non linear analysis of shells with arbitrary evolving cracks using xfem a new formulation and numerical procedures are developed for the analysis of arbitrary crack propagation in shells using the extended finite element method the method is valid for completely non linear problems through the thickness cracks in sandwich shells are considered an exact shell kinematics is presented and a new enrichment of the rotation field is proposed which satisfies the director inextensibility condition to avoid locking an enhanced strain formulation is proposed for the 4 node cracked shell element a finite strain plane stress constitutive model based on the logarithmic corotational rate is employed a cohesive zone model is introduced which embodies the special characteristics of the shell kinematics stress intensity factors are calculated for selected problems and crack propagation problems are solved copyright 2004 john wiley sons ltd

approach to equilibrium of glauber dynamics in the one phase region i the attractive case various finite volume mixing conditions in classical statistical mechanics are reviewed and critically analyzed in particular somefinite size conditions are discussed together with their implications for the gibbs measures and for the approach to equilibrium of glauber dynamics inarbitrarily large volumes it is shown that dobrushin shlosman s theory ofcomplete analyticity and its dynamical counterpart due to stroock and zegarlinski cannot be applied in general to the whole one phase region since it requires mixing properties for regions ofarbitrary shape an alternative approach based on previous ideas of oliveri and picco is developed which allows to establish results on rapid approach to equilibrium deeply inside the one phase region in particular in the ferromagnetic case we considerably improve some previous results by holley and aizenman and holley our results are optimal in the sene that for example they show for the first time fast convergence of the dynamicsfor any temperature above the critical one for thed dimensional ising model with or without an external field in part ii we extensively consider the general case not necessarily attractive and we develop a new method based on renormalizations group ideas and on an assumption of strong mixing in a finite cube to prove hypercontractivity of the markov semigroup of the glauber dynamics

on the critical percolation probabilities we prove that the critical probabilities of site percolation on the square lattice satisfy the relation p c p 1 furthermore we prove the continuity of the function percolation probability

numerical study of consistency of rate constitutive equations with elasticity at finite deformation the present work is concerned with the numerical study of the elasticity consistency of the spatial rate equations using the conventional oldroyd truesdell cotter rivlin jaumann and green naghdi rates and the three novel co rotational e and l based logarithmic rates and of the rotated material rate equation describing the relationship between the material time derivatives of the rotated kirchhoff stress and material logarithmic strain to this end three integration procedures for updating stress are presented the stress responses of several typical deformation processes are simulated according to the numerical results we know that among the spatial rate equations only the logarithmic rate equation is consistent with elasticity under constant material parameters integrating the other spatial rate equations will provide path dependent stress response these numerical conclusions support the arguments in h xiao et al acta mechanica 1999 138 31 50 the reasons leading to elasticity inconsistency of spatial rate equations are analysed if the material parameters are assumed to be strain dependent the logarithmic rate equation loses also its elasticity consistent property the numerical results prove also that the spatial logarithmic and rotated material rate equations are equivalent to each other copyright 2002 john wiley sons ltd

a sharp transition for the two dimensional ising percolation we show that the percolation transition for the two dimensional ising model is sharp namely we show that for every reciprocal temperature 0 there exists a critical valueh c of external magnetic fieldh such that the following two statements hold we also shows that the percolation probability is continuous in h except on the half line 0 c

on the uniqueness of the infinite occupied cluster in dependent two dimensional site percolation we consider dependent site percolation on the two dimensional square lattice the underlying probability measure being invariant and ergodic under each of the translations and invariant under axis reflections if this measure satisfies the fkg condition and if percolation occurs then we show that the infinite occupied cluster is unique with probability 1 and that all vacant star clusters are finite

