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

stabilized finite element formulation for elastic plastic finite deformations abstract this paper presents a stabilized finite element formulation for nearly incompressible finite deformations in hyperelastic plastic solids such as metals an updated lagrangian finite element formulation is developed where mesh dependent terms are added to enhance the stability of the mixed finite element formulation this formulation circumvents the restriction on the displacement and pressure fields due to the babuska brezzi condition and provides freedom in choosing interpolation functions in the incompressible or nearly incompressible limit typical in metal forming applications moreover it facilitates the use of low order simplex elements i e p1 p1 reducing the degrees of freedom required for the solution in the incompressible limit when stable elements are necessary linearization of the weak form is derived for implementation into a finite element code numerical experiments with p1 p1 elements show that the method is effective in incompressible conditions and can be advantageous in metal forming analysis

computational aspects of incrementally objective algorithms for large deformation plasticity a methodology for computationally efficient formulation of the tangent stiffness matrix consistent with incrementally objective algorithms for integrating finite deformation kinematics and with closest point projection algorithms for integrating material response is developed in the context of finite deformation plasticity numerical experiments illustrate an excellent performance of the proposed formulation in comparison with other algorithms copyright 1999 john wiley sons ltd

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

a new frictional time integration algorithm for large slip multi body frictional contact problems in this paper a new frictional time integration suitable for large slip multibody frictional contact problems is presented the algorithm is introduced within the simple context of a model problem the sliding motion of a particle onto a rough surface time integration of frictional traction is performed introducing a new slip path parametrization which is defined independently of the local surface finite element parametrization used in the spatial triangularization the key point of the algorithm is that now in presence of large slips problems associated with slip motions such that a full incremental slip path is not within a single surface element are completely bypassed remarkably the algorithm is defined on the sole basis of the unit outward normal field to the surface without any appeal to the underlying local surface finite element triangularization geometrically the assumed slip path can be viewed as an approximation to the geodesic passing throughout the initial and final points of each incremental slip path the algorithm is amenable to exact linearization and asymptotic quadratic rate of convergence can be achieved within a newton raphson iterative solution scheme the algorithm can easily be extended to large slip multi body frictional contact problems involving finite strains

finite deformation plasticity based on the additive split of the rate of deformation and hyperelasticity abstract finite deformation plasticity formulation based on additive split of rate of deformation and hyperelasticity is presented this approach is valid for finite elastic and plastic strains while rendering the choice and numerical integration of objective stress rates superfluous as the results are automatically objective for small elastic strains our method reduces to the classical hypoelastic corotational formulation provided that the dienes objective stress rate is employed while in the absence of inelastic deformation it coincides with the hyper elastic formulation the validity of the model has been examined on four test problems and the numerical results were found to be in good agreement with either the exact solution or experimental data

techniques for stress and strain controlled homogenization of inelastic periodic composites abstract a framework is developed within the context of the displacement finite element method for applying periodic boundary conditions to uni period basic cells under the influence of applied macroscopically homogeneous stresses the resulting approach supplements the more common strain controlled method which is also presented and which relies on an additive decomposition of the displacement field into linear imposed and periodic unknown contributions as implemented here the stress controlled method employs a penalty formulation to insure that the displacement solution satisfies the linearperiodic decomposition the performance of both the stress and strain driven methods are demonstrated and assessed on a complete set of homogenization computations for an elasto plastic composite

shakedown and steady state responses of elastic plastic solids in large displacements abstract elastic perfectly plastic solids or structures subjected to loads quasi statically varying within a specified domain are addressed in the framework of large displacements and the additive strain decomposition rule on the ground of drucker s principle of stability in the large an appropriate stability requisite called d stability is formulated as the positive definiteness property of a specific functional sum of the second variation of the helmholtz free energy with an additional term depending on higher order geometry change effects for a d stable structure for which the additive strain decomposition rule is applicable melan s and koiter s theorems of classical shake down theory are reconsidered and reformulated for large displacements the extended melan and koiter theorems so established save the essential features of the classical ones but exhibit a greater formal complexity with consequent difficulties for engineering applications for structures subjected to periodic loads it is shown that as long as the structure does not incur loss of d stability a long term steady state response or steady cycle occurs which exhibits the same periodicity characteristics as in case of small displacements that is the second piola kirchhoff stresses and the plastic green lagrange strain rates become periodic as the load a few illustrative numerical results are presented

stationary states in langevin dynamics under asymmetric levy noises properties of systems driven by white non gaussian noises can be very different from these of systems driven by the white gaussian noise we investigate stationary probability densities for systems driven by ensuremath alpha stable l evy type noises which provide natural extension to the gaussian noise having however a new property namely a possibility of being asymmetric stationary probability densities are examined for a particle moving in parabolic quartic and in generic double well potential models subjected to the action of ensuremath alpha stable noises relevant solutions are constructed by methods of stochastic dynamics in situations where analytical results are known they are compared with numerical results furthermore the problem of estimation of the parameters of stationary densities is investigated

