subdivision based mixed methods for isogeometric analysis of linear and nonlinear nearly incompressible materials this paper addresses the use of isogeometric analysis to solve solid mechanics problems involving nearly incompressible materials the present work is focused on extension of two field mixed variational formulations in both small and large strains to isogeometric analysis inf sup stable displacement pressure combinations for mixed formulations are developed based on the subdivision property of nurbs stability and convergence properties of the proposed displacement pressure combinations are illustrated by computing numerical inf sup constants and error norms the performance of the proposed formulations is assessed by studying several benchmark examples involving nearly incompressible and incompressible elastic and elasto plastic materials in both small and large strain regime

on the physical significance of higher order kinematic and static variables in a three dimensional shell formulation abstract in recent years considerable attention has been given to the development of higher order plate and shell models these models are able to approximately represent three dimensional effects while pertaining the efficiency of a two dimensional formulation due to pre integration of the structural stiffness matrix across the thickness especially the possibility to use unmodified complete three dimensional material laws within shell analysis has been a major motivation for the development of such models while the theoretical and numerical formulation of so called 7 parameter shell models including a thickness stretch of the shell has been discussed in numerous papers no thorough investigation of the physical significance of the additional kinematic and static variables coming along with the extension into three dimensions is known to the authors however realization of the mechanical meaning of these quantities is decisive for both a proper modeling of shell structures e g concerning loading and kinematic boundary conditions and a correct interpretation of the results in the present paper the significance of kinematic and static variables appearing in a 7 parameter model proposed by buchter and ramm 1992a are discussed it is shown how these quantities refine the model behavior and how they can be related to the classical variables such as curvatures and stress resultants furthermore the special role of the material law within such a formulation is addressed it is pointed out that certain requirements must hold for the variation of kinematic and static variables across the thickness to ensure correct results in this context it is found that the considered 7 parameter model can be regarded as optimal with respect to the number of degrees of freedom involved

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

efficient modeling of localized material failure by means of a variationally consistent embedded strong discontinuity approach this paper is concerned with a novel embedded strong discontinuity approach suitable for the analysis of material failure at finite strains focus is on localized plastic deformation particularly relevant for slip bands in contrast to already existing models the proposed implementation allows to consider several interacting discontinuities in each finite element based on a proper re formulation of the kinematics an efficient parameterization of the deformation gradient is derived it permits to compute the strains explicitly that improves the performance significantly however the most important novel contribution of the present paper is the advocated variational constitutive update within this framework every aspect is naturally driven by energy minimization i e all unknown variables are jointly computed by minimizing the stress power the proposed update relies strongly on an extended principle of maximum dissipation this framework provides enough flexibility for different failure types and for a broad class of non associative evolution equations by discretizing the aforementioned continuous variational principle an efficient numerical implementation is obtained it shows in addition to its physical and mathematical elegance several practical advantages for instance the physical minimization principle itself specifies automatically and naturally the set of active strong discontinuities copyright 2011 john wiley sons ltd

new finite elements with embedded strong discontinuities for the modeling of failure in electromechanical coupled solids this paper presents new finite elements with embedded strong discontinuities in the form of jumps in the mechanical displacement field as well as jumps in the electric potential for the modeling of failure in electromechanical coupled solids such materials which are commonly used in smart systems in the form of actuators or sensors are prone to defects in the form of cracks represented by such strong discontinuities in this work a discrete account of the individual jumps is made with the possibility of their propagation through the individual finite elements without the need of remeshing or refinement strategies originated for purely mechanical based materials and commonly referred as the strong discontinuity approach an extension to account for the electromechanical coupling and the additional jumps in the electric potential is made in this work the decomposition of that methodology into a global problem representing here the electromechanical boundary value problem and a local problem through which the strong discontinuities are introduced serves convenient when developing the corresponding finite elements based on the requirement to avoid stress locking phenomena this idea is extended in this work to develop new finite elements based on the incorporation of electrical separation modes directly into the discrete formulation keeping its local and computational efficient property with regard to the storage and possible static condensation of the parameters used to describe the mechanical and electrical discontinuities on a constitutive level the mechanical traction separation law is extended to account for a softening type behavior in the relation between the normal component of the electric displacement field and the surface charge density this is accomplished through the derivation of a localized electromechanical damage model based on the principle of maximum damage dissipation the performance of the resulting new finite elements is illustrated with several numerical simulations including a compact tension test and a three point bending test of piezoelectric ceramics and compared with experimental results available in the literature

a strain gradient isotropic elastoplastic damage model with j3 dependence abstract a plastic strain gradient version of an isotropic elastoplastic damage model that depends on the third invariant j3 of the stress deviator is developed the model is based on the non local equivalent plastic strain ep defined by peerlings et al 2001 and engelen et al 2003 and introduces a material length l to the constitutive equations it is shown that the non local equivalent plastic strain ep at a material point p can be identified with the average value of the local von mises equivalent plastic strain e p over a sphere centered at p and of radius approximately equal to 3 l a methodology for the numerical integration of the constitutive equations is presented the algorithm is appropriate for rate independent as well as rate dependent viscoplastic models the model is implemented in the abaqus general purpose finite element program and both quasi static and dynamic problems are solved two possible abaqus implementations are discussed first user elements are developed which can be used for the solution of both quasi static and dynamic problems reduced 1 point gauss integration is discussed in 8 node hexahedral elements and the physical stabilization method of puso 2000 is used to remove the resulting numerical singularities hourglass control second the implementation of the model via user material subroutines is discussed quasi static problems can be solved with abaqus standard using a coupled temperature displacement steady state analysis together with user subroutine umat in which temperature is identified with the non local equivalent plastic strain ep the solution of dynamic problems requires use of abaqus explicit together with a dynamic temperature displacement analysis option and user subroutines vumat and dflux several example problems are solved

numerical simulations of strain localization in inelastic solids using mesh free methods in this paper a comprehensive account on using mesh free methods to simulate strain localization in inelastic solids is presented using an explicit displacement based formulation in mesh free computations high resolution shear band formations are obtained in both two dimensional 2 d and three dimensional 3 d simulations without recourse to any mixed formulation discontinuous incompatible element or special mesh design the numerical solutions obtained here are insensitive to the orientation of the particle distributions if the local particle distribution is quasi uniform which to a large extent relieves the mesh alignment sensitivity that finite element methods suffer moreover a simple h adaptivity procedure is implemented in the explicit calculation and by utilizing a mesh free hierarchical partition of unity a spectral wavelet adaptivity procedure is developed to seek high resolution shear band formations moreover the phenomenon of multiple shear band and mode switching are observed in numerical computations with a relatively coarse particle distribution in contrast to the costly fine scale finite element simulations copyright 2000 john wiley sons ltd