the critical probability for random voronoi percolation in the plane is 1 2 we study percolation in the following random environment let z be a poisson process of constant intensity on 2 and form the voronoi tessellation of 2 with respect to z colour each voronoi cell black with probability p independently of the other cells we show that the critical probability is 1 2 more precisely if p 1 2 then the union of the black cells contains an infinite component with probability 1 while if p 1 2 then the distribution of the size of the component of black cells containing a given point decays exponentially these results are analogous to kesten s results for bond percolation in 2 the result corresponding to harris theorem for bond percolation in 2 is known zvavitch noted that one of the many proofs of this result can easily be adapted to the random voronoi setting for kesten s results none of the existing proofs seems to adapt the methods used here also give a new and very simple proof of kesten s theorem for 2 we hope they will be applicable in other contexts as well

finite element study of the energy dissipation and residual stresses in the closed elastic deformation path in this paper energy dissipation and residual stress developments are numerically studied in three dimensional closed deformation paths different objective stress rates coded in a finite element program are compared in order to update the stresses implicit integration algorithm based on mid point rule for corotational and non corotational objective rates is used several corotational objective rates such as jaumann green naghdi eulerian and lagrangian triad based rates and non corotational rates such as truesdell and cotter rivlin rates are considered it is shown in this work that in some cases also a non integrable model may exhibit no dissipation energy at the end of a closed deformation path this study underlines some results previously obtained by other researchers i e among all considered stress rates the logarithmic rate manifests the best result in respect of elasticity requirements copyright 2006 john wiley sons ltd

on objective corotational rates and their defining spin tensors abstract in this paper we prove a general result on objective corotational rates and their defining spin tensors let be a spin tensor that is associated with the rotation and deformation of a deforming material body in an arbitrary manner indicated by y b d w where b and d and w are the left cauchy green tensor and the stretching tensor and the vorticity tensor respectively then the corotational rate of defined by the spin i e the tensor field is objective for every time differentiable objective eulerian symmetric tensor field a if and only if the spin tensor assumes the form w y b d where y b d is an antisymmetric tensor valued isotropic function furthermore by virtue of certain necessary or reasonable requirements it is found that a single antisymmetric function of two positive real variables can be introduced to characterize a general class of spin tensors defining objective corotational rates accordingly a general explicit basis free expression for the latter is established in terms of the left cauchy green tensor b the vorticity tensor w and the stretching tensor d as well as the introduced antisymmetric function by choosing several particular forms of the latter it is shown that all commonly used spin tensors are incorporated into this general expression in a natural way

the stress conjugate to logarithmic strain abstract a stress s is said to be conjugate to a strain measure e if the inner product s e is the power per unit volume the logarithmic strain in u with u the right stretch tensor has been considered an interesting strain measure because of the relationship of its material time derivative ln u with the stretching tensor d in a previous article int j solids structures 22 1019 1032 1986 a formula for ln u was obtained in direct notation for the cases where the principal stretches are repeated as well as for the case where they are all distinct here the formula for ln u and the definition of conjugate stress are used to derive an explicit properly invariant expression for the stress conjugate to the logarithmic strain

parametric flutter margin method for aeroservoelastic stability analysis a new parametric flutter margin method for linear and nonlinear stability analysis of aeroservoelastic systems is presented the method is based on frequency response calculations with the system s

on the existence and nonexistence of finitary codings for a class of random fields we study the existence of finitary codings also called finitary homomorphisms or finitary factor maps from a finite valued i i d process to certain random fields for markov random fields we show using ideas of marton and shields that the presence of a phase transition is an obstruction for the existence of the above coding this yields a large class of bernoulli shifts for which no such coding exists conversely we show that for the stationary distribution of a monotone exponentially ergodic probabilistic cellular automaton such a coding does exist the construction of the coding is partially inspired by the propp wilson algorithm for exact simulation in particular combining our results with a theorem of martinelli and olivieri we obtain the fact that for the plus state for the ferromagnetic ising model on mathbf z d d geq 2 there is such a coding when the interaction parameter is below its critical value and there is no such coding when the interaction parameter is above its critical value