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

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

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

the fractional order governing equation of levy motion a governing equation of stable random walks is developed in one dimension this fokker planck equation is similar to and contains as a subset the second order advection dispersion equation ade except that the order a of the highest derivative is fractional e g the 1 65th derivative fundamental solutions are levy s a stable densities that resemble the gaussian except that they spread proportional to time 1 a have heavier tails and incorporate any degree of skewness the measured variance of a plume undergoing levy motion would grow faster than fickian plume at a rate of time 2 a where 0 a 2 the equation is parsimonious since the parameters are not functions of time or distance the scaling behavior of plumes that undergo levy motion is accounted for by the fractional derivatives which are appropriate measures of fractal functions in real space the fractional derivatives are integrodifferential operators so the fractional ade describes a spatially nonlocal process that is ergodic and has analytic solutions for all time and space

finite deformation plasticity in principal axes from a manifold to the euclidean setting abstract this contribution presents a link between early developments in finite deformation plasticity where the notion of a covariant formulation is introduced and employed and more recent developments where rediscovery of a fundamental work of hill on the method of principal axes led to a very efficient implementation scheme more precisely we demonstrate how to develop a covariant theory of finite deformation plasticity in an invariant form by making use of the elastic principal stretches we also show how to implement principal axis formulation in the framework of manifold to carry out all the necessary manipulations by exploiting the lie derivative formalism and eventually to simplify the final result to the euclidean setting much of our work on numerical implementation reflects the fruitful cross fertilization of ideas with those from theoretical formulation in particular we show how the operator split method which is typically used to simplify the plastic flow computation can also be used to reduce the computational cost related to the special finite element interpolation schemes based on incompatible modes the latter proves to be an indispensable ingredient for accommodating the near incompressibility constraint arising in the finite deformation deviatoric plasticity an important advantage of the proposed formulation as opposed to alternative remedies e g b bar method is that the basic structure of the governing equations need not be modified

two stress update algorithms for large strains accuracy analysis and numerical implementation two algorithms for the stress update i e time integration of the constitutive equation in large strain solid mechanics are compared from an analytical point of view the order of the truncation error associated to the numerical integration is deduced for each algorithm a priori using standard numerical analysis this accuracy analysis has been performed by means of a convected frame formalism which also allows a unied derivation of both algorithms in spite of their inherent dierences then the two algorithms are adapted from convected frames to a xed cartesian frame and implemented in a small strain nite element code the implementation is validated by means of a set of simple deformation paths simple shear extension extension and compression extension and rotation and two benchmark tests in non linear mechanics the necking of a circular bar and a shell under ring loads in these numerical tests the observed order of convergence is in very good agreement with the theoretical order of convergence thus corroborating the accuracy analysis 1997 john wiley sons ltd

on the numerical implementation of inelastic time dependent and time independent finite strain constitutive equations in structural mechanics abstract a number of complex issues are resolved in a way that allows the incorporation of finite strain inelastic material behavior into the piecewise numerical construction of solutions in solid mechanics without recourse to extensive continuum mechanics preliminaries an elementary time independent plasticity model an elementary time dependent creep model and a viscoelastic model are introduced as examples of constitutive equations which are routinely used in engineering calculations the constitutive equations are all suitable for problems involving large deformations and finite strains the plasticity and creep models are in rate form and use the symmetric part of the velocity gradient or the stretching to compute the co rotational time derivative of the cauchy stress the viscoelastic model computes the current value of the cauchy stress from a hereditary integral of a materially invariant form of the stretching history the current configuration is selected for evaluation of equilibrium as opposed to either the reference configuration or the last established equilibrium configuration the process of strain incrementation is examined in some depth the stretching evaluated at the mid interval and multiplied by the time step is identified as the appropriate finite strain increment to use with the selected forms of the constitutive equations discussed is the conversion of rotation rates based on the spin into incremental orthogonal rotations these rotations are used to update stresses and state variables due to rigid body rotation during the load increment comments and references to the literature are directed at numerical integration of the constitutive equations with an emphasis on doing this accurately if not exactly for any time step and stretching this material taken collectively provides an approach to numerical implementation which is marked by its simplicity

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

a general procedure for the direct computation of turning and bifurcation points we address the formulation and numerical implementation of general purpose algorithme suitable for the direct computation of stability points in non linear solid mechanics the effectiveness of the resulting algorithm is illustrated by numerical simulation that include bifurcation and loss of stability in elastoplasticity non linear rods and non linear three dimensional shells