enhanced assumed strain elements and locking in membrane problems abstract the assumptions which guarantee convergence of eas elements first introduced by simo and rifai can be reduced to two postulates specifically the stability condition refers to a relaxed stability of an associated hu washizu principle we investigate the problem of volume locking of membrane problems estimates of a certain type which for instance imply volume locking of the q1 element are fortunately not present with eas elements finally we verify an equivalence of the eas concept with a hellinger reissner method which was observed in numerical computations by andelfinger and ramm

stabilized hybrid finite element methods based on the combination of saddle point principles of elasticity problems how in a discretized model to utilize the duality and complementarity of two saddle point variational principles is considered in the paper a homology family of optimality conditions different from the conventional saddle point conditions of the domain decomposed hellinger reissner principle is derived to enhance stability of hybrid finite element schemes based on this a stabilized hybrid method is presented by associating element interior displacement with an element boundary one in a nonconforming manner in addition energy compatibility of strain enriched displacements with respect to stress terms is introduced to circumvent poisson locking

analytic trapezoidal fourier p element for vibrating plane problems a trapezoidal fourier p element for the in plane vibration analysis of two dimensional elastic solids is presented trigonometric functions are used as enriching functions instead of polynomials to avoid ill conditioning problems the element matrices are analytically integrated in closed form with the additional fourier degrees of freedom d o f s the accuracy of the computed natural frequencies is greatly increased one element can predict many modes accurately since a triangle can be divided into three trapezoidal elements the range of application is much wider than the previously derived rectangular fourier p element numerical examples show that convergence is very fast with respect to the number of trigonometric terms comparison of natural modes calculated by the trapezoidal fourier p element and the conventional finite elements is carried out the results show that the trapezoidal fourier p element produces much higher accurate modes than the conventional finite elements with the same number of d o f s for a benchmark problem the condition number of the mass matrix using legendre p element increases rapidly and it becomes non positive with 22 terms the condition numbers of the fourier p element matrices are consistently much lower than those of the legendre p element

consistent third order shell theory with application to composite cylindrical cylinders a consistent third order shell theory with applications to composite circular cylinders is presented and its finite element formulation is developed the formulation has seven displacement functions and requires c 0 continuity in the displacement field the exact computation of stress resultants is carried out through numerical integration of material stiffness coefficients of the laminate a displacement finite element model is developed using lagrange elements with higher order interpolation polynomials these elements preclude any effect of shear and membranes locking comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic and composite cylindrical shells are found to be excellent and show the validity of the developed shell theory and its implementation into a finite element code

elements of a theory of simulation ii sequential dynamical systems we study a class of discrete dynamical systems that is motivated by the generic structure of simulations the systems consist of the following data a a finite graph y with vertex set 1 n where each vertex has a binary state b functions f i f 2 n f 2 n and c an update ordering p the functions f i update the binary state of vertex i as a function of the state of vertex i and its y neighbors and leave the states of all other vertices fixed the update ordering is a permutation of the y vertices by composing the functions f i in the order given by p one obtains the sequential dynamical system sds f y p email protected i 1nf p i f 2 n f 2 n we derive a decomposition result characterize invertible sds and study fixed points in particular we analyse how many different sds that can be obtained by reordering a given multiset of update functions and give a criterion for when one can derive concentration results on this number finally some specific sds are investigated

selective and reduced numerical integrations for nurbs based isogeometric analysis we propose a new approach to construct selective and reduced integration rules for isogeometric analysis based on nurbs elements the notion of an approximation space that approximates the target space is introduced we explore the use of various approximation spaces associated with optimal patch wise numerical quadratures that exactly integrate the polynomials in approximation spaces with the minimum number of quadrature points patch rules exploit the higher continuity of spline basis functions the tendency of smooth spline functions to exhibit numerical locking in nearly incompressible problems when using a full gauss legendre quadrature is alleviated with selective or reduced integration stability and accuracy of the schemes are examined analyzing the discrete spectrum in a generalized eigenvalue problem we propose a local algorithm which is robust and computationally efficient to compute element by element the quadrature points and weights in patch rules the performance of the methods is assessed on several numerical examples in two dimensional elasticity and reissner mindlin shell structures

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

stabilized mixed finite element formulations for materially nonlinear partially saturated two phase media standard and enhanced bbar or eas low order finite elements applied to the problem of consolidation of two phase nonlinear continua do not satisfy the lbb condition when the same interpolation functions are used for both displacement and pore pressure fields strong spatial pressure oscillations are the main consequence of the lbb condition violation the class of direct stabilized methods widely used in the field of fluid mechanics is a powerful tool to circumvent violation of the aforementioned condition three stabilized formulations designed for the problem of consolidation of fully or partially saturated media are presented galerkin least squares gls with the least squares term construction based on the residuum of the local fluid mass conservation equation the pressure stabilized formulation fpl in which the rate of the pore pressure laplacian residual free in the incompressibility limit is added to the fluid mass conservation equation and finally a stabilized formulation in which the stabilization term is constructed based on the rate of the residuum of the local momentum equation an h convergence study and test problems for the three stabilized schemes are discussed

approximate inference for disease mapping with sparse gaussian processes gaussian process gp models are widely used in disease mapping as they provide a natural framework for modeling spatial correlations their challenges however lie in computational burden and memory requirements in disease mapping models the other difficulty is inference which is analytically intractable due to the non gaussian observation model in this paper we address both these challenges we show how to efficiently build fully and partially independent conditional fic pic sparse approximations for the gp in two dimensional surface and how to conduct approximate inference using expectation propagation ep algorithm and laplace approximation la we also propose to combine fic with a compactly supported covariance function to construct a computationally efficient additive model that can model long and short length scale spatial correlations simultaneously the benefit of these approximations is computational the sparse gps speed up the computations and reduce the memory requirements the posterior inference via ep and laplace approximation is much faster and is practically as accurate as via markov chain monte carlo