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

influence and sharp threshold theorems for monotonic measures the influence theorem for product measures on the discrete space 0 1 n may be extended to probability measures with the property of monotonicity which is equivalent to strong positive association corresponding results are valid for probability measures on the cube 0 1 n that are absolutely continuous with respect to lebesgue measure these results lead to a sharp threshold theorem for measures of random cluster type and this may be applied to box crossings in the two dimensional random cluster model

representations of kronecker powers of orthogonal tensors with applications to material symmetry two explicit representations are obtained for the kronecker powers of orthogonal second order tensors the derivations rely on the mathematical properties of kronecker products and on classical parametrizations of orthogonal tensors these representations are subsequently employed in the systematic construction of structural tensors and in the analysis of corotational rates of tensor functions

sharpness of the phase transition in percolation models the equality of two critical points the percolation threshold ph and the point p where the cluster size distribution ceases to decay exponentially is proven for all translation invariant independent percolation models on homogeneous d dimensional lattices d 1 the analysis is based on a pair of new nonlinear partial differential inequalities for an order parameter m h which for h q reduces to the percolation density p at the bond density p l e in the single parameter case these are 1 m hdm dh m2 mdm d and 2 dm d j mdm dh inequality 1 is intriguing in that its derivation provides yet another hint of a 3 structure in percolation models moreover through the elimination of one of its derivatives 1 yields a pair of ordinary differential inequalities which provide information on the critical exponents and one of these resembles an ising model inequality of fr hlich and sokal and yields the mean field bound 5 2 and the other implies the result of chayes and chayes that an inequality identical to 2 is known for ising models where it provides the basis for newman s universal relation 5 1 1 and for certain extrapolation principles which are now made applicable also to independent percolation these results apply to both finite and long range models with or without orientation and extend to periodic and weakly inhomogeneous systems

is an additive decomposition of a rate of deformation and objective stress rates passe abstract the manuscript critically examines a half a century old idea of decomposing the rate of deformation into elastic and plastic parts we show that even the most recent additive variant based on the logarithmic rate is inconsistent with the notion of elasticity in so called unloading stress ratchetting obstacle test while the earlier corotational variants based on the jaumann and green naghdi rates are well known not to be integrable we then propose a stress dependent so called kinetic logarithmic stress rate that is both integrable and passes the unloading stress ratchetting obstacle test we also demonstrate that the additive hypo elasto plasticity model based on the proposed kinetic logarithmic rate is weakly invariant under isochoric reference change for simple materials in the sense of noll

coexistence of infinite clusters ii ising percolation in two dimensions we show a strong type of conditionally mixing property for the gibbs states ofd dimensional ising model when the temperature is above the critical one by using this property we show that there is always coexistence of infinite and clusters when is smaller than c andh 0 in two dimensions it is also possible to show that this coexistence region extends to some non zero external field case i e for every c there exists someh c 0 such that h h c implies the coexistence of infinite clusters with respect to the gibbs state for h

an iterative procedure for nonlinear flutter analysis an iterative procedure in the frequency domain is presented for flutter analysis of large dynamic systems with multiple structural nonlinearities the major components of the procedure are the describing function approach for system linearization a structural dynamics modification method for shifting system mode shapes and frequencies and a complex eigenvalue algorithm for solution of the flutter equation the purpose of the procedure is to achieve alignment of the oscillatory amplitude in each nonlinear spring with the describing function prediction of stiffness before computing the final stability characteristics the result is a system tuned to the flutter frequency at the time of instability to support the development and validation of the procedure several describing functions are formulated and a quantitative measure of the errors in each is presented validation of the iterative method is accomplished through examples involving dynamic systems of increasing complexity coupled with various representations of the unsteady aerodynamic forces both numerical simulations and experimental data are used to compare with the iterative predictions in the cases studied the agreement is good to excellent with the method accurately predicting the amplitude of a limit cycle flutter as well as the initial disturbance required to produce flutter