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

some computational aspects of large deformation rate dependent plasticity problems abstract the governing equations for a finite element formulation of boundary value problems for large deformation metal forming processes are derived using a principle of virtual work formulated in a lagrangian reference system the updated lagrangian method is used to simplify the equations the resulting nonlinear equilibrium equations are solved using newton s method a constitutive model for large deformation rate dependent plasticity is developed the model incorporates a one parameter implicit integration operator for stability and accuracy the stressrate strain rate relation is written in terms of the jaumann rate of stress numerous example problems are solved to demonstrate the effectiveness of the numerical algorithms

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

isogeometric kirchhoff love shell formulation for elasto plasticity abstract an isogeometric thin shell formulation allowing for large strain plastic deformation is presented a stress based approach is adopted which means that the constitutive equations are evaluated at different integration points through the thickness allowing the use of general 3d material models the plane stress constraint is satisfied by iteratively updating the thickness stretch at the integration points the deformation of the shell structure is completely described by the deformation of its midsurface and furthermore the formulation is rotation free which means that the discrete shell model involves only three degrees of freedom several numerical benchmark examples with comparison to fully 3d solid simulations confirm the accuracy and efficiency of the proposed formulation

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

finite strain generalization of smallstrain constitutive relations for any finite strain tensor and additive volumetric deviatoric split abstract the paper deals with finite strain generalization of small strain constitutive equations for isotropic materials for which the strain is split into a volumetric part and a deviatoric part the latter characterizing the isochoric strain i e a strain at constant volume the volumetric deviatoric split has so far been handled by a multiplicative decomposition of the transformation tensor but the existing sophisticated complex constitutive models for small strains of cohesive pressure sensitive dilatant materials such as concrete and geomaterials involve an additive decomposition and would be difficult to convert a multiplicative decomposition it is shown that an additive decomposition of any finite strain tensor and of the green lagrange strain tensor in particular is possible provided that the higher order terms of the deviatoric strain tensor are allowed to depend on the volumetric strain this dependence is negligible for concrete and geomaterials because the volumetric strains are normally small whether or not the deviatoric strains are large furthermore the related question of the choice of the finite strain measure to be used for the finite strain generalization is analysed a transformation of the green lagrange finite strain tensor whose parameters approximately reflect the degrees of freedom equivalent to replacing the small strain tensor by any other possible finite strain measure is proposed finally a method by which the stress tensor that is workconjugate to any finite strain tensor can be converted to the green lagrange strain tensor is presented

implicit objective integration for sensitivity analysis in non linear solid mechanics incrementally objective integration schemes are proposed for the accurate and efficient determination of design sensitivity coefficients dscs for solid mechanics problems with both material and geometrical non linearities the derivation of these schemes are based on the direct differentiation of objective schemes that are used in stress analysis for problems of this class two widely used objective stress rates the jaumann rate and the green naghdi rate are considered here within the same setting with only minor changes of the integration scheme numerical results are presented for a simple shear problem with different material constitutive laws including a hypoelastic model and a unified isotropic viscoplastic model for these two objective rates the numerical results are compared with analytical solutions or direct integration solutions the close agreement among these solutions demonstrates the accuracy and efficiency of the proposed scheme

solution of the slump test using a finite deformation elasto plastic drucker prager model summary development of a finite deformation elasto plasticity model based on the multiplicative decomposition of the deformation gradient is presented and discussed in detail the formulation presented in this paper includes the derivation of the full set of equations for the drucker prager yield criterion the equations which are not available elsewhere are developed within a framework using a spectral decomposition approach further expressions for the consistent algorithmic tangent moduli in the finite strain regime are developed since the finite deformation framework employed to obtain the expressions presented here collapses to the classical infinitesimal plasticity framework when the finite strain assumption is no longer necessary the finite deformation consistent tangent moduli are compared to the consistent tangent moduli valid for use with infinitesimal plasticity validation of the implemented finite deformation elasto plastic drucker prager model is performed through the solution of the concrete slump test comparisons between an existing approximate analytical solution and experimental data are presented and results are discussed in detail

a new solution procedure for application of energy conserving algorithms to general constitutive models in nonlinear elastodynamics abstract this paper develops a novel solution strategy for temporal discretization of initial value problems in nonlinear elastodynamics enabling exact energy and momentum conservation for a spatially discretized problem this new energy momentum algorithm fits into the general framework established by simo and tarnow z angew math phys 43 1992 757 however in contrast to the presentation given in that reference the current approach extends the critical stress update formula to encompass generic stored energy functions for the hyperelastic continuum in a manner which also allows for quadratically convergent newton raphson solution of the nonlinear algorithmic equations numerical examples using a neo hookean material model are given to illustrate the excellent performance of the proposed scheme not only is the new algorithm guaranteed to be second order accurate and unconditionally stable in the fully nonlinear regime as are other energy momentum strategies but also the approach advocated is demonstrated to be more robust and versatile than its predecessors