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

relations between enhanced strain methods and the hr method abstract the three field hu washizu functional is the starting point to develop a comparative analysis of approximate linear elastostatic problems in particular we will analyse the limitation phenomena concerning two mixed methods respectively denoted the strain gap method and the mixed enhanced strain method and the two field hellinger reissner hr finite element formulation accordingly two original limitation principles are contributed we provide the theoretical motivation of the numerical observations provided in computational literature on the coincidence of the displacement and stress solutions between the enhanced assumed strain method and the hr method if different choices of shape functions are made it is further shown that the hr method provides the exact stress solution and the exact nodal displacements with one element the related analytical motivation are thus given the theoretical analyses presented in the paper are supported by numerical examples on tipical benchmarks

a four node corotational quadrilateral elastoplastic shell element using vectorial rotational variables four node corotational quadrilateral elastoplastic shell element summary a four node corotational quadrilateral elastoplastic shell element is presented the local coordinate system of the element is defined by the two bisectors of the diagonal vectors generated from the four corner nodes and their cross product this local coordinate system rotates rigidly with the element but does not deform with the element as a result the element rigid body rotations are excluded in calculating the local nodal variables from the global nodal variables the two smallest components of each nodal orientation vector are defined as rotational variables leading to the desired additive property for all nodal variables in a nonlinear incremental solution procedure different from other existing corotational finite element formulations the resulting element tangent stiffness matrix is symmetric owing to the commutativity of the local nodal variables in calculating the second derivative of strains with respect to these variables for elastoplastic analyses the maxwell huber hencky von mises yield criterion is employed together with the backward euler return mapping method for the evaluation of the elastoplastic stress state the consistent tangent modulus matrix is derived to eliminate locking problems we use the assumed strain method several elastic patch tests and elastoplastic plate shell problems undergoing large deformation are solved to demonstrate the computational efficiency and accuracy of the proposed formulation copyright 2013 john wiley sons ltd

extrapolated fields in the formulation of the assumed strain elements part ii three dimensional problems abstract a new assumed strain quadrilateral element with accurate in plane bending behavior is presented the basic idea consists in introduction of a parallelogram domain associated with the given quadrilateral element development of the related assumed strain field for the parallelogram and subsequent extrapolation of this field to the domain of the original quadrilateral the assumed strain field for the parallelogram is constructed by identification of various modes of its deformation and then by proper modification of the strain field in some of these modes in particular the strain operator with respect to the so called in plane bending modes is modified so as to simulate the strain field resulting from the assumptions usually made in structural mechanics the modification of the strain fields leads to the assumed strain operator the proposed new assumed strain quadrilateral element exhibits remarkably accurate performance for both membrane and bending dominated problems even when severely distorted and high aspect ratio meshes are considered and when materials are nearly incompressible

four node semi eas element in six field nonlinear theory of shells we propose a new four node c finite element for shell structures undergoing unlimited translations and rotations the considerations concern the general six field theory of shells with asymmetric strain measures in geometrically nonlinear static problems the shell kinematics is of the two dimensional cosserat continuum type and is described by two independent fields the vector field for translations and the proper orthogonal tensor field for rotations all three rotational parameters are treated here as independent hence as a consequence of the shell theory the proposed element has naturally six engineering degrees of freedom at each node with the so called drilling rotation this property makes the element suitable for analysis of shell structures containing folds branches or intersections to avoid locking phenomena we use the enhanced assumed strain eas concept we derive and linearize the modified hu washizu principle for six field theory of shells what makes the present approach original is the combination of eas method with asymmetric membrane strain measures based on literature we propose new enhancing field and specify the transformation matrix that accounts for the lack of symmetry to gain knowledge about the suitability of this field for asymmetric strain measures and to assess the performance of the element we solve typical benchmark examples with smooth geometry and examples involving orthogonal intersections of shell branches

a co rotational quasi conforming 4 node resultant shell element for large deformation elasto plastic analysis abstract a co rotational quasi conforming formulation of a 4 node stress resultant shell element is presented for non linear analysis of plate and shell structures the tangent stiffness matrix in this quasi conforming formulation is explicitly integrated this makes the element computationally efficient in incremental non linear analysis it includes drilling degrees of freedom which improves membrane behavior and allows the modeling of stiffened plates and shells it is also free of shear locking behavior the formulation of the geometrical stiffness is derived using the full definition of green strain tensor the inclusion of the bending moment and transverse shear resultant forces in the geometric stiffness allows effective analysis of stability problems of moderately thick plates and shells the stresses are accurately taken at the nodal points without extrapolation the plasticity is traced by applying the von mises yield condition and prandtl reuss flow rule to discrete points through the thickness the multi layered approach is based on equally spaced stations including extreme fibers a modified trapezoidal rule is used for the numerical integration of the constitutive relation in the plasticity part numerous tests are carried out for the non linear validation of present 4 node shell element and the results are in good agreement with references

conditions for equivalence between the hu washizu and related formulations and computational behavior in the incompressible limit the relationship of the hu washizu mixed formulation to other mixed and enhanced formulations is examined in detail in the context of linear elasticity with a view to presenting a unified framework for such formulations the hu washizu formulation is considered in both its classical form and in a modified form that is suited to establishing well posedness in the incompressible limit recently established theoretical results on uniform well posedness are studied computationally by considering a range of numerical examples which illustrate where appropriate the good behavior predicted by the theory as well as the locking behavior that is evident in those problems in which the conditions for stability and convergence are not satisfied 2005 elsevier b v all rights reserved

a meshfree enriched finite element method for compressible and near incompressible elasticity summary in this paper a two dimensional displacement based meshfree enriched fem me fem is presented for the linear analysis of compressible and near incompressible planar elasticity the me fem element is established by injecting a first order convex meshfree approximation into a low order finite element with an additional node the convex meshfree approximation is constructed using the generalized meshfree approximation method and it possesses the kronecker delta property on the element boundaries the gradient matrix of me fem element satisfies the integration constraint for nodal integration and the resultant me fem formulation is shown to pass the constant stress test for the compressible media the me fem interpolation is an element wise meshfree interpolation and is proven to be discrete divergence free in the incompressible limit to prevent possible pressure oscillation in the near incompressible problems an area weighted strain smoothing scheme incorporated with the divergence free me fem interpolation is introduced to provide the smoothing on strains and pressure with this smoothed strain field the discrete equations are derived based on a modified hu washizu variational principle several numerical examples are presented to demonstrate the effectiveness of the proposed method for the compressible and near incompressible problems copyright 2012 john wiley sons ltd

