastic differential equations describing random physical processes first a construction of the characteristics functional is shown in a general case of the stochastic evolution equation in hilbert space then making use of the construction presented the analysis of three random physical processes is performed the random harmonic oscillator random wave process and random heat conduction special attention in these applications is focused on the cases where an excitation process has the form of a sequence of randomly arriving impulses

on a class of constitutive equations in viscoplasticity formulation and computational issues the viscoplastic constitutive model is formulated based on the existence of the dissipation potential which embodies the notion of the gauge minkowski function of the convex set a perturbation method is used for a solution of stiff differential equations characterizing the associated problem of evolution it relies on a discrete formulation of viscoplasticity which results from the regularized version of the principle of maximum plastic dissipation the operator split methodology and the newton raphson method are used to obtain the numerical solution of the discretized equations of evolution the consistent tangent modulus is expressed in a closed form as a result of the exact linearization of the discretized evolution equations for several variants of the flow potential function including some representative stiff functional forms numerical tests of the integration algorithm based on iso error maps are provided finally a numerical example is presented to illustrate the robustness and the effectiveness of the proposed approach

an incremental energy minimization state update algorithm for 3d phenomenological internal variable sma constitutive models based on isotropic flow potentials summary an incremental energy minimization approach for the solution of the constitutive equations of 3d phenomenological models for shape memory alloys sma is presented a robust algorithm for the solution of the resulting nonsmooth constrained minimization problem is devised without introducing any regularization in the dissipation or chemical terms the proposed algorithm is based on a thorough detection of the singularities relevant to the incremental energy formulation in conjunction with a newton raphson method equipped with a wolfe line search dealing with regular solutions the saturation constraint on the transformation strain is treated by means of an active set strategy thus avoiding any need for a two stage return mapping algorithm a parametrization of the saturation constraint manifold is introduced thus reducing the problem dimensionality with improved computational performance finally an efficient algorithm for the computation of the dissipation function in terms of haigh westergaard invariants is presented allowing for a quite general choice of deviatoric transformation functions numerical results confirm the robustness and consistency of the proposed state update algorithm copyright 2015 john wiley sons ltd

on the numerical integration of a class of pressure dependent plasticity models an unconditionally stable algorithm for the numerical integration of elastoplastic pressure dependent constitutive relations is analysed in detail in this paper the application of the method to plane stress problems in which the out of plane strain component is not defined kinematically is discussed the tangent moduli resulting from this integration algorithm are obtained by consistent linearization of the elastoplastic constitutive equations the algorithm is applied to gurson s constitutive model some one dimensional problems are solved and comparisons with exact solutions are made the paper closes with a numerical study of the necking of an axi symmetric specimen using gurson s plasticity model to describe the constitutive behaviour of the material