three dimensional elastoplastic contact analysis at large strains with enhanced assumed strain elements in this paper a model for elastoplastic contact analysis under large strain conditions is presented consideration of the impenetrability constraints follows through a penalty formulation due to the presence of large strains and to the impenetrability restrictions special care by the choice of the finite element formulation is required here the enhanced assumed strain concept is employed since this concept is based on the enhancement of the strain fields with no interelement continuity requirement imposed the simple global structure of the displacement based model remains unchanged

on the performance of two tangent operators for finite element analysis of large deformation inelastic problems an important step in the solution of non linear deformation problems using a newton raphson type of iterative scheme is the calculation of a tangent operator the so called jacobian by linearizing the involved field equations in this paper full linearization of the virtual work equation is performed in an updated lagrangian framework together with a calculation of the consistent linearized material moduli to update the material state a material frame indifferent two parameter integration scheme introduced earlier by the authors is used in general the reference configuration is updated after each iteration to coincide instantaneously with the present guess of the unknown equilibrium configuration another approach is to use the previous equilibrium state at the beginning of a time step as the reference configuration until the new equilibrium configuration at the end of the time step is found the present paper explores the performance of two different jacobians based on the above two approaches with emphasis on their accuracy and convergence characteristics when large incremental steps are used finally some details of their finite element implementation are given and results for several numerical tests including upset forging and extrusion of an axisymmetric billet are presented and discussed

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

elastic plastic multiplicative decomposition with a stressed intermediate configuration abstract this paper presents an extension to the elastic plastic multiplicative decomposition to permit the origin in stress space to reside outside the closure of the elastic domain in this work the classical assumption of a stress free intermediate configuration is abandoned in favor of a new one where the intermediate configuration could be stressed this stress is identified as the maximal unloading point in stress space and denoted the plastic stress to motivate the discussion the infinitesimal plasticity model is considered first a remarkable result is obtained where for the case of linear elastic response the classical infinitesimal model is after some reinterpretation recovered the fully nonlinear model is developed and is shown to reduce to the classical one when the intermediate configuration is stress free the new framework is then applied to the case of j 2 plasticity where it is shown that when coupled with neo hookean elasticity as in the infinitesimal case after some reinterpretation the classical model is recovered i e the total stress is independent of the plastic stress numerical simulations are used to illustrate the importance of properly modeling the hardening behavior even during external loading in cases where load redistribution may take place

on nonisothermal elastoplastic analysis of shell components employing realistic hardening responses abstract in the present paper efficient numerical algorithms for elastoplastic analysis of shell like structural components will be proposed employing nonisothermal realistic highly nonlinear hardening responses the closest point projection integration algorithm is presented using a reissner mindlin type kinematic shell model completely formulated in tensor notation further a consistent elastoplastic tangent modulus is derived which ensures high convergence rates in the global iteration approach the integration algorithm has been implemented into a layered assumed strain isoparametric finite element which also enables geometrical nonlinearities including finite rotations the nonisothermal elastoplastic response of a circular cylindrical shell and a box column under axial compression is analysed under the assumption of an adiabatic process the increase in temperature is computed during elastoplastic deformation robustness and numerical stability of the proposed algorithms are demonstrated

design sensitivity analysis in large deformation elasto plastic and elasto viscoplastic problems implicit time integration algorithm derived by simo for his large deformation elasto plastic constitutive model is generalized for the case of isotropy and associative flow rule towards viscoplastic material behaviour and consistently differentiated with respect to its input parameters combining it with the general formulation of design sensitivity analysis dsa for non linear finite element transient equilibrium problem we come at a numerically efficient closed form finite element formulation of dsa for large deformation elasto plastic and elasto viscoplastic problems with various types of design variables material constants shape parameters the paper handles several specific issues like the use of a non algorithmic coefficient matrix or sensitivity discontinuities at points of instantaneous structural stiffness change computational examples demonstrate abilities of the formulation and quality of results copyright 2005 john wiley sons ltd

variational gradient plasticity at finite strains part ii local global updates and mixed finite elements for additive plasticity in the logarithmic strain space the second part of our work on variational inelasticity with long range effects outlines the formulation and finite element implementation of additive finite gradient plasticity in the logarithmic strain space it is considered to be the most simple approach to finite plasticity suitable for the purely phenomenological description of polycrystalline metals or amorphous materials if structures of the geometrically linear theories are defined in the lagrangian logarithmic strain space we start from a mixed saddle point principle for metric type additive plasticity which is specified for the important model problem of isochoric von mises plasticity with gradient extended hardening softening response the mixed variational structure includes the hardening softening variable itself as well as its dual driving force the numerical implementation exploits the underlying variational structure yielding a canonical symmetric structure of the monolithic problem it results in a novel finite element design of the coupled problem incorporating a long range hardening softening parameter and its dual driving force this allows a straightforward local definition of plastic loading unloading driven by the long range fields providing very robust finite element implementations of gradient plasticity it includes a rational method for the definition of elastic plastic boundaries epbs in gradient plasticity along with a postprocessor that defines the plastic variables in the elastic range we discuss alternative mixed finite element designs of the coupled problem including a local global solution strategy of short and long range fields all methods are derived in a rigorous format from variational principles numerical benchmarks demonstrated the excellent performance of the proposed mixed variational approach to gradient plasticity in the logarithmic strain space