mean strain eight node hexahedron with stabilization by energy sampling summary a method for stabilizing the mean strain hexahedron is described that differs from the currently known approaches for simplicity the developments are limited to linear elasticity but with an arbitrarily anisotropic elasticity matrix the technique relies on a sampling of the stabilization energy using two quadrature rules the mean strain quadrature and the full gaussian integration rule the use of two quadrature rules is shown to guarantee consistency and stability the stabilization energy is assumed to be generated by a modified constitutive matrix based on the spectral decomposition the spectral decomposition of the constitutive matrix identifies the stiff and flexible modes of deformation the stiff modes of deformation are only sampled by the mean strain integration which eliminates volumetric locking for isotropic materials as well as locking due to strongly anisotropic material properties the accuracy and convergence characteristics of the present formulations compare favorably with the capabilities of mean strain and other high performance hexahedral elements as implemented in abaqus copyright 2014 john wiley sons ltd

a high performance element for the analysis of 2d elastoplastic continua abstract the paper presents a four node element for the analysis of 2d continua described by elastic perfectly plastic von mises laws its formulation is based on the assumed stress approach which has been widely tested in the elastic field the elastoplastic formulation of the element is obtained by enriching its variational basis with the weak enforcement of the plastic loading unloading conditions in this way the elastoplastic problem is formulated with respect to the stress parameters of the element consistently with the weak statement of the compatibility condition

large elasto plastic finite element analysis of solids and shells with the enhanced assumed strain concept abstract a finite element simulation of arbitrarily large elasto plastic deformations of three dimensional and shell structures is described two numerical aspects originally developed by j c simo have been combined i e the multiplicative large strain plasticity and the enhanced assumed strain finite element concept the constitutive model is worked out in its algorithmic version applying projection methods and consistent linearization the enhanced strain field is added to the conventional hexahedral displacement elements avoiding volumetric locking in the plastic range in addition to solid structures the three dimensional material model without any modifications is also applied to thin walled shell structures here an extended shell formulation a so called seven parameter model is used in which the thickness strain is augmented by a linear term the applicability of the entire formulation is demonstrated by several numerical examples

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

large deformation triangular and tetrahedral element formulations for unstructured meshes abstract the increasing use of automatic mesh generators and remeshers has spurred the need for accurate and efficient triangular and tetrahedral elements in unstructured meshes in large deformation analysis of solids accuracy and efficiency require the treatment of volumetric locking and element distortions respectively in this paper a mixed formulations is proposed to treat these issues and applied to triangular and tetrahedral elements the formulations enforces in the weak sense the expression for the volumetric strain in terms of the deformation gradient the mixed formulation is combined with an irreducible formulation to provide a balance between the treatment of volumetric locking and the maintenance of an adequate critical timestep three techniques are proposed to determine such a balance at the local element level example computations in two and three dimensions of an iron cylinder impacting a rigid surface are used to demonstrate the formulations and to compare them to the irreducible displacement based formulation

treatment of internal constraints by mixed finite element methods unification of concepts a general method to generate assumed stress and strain fields within the context of mixed finite element methods is presented the assumed fields are constructed in such a way that internal constraints are satisfied a priori consequently the locking behaviour commonly observed in finite element solutions of problems with internal constraints is avoided to this end the assumed stress and strain fields are constructed to satisfy a priori the homogeneous part of the equilibrium equations thus avoiding fraeijs de veubeke s limitation principle results obtained using the proposed methodology on a nearly incompressible plane strain problem and thin plate application using a shear deformable theory are indicated

a generalization of the method of incompatible modes a generalization of the classical method of incompatible modes is presented containing the original formulation as a special case the method constitutes a class of finite elements which is equivalent to the class of enhanced assumed strain elements yet based on a pure displacement formulation copyright 2006 john wiley sons ltd

enrichment of enhanced assumed strain approximations for representing strong discontinuities addressing volumetric incompressibility and the discontinuous patch test summary we present a geometrically nonlinear assumed strain method that allows for the presence of arbitrary intra finite element discontinuities in the deformation map special attention is placed on the coarsemesh accuracy of these methods and their ability to avoid mesh locking in the incompressible limit given an underlying mesh and an arbitrary failure surface we first construct an enriched approximation for the deformation map with the nonlinear analogue of the extended finite element method x fem with regard to the richer space of functions spanned by the gradient of the enriched approximation we then adopt a broader interpretation of variational consistency for the construction of the enhanced strain in particular in those elements intersected by the failure surface we construct enhanced strain approximations which are orthogonal to piecewise constant stress fields contrast is drawn with existing strong discontinuity approaches where the enhanced strain variations in localized elements were constructed to be orthogonal to constant nominal stress fields importantly the present formulation gives rise to a symmetric tangent stiffness matrix even in localized elements the present modification also allows for the satisfaction of a discontinuous patch test wherein two different constant stress fields on each side of the failure surface lie in the solution space we demonstrate how the proposed modifications eliminate spurious stress oscillations along the failure surface particularly for nearly incompressible material response additional numerical examples are provided to illustrate the efficacy of the modified method for problems in hyperelastic fracture mechanics copyright c 2000 john wiley sons ltd

least squares mixed finite elements for small strain elasto viscoplasticity the main aim of this contribution is to provide a mixed finite element for small strain elasto viscoplastic material behavior based on the least squares method the l2 norm minimization of the residuals of the given first order system of differential equations leads to a two field functional with displacements and stresses as process variables for the continuous approximation of the stresses lowest order raviart thomas elements are used whereas for the displacements standard conforming elements are employed it is shown that the non linear least squares functional provides an a posteriori error estimator which establishes ellipticity of the proposed variational approach further on details about the implementation of the least squares mixed finite elements are given and some numerical examples are presented copyright 2008 john wiley sons ltd

variationally consistent state determination algorithms for nonlinear mixed beam finite elements abstract this paper presents and evaluates several variationally consistent state determination algorithms for geometric and material nonlinear beam finite elements based on the hellinger reissner hr assumed stress variational principle the specifically targeted element type is derived from the two field displacement and generalized stress form of this principle momentum balance and strain compatibility are expressed in a weak form and the constitutive equations are satisfied directly at each integration point i e section along the element length a specific formulation of one element of this type is presented in a companion paper interelement compatibility is not enforced in the dual stress resultant variables for this element and thus various state determination algorithms can be formulated at the local i e element and section levels four state determination algorithms referred to as the l l l n n l and n n procedures are considered the first symbol in these names indicates the element level and the second denotes the section level furthermore the symbol n indicates that local nonlinear iteration is performed prior to returning to the higher level whereas the symbol l indicates that only the linearized equations are satisfied at the corresponding local level the l l algorithm corresponds to conventional newton iteration on both the element and section levels whereas the n n algorithm entails the iterative satisfaction of the nonlinear element compatibility and section constitutive equations for each global iteration the performance of these algorithms is evaluated and compared it is found that the algorithms in which the local nonlinear strain displacement compatibility conditions are solved iteratively at the element level for every global iteration lead to fewer global iterations at the expense of iterations at the element level in particular the n n algorithm is overall the most efficient of the four algorithms for the problems tested also the n n algorithm has substantially smaller element storage requirements the n n algorithm is expected to be particularly advantageous for cases in which a large number of elements remain elastic and inelasticity is concentrated in a few elements