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

analyticity properties and power law estimates of functions in percolation theory we consider percolation on the sites of a graphg e g a regulard dimensional lattice all sites ofg are occupied vacant with probabilityp respectively q 1 p independently of each other w denotes the cluster of occupied sites containing a fixed site which will usually be taken to be the origin andw the cardinality ofw the percolation probability is the probability that w i e p pp w some critical values ofp ph andpt are defined respectively as the smallest value ofp for which p 0 and for which the expectation of w is infinite formally ph inf p p 0 andpt inf p ep w we show for fairly general graphsgthat ifp pt thenpp w n decreases exponentially inn for the special casesg g0 the simple quadratic lattice andg1 the graph which corresponds to bond percolation on 2 we obtain upper and lower bounds for p of the formc p ph and bounds forep w of the formc p ph we also investigate smoothness properties of p ep number of clusters per site ep w 1 w 1 this function was introduced by sykes and essam who assumed that has exactly one singularity namely atp ph for the graphsg0 andg1 i e site or bond percolation on 2 we show that p is analytic atp ph and has two continuous derivatives atp ph the emphasis is on rigorous proofs

discontinuous modelling of shear bands using adaptive meshfree methods a simple methodology to model shear bands as strong displacement discontinuities in an adaptive meshfree method is presented the shear band is represented by a displacement jump at discrete particle positions the displacement jump in normal direction is suppressed with penalty method loss of material stability is used as transition criterion from continuum to discontinuum the method is two and three dimensional examples of complicated shear banding including transition from brittle to ductile failure are studied and compared to experimental data and other examples from the literature

numerical integration of rate constitutive equations in finite deformation analysis abstract in analysis of finite deformation problems the use of constitutive equations in rate form is often required in a spatial setting these equations may express a relationship between some objective rate of spatial stress tensor and the rate of deformation constitutive equations of this type characterize a variety of material models including hyperelasticity hypoelasticity and elastoplasticity employing geometrical concepts a family of unconditionally stable and incrementally objective algorithms is proposed for the integration of such rate constitutive equations these algorithms which are appropriate for finite deformation analysis are applicable to any choice of stress rate and in most cases employ quantities that arise naturally in the context of finite element analysis examples illustrate the objectivity and accuracy of the algorithms

remarks on rate constitutive equations for finite deformation problems computational implications it is explicitly shown that if the spatial elasticity tensor of an elastic material is taken as isotropic for all possible configurations then its coefficients cannot be constants they must depend nontrivially on the jacobian determinant of the deformation gradient moreover the assumption typically made for computational purposes that its coefficients remain constant for all possible configurations is incompatible with elasticity it is further shown that an assumption widely used in the computational literature in the context of finite deformation plasticity namely relating an objective stress rate to the rate of deformation tensor through a fourth rank constant isotropic tensor is also incompatible with elasticity thus furnishing an example of an hypoelastic material which is not elastic

nonlinear response of aeroservoelastic systems using discrete state space approach a generalized direct simulation method using a discrete time domain state space approach for transient response of both open and closed loop nonlinear aeroelastic systems is developed based on a nonlinear parameter scheme that divides the nonlinear system into sublinear systems the method first assembles a set of discrete time domain state space equations and then computes the transient response by switching the time integration procedure between this set of state space equations in so doing various nonlinearities in structures aerodynamics and or control systems can be included the method is validated by correlating the transient response of a three degree of freedom airfoil section in freeplay with the experimental and numerical results obtained by conner et al the stability of a strut braced wing with buckling effects at two trim conditions is also studied which shows that the aeroelastic stability of the present strut braced wing is trim condition dependent such results clearly could not be obtained if using a linear aeroelastic analysis

approximate zero one laws and sharpness of the percolation transition in a class of models including two dimensional ising percolation one of the most well known classical results for site percolation on the square lattice is the equation p c p c 1 in words this equation means that for all values p c of the parameter p the following holds either a s there is an infinite open cluster or a s there is an infinite closed star cluster this result is closely related to the percolation transition being sharp below p c the size of the open cluster of a given vertex is not only a s finite but has a distribution with an exponential tail the analog of this result has been proven by higuchi in 1993 for two dimensional ising percolation at fixed inverse temperature c with external field h the parameter of the model using sharp threshold results approximate zero one laws and a modification of an rsw like result by bollobas and riordan we show that these results hold for a large class of percolation models where the vertex values can be nicely represented in a sense which will be defined precisely by i i d random variables we point out that the ordinary percolation model obviously belongs to this class and we also show that the ising model mentioned above belongs to it