an efficient formulation of integration algorithms for elastoplastic shell analysis based on layered finite element approach for geometrically and physically nonlinear analyses of shell structures a computational model employing a reissner mindlin type kinematic assumption a layered finite element approach and a closest point projection return mapping algorithm completely formulated in tensor notation is presented as a result of a consistent linearization a tangent modulus is derived expressed also in tensor components the applied constitutive model includes a von mises yield criterion and linear isotropic as well as kinematic hardening all stress deviator components are employed in the formulation the material model is implemented into a four noded isoparametric assumed strain finite element which permits the simulation of geometric nonlinear responses considering finite rotations the proposed numerical concept is unconditionally stable and allows large time steps as the numerical examples illustrate further the numerical simulations demonstrate the expected quadratic convergence in a global iterative technique

finite strain logarithmic hyperelasto plasticity with softening a strongly non local implicit gradient framework this paper addresses the extension of a eulerian logarithmic finite strain hyperelasto plasticity model in order to incorporate an isotropic plastic damage variable that leads to softening and failure of the plastic material it is shown that a logarithmic elasto plastic model with a strongly non local degrading yield stress exactly preserves the structure of its infinitesimal counterpart the strongly non local nature of the model makes it an attractive framework for the numerical solution of softening plasticity problems consistent constitutive tangent operators are derived for the particular case of hyperelasto j2 plasticity which are exactly equal to the corresponding infinitesimal tangent operators the finite element implementation along with the geometrically nonlinear contributions and the incremental solution strategy is outlined a benchmark example is solved illustrating the main differences between the purely elasto plastic case and the case with plastic damage finally the main model characteristics and its practical use are emphasized

finite rotation elements for the non linear analysis of thin shell structures abstract for the numerical analysis of shells undergoing finite rotations doubly curved finite shell elements are developed via the displacement formulation the derivation starts from a consistent finite rotation shell theory which is transformed by a variational procedure into an incremental formulation thus the non linearity can be treated by an incremental iterative technique the non linear element matrices are obtained by a tensor oriented procedure permitting a direct transformation of the initial equations into efficient numerical models unlike in the usual procedure the kirchhoff love assumption is treated as a subsidiary condition at the element level this computer oriented approach permits the elimination of the dependent rotational degrees of freedom without loss of accuracy finally some examples are presented to demonstrate the ability of the resulting finite elements to deal with finite rotation problems

dynamic sensitivity analysis of frictional contact impact response of axisymmetric composite structures abstract a computational procedure is presented for evaluating the sensitivity coefficients of the dynamic frictional contact impact response of axisymmetric composite structures the structures are assumed to consist of an arbitrary number of perfectly bonded homogeneous anisotropic layers the material of each layer is assumed to be hyperelastic and the effect of geometric non linearity is included the sensitivity coefficients measure the sensitivity of the response to variations in different material lamination and geometric parameters of the structure a displacement finite element model is used for the discretization the normal contact conditions are incorporated into the formulation by using a perturbed lagrangian approach with the fundamental unknowns consisting of the nodal displacements and the lagrange multipliers associated with the contact conditions the lagrange multipliers are allowed to be discontinuous at interelement boundaries tangential contact conditions are incorporated by using a penalty method in conjuction with the classical coulomb s friction model temporal integration is performed by using the newmark method the newton raphson iterative scheme is used for the solution of the resulting non linear algebraic equations and for the determination of the contact region contact conditions sliding or sticking and the contact pressures the sensitivity coefficients are evaluated by using a direct differentiation approach numerical results are presented for the frictional contact impact response of a composite spherical cap impacting on a rigid plate

a field boundary element formulation for material nonlinear problems at finite strains abstract a boundary element formulation for geometrical nonlinear problems is presented which is applicable for arbitrary constitutive equations based on the concept of hyperelastic response relative to an intermediate configuration this includes purely hyperelastic problems at large elastic strains in contrast to other formulations the total lagrange framework employed in this work significantly increases the numerical efficiency as the system matrices remain constant during the incremental solution and have to be computed only once a nonlinear set of equations with an identical structure for both boundary and internal unknowns is derived the basic unknowns are displacement gradients which are calculated via integral equations and not by differentiation of the shape functions the formulation can be consistently linearised to allow for the implementation of efficient iteration schemes using gradients e g the newton raphson scheme

implicit finite element formulation of multiresolution continuum theory abstract the multiresolution continuum theory is a higher order continuum theory where additional kinematic variables account for microstructural inhomogeneities at several distinct length scales this can be particularly important for localization problems the strength of this theory is that it can account for details in the microstructure of a material without using an extremely fine mesh the present paper describes the implementation and verification of a 3d elastic plastic multiresolution element based on an implicit time stepping algorithm it is implemented in the general purpose finite element program feap the mesh independency associated with the length scale parameter is examined and the convergence rate of the element is also evaluated