a unified 3d based technique for plate bending analysis using scaled boundary finite element method summary this paper presents a unified technique for solving the plate bending problems by extending the scaled boundary finite element method the formulation is based on the three dimensional governing equation without enforcing the kinematics of plate theory only the in plane dimensions are discretised into finite elements any two dimensional displacement based elements can be employed the solution along the thickness is expressed analytically by using a matrix function the proposed technique is consistent with the three dimensional theory and applicable to both thick and thin plates without exhibiting the numerical locking phenomenon moreover the use of higher order spectral elements allows the proposed technique to better represent curved boundaries and to achieve high accuracy and fast convergence numerical examples of various plate structures with different thickness to length ratios demonstrate the applicability and accuracy of the proposed technique copyright 2012 john wiley sons ltd

a reduced integration solid shell finite element based on the eas and the ans concept geometrically linear problems in this paper a new reduced integration eight node solid shell finite element is presented the enhanced assumed strain eas concept based on the hu washizu variational principle requires only one eas degree of freedom to cure volumetric and poisson thickness locking one key point of the derivation is the taylor expansion of the inverse jacobian with respect to the element center which closely approximates the element shape and allows us to implement the assumed natural strain ans concept to eliminate the curvature thickness and the transverse shear locking the second crucial point is a combined taylor expansion of the compatible strain with respect to the center of the element and the normal through the element center leading to an efficient and locking free hourglass stabilization without rank deficiency hence the element requires only a single integration point in the shell plane and at least two integration points in thickness direction the formulation fulfills both the membrane and the bending patch test exactly which has to the authors knowledge not yet been achieved for reduced integration eight node solid shell elements in the literature owing to the three dimensional modeling of the structure fully three dimensional matenal models can be implemented without additional assumptions

a variational multiscale approach to strain localization formulation for multidimensional problems abstract the multiscale approach to strain localization problems developed earlier is generalized to higher dimensions the key idea is the identification of the fine scale field with a component of the displacement that has a large gradient the difference between the total displacement and the fine scale is the coarse scale field the formulation is variationally based with the weak form as the point of departure with suitable assumptions on the space of fine scale fields the weak form is separable into coarse and fine scale parts the weak form of the fine scale problem is used to eliminate the fine scales from the formulation this is achieved by way of a projection onto the fine scale space and allows a reformulation of the full problem in terms of coarse scale components alone in this framework fine scale interpolations are identified that ensure sharp resolution of localized displacement irrespective of the underlying finite element mesh it is demonstrated that by correctly accounting for the microstructural fine scale behavior the formulation results in solutions devoid of pathological mesh sensitivity for problems wherein the detailed structure of the localized displacement is of interest recovery of the fine scale components can be performed to reconstruct the entire displacement field several numerical examples are presented that demonstrate the robustness of the formulation

a new stabilized enhanced strain element with equal order of interpolation for soil consolidation problems abstract in order to accurately model the behaviour of geostructures it is usually not possible to neglect the interaction between the soil skeleton and the pore fluid classical finite element models taking into account this interaction are formulated in terms of the displacement and pore pressure fields and are based on the assumption that the fluid acceleration relative to the soil skeleton is negligible this type of mixed problems is similar to others found in solid and fluid mechanics and might give rise to numerical instabilities unless certain requirements are met there are two classical approaches to this problem the first is usually known as the zienkiewicz taylor patch test for mixed formulations as a consequence of this test the interpolation degree of the displacement field is required to be higher than the corresponding one of the pressure field mathematically speaking this is a necessary condition for stability the second approach mathematically more involved is usually known as the bab ska brezzi inf sup condition and constitutes a sufficient condition for stability however it is possible to obtain stable formulations circumventing the interpolation degree requirement through the so called stabilization techniques these techniques were initially applied in the context of fluid mechanics and later extended to solid mechanics this article presents a new formulation in which stabilization is achieved through an approach based on the simo rifai enhanced strain element

on the incompressible constraint of the 4 node quadrilateral element the standard plane 4 node element is written as the summation of a constant gradient matrix usually obtained from underintegration and a stabilization matrix the split is based on a taylor series expansion of element basis functions in the incompressible limit the locking effect of the quadrilateral is traced back to the stabilization matrix which reflects the incomplete higher order term in the taylor series the incompressibility condition is formulated in a weak sense so that the element displacement field is divergence free when integrated over the element volume the resulting algebraic constraint is shown to coincide with a particular eigenvector of the constant gradient matrix which is obtained from the first order terms of the taylor series the corresponding eigenvalue enforces incompressibility implicitly by means of a penalty constraint analytical expressions for that constant dilatation eigenpair are derived for arbitrary element geometries it is shown how the incompressible constraint carries over to the element stiffness matrix if the element stabilization is performed in a particular manner for several classical and recent elements the eigensystems are analysed numerically it is shown that most of the formulations reflect the incompressible constraint identically in the incompressible limit the numerical accuracies of the elements are compared

development and testing of stable invariant isoparametric curvilinear 2 and 3 d hybrid stress elements abstract linear and quadratic serendipity hybrid stress elements are examined in respect of stability coordinate invariance and optimality a formulation based upon symmetry group theory successfully addresses these issues in undistorted geometries and is fully detailed for plane elements the resulting least order stable invariant stress polynomials can be applied as astute approximations in distorted cases through a variety of tensor components and variational principles a distortion sensitivity study for two and three dimensional elements provides favourable numerical comparisons with the assumed displacement method

a quadratic plane triangular element immune to quadratic mesh distortions under quadratic displacement fields abstract a quadratic plane triangular element is developed extending the concepts of us quad8 element the element belongs to the broad class of petrov galerkin formulation which is characterized by the choice of test and trial functions from different spaces the performance of the proposed element has been studied for typical static and free vibration problems the element exhibits a high degree of tolerance to mesh distortions as compared to the classical isoparametric quadratic triangular element for undistorted meshes however the performance is similar to that of the classical element