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

elasto plastic analysis of shells with the triangular element tric tric is a simple but sophisticated three node shear deformable isotropic and composite facet shell element suitable for large scale linear and nonlinear engineering computations of thin and moderately thick anisotropic plate and complex shell structures in the present work an elasto plastic constitutive model based on the von mises yield criterion with isotropic hardening is incorporated into the element the characteristic feature of this formulation is that the nonlinear material behaviour is taken into account entirely in the natural system of the element this is achieved by transforming quantities such as equivalent plastic strain equivalent stress the expression of the yield surface and the components of flow vector from the material coordinate system to the natural coordinate system these transformations lead to simple and elegant expressions for the respective quantities in the natural system which eventually result to an efficient and cost effective treatment of the nonlinear analysis of arbitrary shells including material and geometrical nonlinearities

a cascade optimization methodology for automatic parameter identification and shape process optimization in metal forming simulation computer simulations of metal forming processes using the finite element method fem are today well established this form of simulation uses an increasing number of sophisticated geometrical and material models relying on a certain number of input data which are not always readily available the aim of inverse problems which will be considered here is to determine one or more of the input data relating to these forming process simulations thereby leading to a desired result in this paper we will focus on two categories of such inverse problems the first category consists of parameter identification inverse problems these involve evaluating the material parameters for material constitutive models that would lead to the most accurate results with respect to physical experiments i e minimizing the difference between experimental results and fem simulations the second category consists of shape process optimization inverse problems these involve determining the initial geometry of the specimen and or the shape of the forming tools as well as some parameters of the process itself in order to provide the desired final geometry after the forming process these two categories of inverse problems can be formulated as optimization problems in a similar way i e by using identical optimization algorithms in this paper we intend firstly to solve these two types of optimization problems by using different non linear gradient based optimization methods and secondly to compare their efficiency and robustness in a variety of numerical applications

a new numerically stable sequential algorithm for coupled finite strain elastoplastic geomechanics and flow abstract we propose a new numerically stable sequential implicit method for coupled flow and finite strain multiplicative elastoplastic geomechanics we find from stability analysis that the sequential method that solves the flow problem first by fixing the first piola kirchhoff total stress solving the geomechanics solid deformation problem at the next step is unconditionally stable contractive and b stable in this sense this method named the fixed first piola kirchhoff stress method is an extension of the fixed stress method in coupled flow and infinitesimal geomechanics we also study the fixed second piola kirchhoff stress method comparing it with the fixed first piola kirchhoff stress method because the constitutive relations are formulated by the second piola kirchhoff total stress although fixing the second piola kirchhoff total stress field does not provide theoretical unconditional stability in space discretization we use the finite element method for the geomechanics problem with the total lagrangian approach while employing the finite volume method for the flow problem geometrical nonlinearity from the total lagrangian approach results in full tensor permeability even if the initial permeability is isotropic to consider the full tensor permeability accurately we employ the multipoint flux approximation in solving the flow problem in time discretization the backward euler method is used then we perform numerical experiments of the two fixed stress sequential methods with various scenarios and find superiority of their numerical stability specifically the two fixed stress sequential methods provide almost identical results for elasticity for j 2 plasticity the two sequential methods yield slightly different numerical results although the trends of the results are similar for the drucker prager plasticity we find that the results from the two methods are almost identical for all the test cases the two sequential methods are numerically stable

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

objectivity of incremental constitutive relations over finite time steps in computational finite deformation analyses abstract computational techniques which preserve the objectivity of incremental constitutive relations for finite elastic or inelastic materials for finite time steps during which the material elements may undergo finite rotations are presented these techniques are useful in finite deformation finite rotations and finite strain computational analysis of two as well as three dimensional solids and structures

on consistent stress rates in solid mechanics computational implications summary in the context of general isothermal elastic processes issues related to work conjugacy and its effect on the choice of a stress rate are discussed for processes involving large strains it is shown that a unique stress rate consistent with hyperelasticity can be defined for every conjugate pair chosen through the rate form of the associated hyperelastic constitutive equation that results in non constant and generally anisotropic spatial elasticity tensors even for a linear isotropic material the anisotropic spatial elasticity tensor connected with the green naghdi rate of kirchhoff stress is evaluated which provides a basis for the spatial formulation of processes governed by the hencky s strain energy function 8949 notions of equivalent and irreducible form of stress rate are introduced using a workless component of the deformation rate the hyperelastic constitutive models for the conjugate pairs s e and t in u which are of significance for computation are stated in their explicit form exact rate forms are derived and the order of approximation of currently employed computational algorithms discussed finally computational implications of the work presented are reviewed