mixed enhanced formulation for finite deformation axisymmetric torsion the development and implementation of a four noded quadrilateral element for the analysis of the axisymmetric torsion problem is presented in the context of the mixed enhanced method the deformation gradient is developed from two sets of element interpolants of which one may be explicitly obtained resulting in only two undetermined enhanced parameters needed for the satisfaction of the near incompressible limit the resulting element arrays yield proper rank with standard 2 2 quadrature the introduction of a three field variation statement for the problem along with the interpolations for the stress and deformation gradient render a variational stress recovery permissible several numerical examples are explored in the setting of finite kinematics with physically non linear material properties to further induce coupling between the radial and axial displacement and the longitudinal rotation copyright 2004 john wiley sons ltd

on a systematic development of trilinear three dimensional solid elements based on simo s enhanced strain formulation a systematic development of eight node trilinear three dimensional solid elements based on simo s theoretical framework for the enhanced assumed strain formulation is presented for linear elasticity the starting point is a regular brick followed by parallelepipeds and then arbitrarily distorted elements the advantages and deficits of various enhanced strain formulations are extensively discussed using the regular brick for arbitrarily distorted elements a simple modification of the element stiffness matrix is proposed to achieve a more reliable and very efficient element on some numerical examples the advantages and limits of the family of enhanced strain elements and the improved elements are discussed

new stable mixed finite element approximations for problems in linear elasticity we construct stable and convergent finite element approximations for two and three dimensional problems in elasticity the approximations are based on three field mixed variational formulations and are uniformly convergent in the incompressible limit the basis for the constructions is a set of general sufficient conditions established in lamichhane reddy and wohlmuth numer math 104 2006 in that work the focus was on low order quadrilateral elements here it is shown that the methodology is readily extended to families of elements that are built on stable velocity pressure pairs for the stokes problem various numerical examples serve to illustrate the convergence behaviour of the new elements

conditions for locking free elasto plastic analyses in the element free galerkin method the use of finite elements with linear displacement fields in volume preserving elasto plastic problems can lead to volumetric locking due to the inability of the shape functions to describe certain displacement modes a response of the structure can be obtained which is much too stiff the element free galerkin efg method can provide shape functions that have an intrinsic richer nature and do not exhibit volumetric locking it is shown that the finite element fe method can be conceived as a specialisation of the efg method and that for a specific choice of the efg parameters the fe shape functions are retrieved then volumetric locking behaviour is found again however for other choices of the efg parameters shape functions are obtained that are able to describe isochoric elasto plasticity without volumetric locking

a finite element method for nearly incompressible elasticity problems a finite element method is considered for dealing with nearly incompressible material in the case of large deformations the nonlinear character of the volumetric contribution has to be taken into account the proposed mixed method avoids volumetric locking also in this case and is robust for with a being the well known lame constant error estimates for the l norm are crucial in the control of the nonlinear terms

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

enhanced linear triangle for plasticity problems in j 2 solids due to their economy and capability to reproduce high gradient zones low order elements are of great interest in the calculations involving localized failure however the performance of the simplest element the three nodes triangle under incompressible and bending dominated situations is very poor and the computed results unreliable this paper presents an inexpensive three fields u p formulation solving these issues as shown in the examples of application

error indicators for mixed finite elements in 2 dimensional linear elasticity abstract we establish a posteriori error indicators for mixed finite elements in plane elasticity the error estimators refer to residuals of the strong equations and to jumps of the displacements on interelement boundaries for the bdm elements of lowest order the error indicators are computed with displacement fields which are obtained by a postprocessing procedure numerical examples show that adaptive mesh refinements based on these estimators lead to very efficient algorithms

quadrilateral membrane elements with analytical element stiffness matrices formulated by the new quadrilateral area coordinate method qacm ii a novel strategy for developing low order membrane elements with analytical element stiffness matrices is proposed first some complete low order basic analytical solutions for plane stress problems are given in terms of the new quadrilateral area coordinates method qacm ii then these solutions are taken as the trial functions for developing new membrane elements thus the interpolation formulae for displacement fields naturally possess second order completeness in physical space cartesian coordinates finally by introducing nodal conforming conditions new 4 node and 5 node membrane elements with analytical element stiffness matrices are successfully constructed the resulting models denoted as qac atf4 and qac atf5 have high computational efficiency since the element stiffness matrices are formulated explicitly and no internal parameter is added these two elements exhibit excellent performance in various bending problems with mesh distortion it is demonstrated that the proposed strategy possesses advantages of both the analytical and the discrete method and the qacm ii is a powerful tool for constructing high performance quadrilateral finite element models copyright 2008 john wiley sons ltd

a systematic construction of b bar functions for linear and non linear mixed enhanced finite elements for plane elasticity problems in a previous paper a modified hu washizu variational formulation has been used to derive an accurate four node plane strain stress finite element denoted qe2 for the mixed element qe2 two enhanced strain terms are used and the assumed stresses satisfy the equilibrium equations a priori for the linear elastic case in this paper an alternative approach is discussed the new formulation leads to the same accuracy for linear elastic problems as the qe2 element however it turns out to be more efficient in numerical simulations especially for large deformation problems using orthogonal stress and strain functions we derive b functions which avoid numerical inversion of matrices the b strain matrix is sparse and has the same structure as the strain matrix b obtained from a compatible displacement field the implementation of the derived mixed element is basically the same as the one for a compatible displacement element the only difference is that we have to compute a b strain matrix instead of the standard b matrix accordingly existing subroutines for a compatible displacement element can be easily changed to obtain the mixed enhanced finite element which yields a higher accuracy than the q4 and qm6 elements copyright 1999 john wiley sons ltd

finite element methods for the analysis of strong discontinuities in coupled poro plastic media this paper presents the formulation of finite element methods for the numerical resolution of strong discontinuities in poro plastic solids fully coupled infinitesimal conditions are considered these solutions are characterized by a discontinuous displacement field with the associated singular strains and a singular distribution of the fluid content here singular distributions refer to dirac delta functions the singular component of the fluid content distribution models the fluid accumulated per unit area of the discontinuity surface and it is directly related with the dilatancy characterizing singular inelastic strains localized along such a surface it further accounts for a discontinuous fluid flow vector given by darcy s law in terms of a continuous pore pressure field all these considerations are incorporated in the proposed finite element methods through a local enhancement of the finite element interpolations as these discontinuities appear the local character of these interpolations lead after the static condensation of the enhanced fields to a large scale problem exhibiting the same structure as common finite element models of the global poro plastic problem but incorporating now crucially the localized dissipative effects characteristic of the localized failures several numerical simulations are presented to evaluate the performance of the proposed methods

a unified co rotational framework for solids shells and beams abstract the paper describes a unified framework for applying the co rotational method to the analysis of solids shells and beams the general method stems from an unusual application of the technique which involves solid elements the proposed framework allows a formulation that is simpler than many of the earlier procedures and in addition gives a direct indication of the terms in the tangent stiffness which may be ignored

extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids abstract this paper addresses novel extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids on one hand based upon the unified multiscale kinematics of strong discontinuities standard finite elements at the coarse scale are enriched with fine scale kinematics in which non uniform discontinuity modes are incorporated on the other hand the traction continuity condition across the discontinuity is enforced in the statically optimal form as the fine scale statics the admissible discontinuity modes satisfying a priori the traction continuity condition are derived in addition to the relative rigid body motions translations and rotations more general relative stretching modes that induce discontinuous strain stress fields in the bulk are obtained with no limit of a vanishing poisson s ratio the proposed model then particularizes to 2d quadrilateral elements the displacement jumps at the discontinuity nodes are selected as the enrichment parameters and regarded as global variables shared by neighboring elements the resulting model not only is intrinsically stress locking free for a fully softened discontinuity but also automatically guarantees global continuity of the displacement jumps another benefit is that the numerical instability suffered under the unfavorable element discontinuity configuration can be easily circumvented furthermore the vanishing displacement jumps at the discontinuity tip can be enforced trivially as conventional essential boundary conditions and those complex strategies introduced in existing models are avoided together with the failure criterion related to the element average stress and the propagation orientation based on a simplified nonlocal stress a local crack tracking algorithm is adopted to guarantee global continuity of the discontinuity path representative numerical simulations of element and structure benchmark tests are presented to verify the performance of the proposed approach in the modeling of arbitrary discontinuity propagation in solids

a robust non linear mixed hybrid quadrilateral shell element in the paper a non linear quadrilateral shell element for the analysis of thin structures is presented the variational formulation is based on a hu washizu functional with independent displacement stress and strain fields the interpolation matrices for the mid surface displacements and rotations as well as for the stress resultants and strains are specified restrictions on the interpolation functions concerning fulfillment of the patch test and stability are derived the developed mixed hybrid shell element possesses the correct rank and fulfills the in plane and bending patch test using newton s method the finite element approximation of the stationary condition is iteratively solved our formulation can accommodate arbitrary non linear material models for finite deformations in the examples we present results for isotropic plasticity at finite rotations and small strains as well as bifurcation problems and post buckling response the essential feature of the new element is the robustness in the equilibrium iterations it allows very large load steps in comparison to other element formulations copyright 2005 john wiley sons ltd

generalized energy momentum method for non linear adaptive shell dynamics in the present study a generalization of the energy momentum method denoted by generalized energy momentum method applied to the non linear dynamics of shells will be developed within the framework of the generalized a method this algorithmic environment contains the unconditionally stable energy momentum method and its numerically damped version as well as the classical newmark and a methods as special cases in order to control the size of the time steps of the integration scheme with respect to accuracy and eaciency an adaptive time stepping procedure based on local a posteriori error estimation will be improved for non linear dynamical systems and applied to the proposed class of algorithms the spatial discretization is realized by an eight noded finite shell element of reissner mindlin type including an extensible shell director field permitting the application of three dimensional material laws the original formulation of this finite element will be developed for non linear dynamic analysis and adapted for the employment within the introduced energy conserving decaying time integration scheme 1999 elsevier science s a all rights reserved

unified analysis of enriched finite elements for modeling cohesive cracks abstract aiming to provide a justified theoretical ground based on which different enriched finite elements can be systematically compared we developed in this work a unified framework for modeling cohesive cracks using the variational multiscale method the kinematics i e coarse and fine scale displacement and strain fields and statics i e coarse and fine scale equilibrium equations are thoroughly investigated in both continuum and discrete settings with respect to the fine scale kinematics and statics adopted in the embedded finite element method efem and the extended finite element method xfem we mainly discuss four groups of enriched finite elements with non uniform discontinuity modes i e the kinematically optimal symmetric efem and xfem as well as the kinematically and statically optimal non symmetric efem and xfem in all these methods the enrichment parameters can be regarded either as element wise local or continuous global variables the enriched finite elements with material element node enrichments are then exemplified in an increasing order of their respective capabilities in representing the fine scale kinematics and the interrelations between them are also discussed owing to this unified framework we are able to clarify some existing points of view related to efem and xfem it is found that if the same fine scale statics is used and the same local global property is assumed for the involved enrichment parameters xfem can be regarded as a kinematically enhanced efem since it accounts for a more general fine scale kinematics than that i e relative rigid body motions and self stretching considered in efem finally several simple but sufficiently representative numerical examples are presented to show the significance in appropriately reflecting the fine scale kinematics and statics in an enriched finite element for modeling cohesive cracks

modeling strong discontinuities at finite strains a novel numerical implementation abstract in this paper a finite element formulation suitable for the modeling of locally embedded strong discontinuities at finite strains is presented following the enhanced assumed strain concept eas the proposed numerical model is based on an additive decomposition of the displacement gradient into a conforming and an enhanced part the enhanced part is associated with the final failure kinematics of solids which are approximated by means of a discontinuous displacement field strong discontinuities referring to the displacement jump no special assumption such as purely mode i or mode ii failure is made the same holds for the class of interface laws considered which govern the evolution of the displacement discontinuity in terms of the traction vector acting at the surface of strong discontinuities consequently the suggested numerical framework can be applied to a broad range of different interface laws including damage based models in contrast to previous works the presented finite element formulation does not require the static condensation technique to be employed more precisely instead of computing the conforming part of deformation and the displacement jump simultaneously from the weak form of equilibrium and the weak form of traction continuity the different parts of the local deformation are decomposed according to a predictor corrector algorithm the proposed predictor and the corrector step are formally identical to that of classical computational plasticity models hence subroutines designed for standard models continuous deformation can be applied with only minor modifications necessary the applicability as well as the performance of the resulting finite element formulation are demonstrated by means of a fully three dimensional analysis of shear band formation in a bar made of a ductile material