three dimensional corotational framework for elasto plastic analysis of multilayered composite shells acontinuum basedlayerwiseshear deformablee niteelementformulationispresentedforelasto plasticanalysis oflayered compositesshells theproposed formulationiscast in a corotationalcone guration for e nitedeformation analysis the elasto plastic constitutive equations that are based on rate independent deviatoric plasticity are also written in the corotational kinematic framework issues of covariance and spatial invariance are addressed and an appropriate stress updating strategy is proposed numerical examples are presented to demonstrate the range of applicability of the proposed framework for bending dominated response of elasto plastic layered composite shells nomenclature b body force vector c e fourth order elastic modulus tensor c i n 1 tangent modului consistent with the radial return algorithm d p plastic strain rate tensor e deviatoric strain tensor e p equivalent plastic strain fn 1 incremental deformation gradient ft x deformation gradient f ae q von mises pressure insensitive yield condition a e p hardening rule for back stress i identity matrix

quadrilateral elements for the solution of elasto plastic finite strain problems in this paper two plane strain quadrilateral elements with two and four variables are proposed these elements are applied to the analysis of finite strain elasto plastic problems the elements are based on the enhanced strain and b bar methodologies and possess a stabilizing term the pressure and dilatation fields are assumed to be constant in each element s domain and the deformation gradient is enriched with additional variables as in the enhanced strain methodology the formulation is deduced from a four field functional based on the imposition of two constraints annulment of the enhanced part of the deformation gradient and the relation between the assumed dilatation and the deformation gradient determinant the discretized form of equilibrium is presented and the analytical linearization is deduced to ensure the asymptotically quadratic rate of convergence in the newton raphson method the proposed formulation for the enhanced terms is carried out in the isoparametric domain and does not need the usually adopted procedure of evaluating the jacobian matrix in the centre of the element the elements are very effective for the particular class of problems analysed and do not present any locking or instability tendencies as illustrated by various representative examples copyright 2001 john wiley sons ltd

effects of levy noise in a neuronal competition model abstract the effects of non gaussian levy noise in a competitive neural model of binocular rivalry are analyzed numerically we first investigate how levy noise added to the input strength changes the period of oscillations and leads to the disappearance of the winner take all behavior noise induced alternations are then studied in terms of their statistical measures we are interested in the overlapping of the regions where the model s behavior satisfies the experimental constraints on the mean dominance duration and the coefficient of variation of the dominance durations the results indicate that changes in each of the parameters of levy noise produce changes in the overlap regions the differences with gaussian noise are emphasized finally we plot the distributions of the perceptual dominance durations for different parameters of levy noise and compare these distributions with gamma log normal and weibull distributions using the kolmogorov smirnov goodness of fit test

model based control of dynamic frictional contact problems using the example of hot rolling abstract we consider hot forming processes in which a metal solid body is deformed by several rolls in order to obtain a desired final shape to minimize cutting scrap and to ensure that this shape satisfies the required tolerances as precisely as possible we formulate an optimal control problem where we use the trajectories of the rolls as control functions the deformation of the solid body is described through the basic equations of nonlinear continuum mechanics which are here coupled with an elasto viscoplastic material model based on a multiplicative split of the deformation gradient we assume that the deformations of the rolls can be neglected thus we add unilateral frictional contact boundary conditions resulting in an evolutionary quasi variational inclusion the associated control to observation map is non differentiable due to changes of state between elastic and plastic material behavior contact and separation and stick and slip motion yet we still want to apply gradient based methods to solve the optimal control problem and therefore have to make sure that derivatives of cost functional and constraints exist to resolve this issue we first regularize all non differentiabilities and subsequently apply the direct differentiation method to obtain sensitivity information finally we formulate a suitable algorithm and discuss numerical results for a real world example to illustrate its capability

computational model for 3 d contact problems with friction based on the penalty method the friction forces are assumed to follow the coulomb law with a slip criterion treated in the context of a standard return mapping algorithm consistent linearization of the field equations is performed which leads to a fully implicit scheme with non symmetric tangent stiffness which preserves asymptotic quadratic convergence of the newton raphson method

phase transition and alternation in a model of perceptual bistability in the presence of levy noise abstract the stochastic dynamics of the energy based model of perceptual bistability are numerically studied under the influence of levy noise we obtain the stationary probability distribution for the system driven by gaussian and non gaussian noise by comparing the results we demonstrate that the interplay of levy noise and the input strength of each percept can generate a variety of different effects we next show the influences of levy noise on the mean dominance duration of each percept the alternation rate is also considered as functions of the different parameters of levy noise it shows that changing the value of one or more of the parameters of levy noise can change the mean dominance duration of the percepts and their alternation rate