optimal solid shells for non linear analyses of multilayer composites ii dynamics abstract we are presenting a simple low order solid shell element formulation having only displacement degrees of freedom dofs i e without rotational dofs that has an optimal number of parameters to pass the patch tests and thus allows for efficient and accurate analyses of large deformable multilayer shell structures using elements at extremely high aspect ratio with the dynamics referred to a fixed inertial frame the elements can be used to analyze multilayer shell structures undergoing large overall motion the formulation of this element is based on the mixed hu washizu variational principle leading to a novel enhancing strain tensor enhanced assumed strain eas method that renders the computation particularly efficient with improved in plane and out of plane bending behavior poisson thickness locking especially in refined analyses of composite structures involving a large number of high aspect ratio layers the energy momentum conserving algorithm in the context of current solid shell element is presented we discuss the eas formulation based on the displacement gradient and its complexity compared to formulation on the green lagrange strain shear locking and curvature thickness locking are treated using the assumed natural strain ans method the element has an optimal combination of the ans method and the minimal number of eas parameters required to pass the plate bending patch test numerical examples involving dynamic analyses with conservation of energy and momentum of multilayer shell structures having a large range of element aspect ratios are presented several implicit direct integration methods with without numerical dissipation are used and compared in terms of the accuracy stability and cost in multilayer shell structure finally we note that the topic in this paper is a fitting dedication to professor ekkehard ramm who has made important pioneering contributions in this research direction

the patch test a condition for assessing fem convergence this paper discusses various forms of the irons patch test and shows again that its satisfaction is a necessary convergence condition being equivalent to consistency further it is shown that the test can be applied for verification of stability requirements thus providing also a sufficient condition of convergence the patch test is useful in testing the order of asymptotic convergence and the satisfaction of the test gives a guide for development of certain incompatible element forms

a direct complementarity approach for the elastoplastic analysis of plane stress and plane strain structures this paper presents a direct complementarity approach for carrying out the elastoplastic analysis of plane stress and plane strain structures founded on a traditional finite step formulation our approach however avoids the typically cumbersome implementation of iterative predictorcorrector procedures associated with the ubiquitous return mapping algorithm instead at each predefined step the governing formulationcast in its most natural mathematical programming format known as a mixed complementarity problemis directly solved by using a complementarity solver run from within a mathematical modeling system we have chosen the industry standard general algebraic modeling system path mixed complementarity problem solver that is called from within the general algebraic modeling system environment we consider both von mises and tresca materials with perfect or hardening kinematic and isotropic behaviors our numerical tests five benchmark examples of which are presented in this paper have been carried out using models constructed from the mixed finite element of capsoni and corradi comput methods appl mech eng 1997 141 6793 which beneficially offers a locking free behavior and coarse mesh accuracy the results indicate in addition to an isochoric locking free behavior good accuracy and the ability to circumvent the difficult singularity problem associated with the corners of tresca yield surfaces

a stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations in this paper a stabilized finite element method to deal with incompressibility in solid mechanics is presented a mixed formulation involving pressure and displacement fields is used and a continuous linear interpolation is considered for both fields to overcome the babuska brezzi condition a stabilization technique based on the orthogonal sub scale method is introduced the main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements which are easy to generate for real industrial applications results are compared with standard galerkin and q1p0 mixed formulations for nearly incompressible problems in the context of linear elasticity

b and f projection methods for nearly incompressible linear and non linear elasticity and plasticity using higher order nurbs elements abstract this paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of isogeometric analysis after reviewing some fundamentals of isogeometric analysis we investigate the use of higher order non uniform rational b splines nurbs within the b projection method the higher continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results a new non linear f projection method based on a modified minimum potential energy principle and inspired by the b method is proposed for the large deformation case it leads to a symmetric formulation for which the consistent linearized operator for fully non linear elasticity is derived and used in a newton raphson iterative procedure the performance of the methods is assessed on several numerical examples and results obtained are shown to compare favorably with other published techniques

finite element simulation of dynamic strain localization a multi scale problem abstract a finite element procedure for the post localization analysis of elasto plastic solids is developed to ensure unique solutions the duvaut lions visco plastic regularization procedure 1 is implemented a bifurcation analysis of the underlying backbone elasto plastic material is performed to locate the shear band and to define its orientation the width of the shear band is assumed to be much smaller than the characteristic element size h to capture the structure of the shear band the kinematics is enriched by incorporating additional degrees of freedom in a patch within the element and overlying the shear band within each localized element compatibility is ensured between the strain fields inside and outside the patch a petrov galerkin type procedure to account for the narrow width of the patch is implemented the results indicate formation of mesh and patch invariant shear bands finally the effects of varying material parameters are studied the results are found to be consistent with known localization characteristics

rational approach for assumed stress finite elements a new method for the formulation of hybrid elements by the hellinger reissner principle is established by expanding the essential terms of the assumed stresses as complete polynomials in the natural coordinates of the element the equilibrium conditions are imposed in a variational sense through the internal displacements which are also expanded in the natural co ordinates the resulting element possesses all the ideal qualities i e it is invariant it is less sensitive to geometric distortion it contains a minimum number of stress parameters and it provides accurate stress calculations for the formulation of a 4 node plane stress element a small perturbation method is used to determine the equilibrium constraint equations the element has been proved to be always rank sufficient

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

a note on enhanced strain methods for large deformations abstract enhanced strain elements have been applied to simulate geometrically and materially non linear problems their main advantage is due to the fact that they perform very good in the incompressible limit as well as in bending situations however in compressive deformation states these elements depict stability modes which are associated with hour glass forms and thus denote a rank deficiency for such deformations in this paper the appearance of these modes will be investigated analytically by means of a simple representative example

on strong discontinuities in anelastic solids a finite element approach taking a frame indifferent gradient of the discontinuous displacements this paper presents a two dimensional 2d large deformation analysis of strong discontinuities in anelastic solids and its numerical implementation we assume associative and ideal plasticity until localization occurs in the post localization phase discontinuous displacements develop and their material gradient is set up in a proper way one leg in the current configuration the other leg in the reference configuration to provide a frame indifferent objective description the numerical implementation via displacement based six node triangular finite elements enriched by a single displacement jump parameter t2 0 in the post localization phase te locte is described in detail the solution procedure is similar to that using assumed enhanced displacement gradient elements with the only but crucial difference that on the discontinuity surface the traction is linked to the displacement jump via a proper constitutive law finally numerical results of the shear test and of the tension test are presented copyright 2000 john wiley sons ltd