a finite strain finite element model for the pseudoelastic behavior of shape memory alloys this paper presents a finite deformation finite element model for the pseudoelastic response of shape memory alloys under stress loading unloading conditions at constant temperature a local multiplicative decomposition of the deformation gradient into volumetricelastic and isochori inelastic components is assumed where the inelastic component is associated with phase transformation and defines an additional intermediate configuration strain measure defined on the intermediate configuration is the hencky strain the constitutive equations are cast in the framework of generalized plasticity and the two way phase transformation is modeled via a kuhn tucker type transformation criteria for the rate independent shape memory behavior these equations are able to predict the stress induced phase transformations during complete loading unloading cycles and can also predict the correct material behavior when incomplete transformations take place the resulting nonlinear system of equations is solved for updated stress variables via the radial return algorithm embedded in the newton raphson iteration scheme numerical results are presented to show the performance of the model

improved versions of assumed enhanced strain tri linear elements for 3d finite deformation problems abstract improved three dimensional tri linear elements for finite deformation problems are developed based on an assumed enhanced strain methodology which in the linear regime incorporates the classical method of incompatible modes as a particular case three crucial modifications of a recently proposed element which reduces to wilson s brick in the linear regime are introduced to prevent locking response in distorted configurations and to maintain proper rank while preserving excellent performance in bending dominated and localization problems i a modified quadrature rule ii an additional enhancement of the divergence term and iii a modification of the isoparametric shape function derivatives for the three dimensional problem moreover these modified shape function derivatives are shown to improve the performance of the standard tri linear brick in distorted configurations in addition a strategy is described to circumvent the memory storage requirements in the static condensation procedure of the enhanced strain parameters the excellent performance of the improved methodology is illustrated in representative numerical simulations

dynamics of two competing species in the presence of levy noise sources we consider a lotka volterra system of two competing species subject to multiplicative stable levy noise the interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence both of a periodic driving term and an additive stable levy noise we study the species dynamics which is characterized by two different regimes exclusion of one species and coexistence of both we find quasiperiodic oscillations and stochastic resonance phenomenon in the dynamics of the competing species analyzing the role of the levy noise sources

adaptive finite element methods in computational mechanics we present a general approach to adaptivity for finite element methods and give applications to linear elasticity non linear elasto plasticity and nonlinear conservation laws including numerical results

computational aspects of the logarithmic strain space description abstract computational aspects of the logarithmic strain space description are discussed and compared with so called updated lagrangian descriptions the shortcomings of the latter are demonstrated on an analytical example of homogeneous finite distortion kinematics the numerical implementation and algorithms of the logarithmic strain space description with respect to the reference configuration are presented simulation results of two special purpose finite element programs which are based on the logarithmic strain space description are shown

newton like methods with limited storage for the solution of elasto viscoplasticity problems quasi newton and secant newton methods have been successful in solving problems of elasto plasticity in this paper these methods are applied to elasto viscoplastic analyses in an algorithm coupling the global solution for displacement increments with local newton raphson stress iteration at each sampling point the familiar rank two dfp and bfgs methods are generalized to the broyden family of algorithms and this generalization is also used to produce a secant newton algorithm corresponding to hoshino s method consideration is given to the most effective strategy when only a limited number of quasi newton iterates may be stored overwriting re start or continuation in secant newton form results are presented for a tunnelling problem using both plane strain and axisymmetric formulations

a perturbed lagrangian formulation for the finite element solution of contact problems making use of a perturbed lagrangian formulation a finite element procedure for contact problems is developed for the general case in which node to node contact no longer holds the proposed procedure leads naturally to a discretization of the contact interface into contact segments within the context of a bilinear interpolation for the displacement field a mixed finite element approximation is introduced by assuming discont naous contact pressure constant on the contact segment because of this piece wise constant approximation the gap function enters into the formulation in an average sense instead of through a point wise definition numerical examples are presented that illustrate the performance of the proposed procedure current finite element formulations for contact problems based on either the classical lagrange parameter procedure l 3 12 203 or the penalty function method 4 6 11 are characterized by a point wise enforcement of the contact constraint condition in the sense that penetration of the bodies is established on a nodal basis moreover in this methods the recovery of the contact pressure over the element from the contact nodal forces generally requires an additional procedure within the framework of classical lagrange multiplier methods the contact condition is exactly satisfied by transforming the constrained problem into an unconstrained one with the introduction of additional variables lagrange multipliers these extra variables add computational effort to the solution process which often requires special procedures to handle the presence of zero diagonal terms penalty methods on the other hand enable one to transform the constrained problem into an unconstrained one without introducing additional variables the constraint condition is now satisfied only approximately for finite values of the penalty parameter the main difhculty associated with these methods however lies in the poor conditioning of the problem as the penalty is increased to more accurately enforce the constraint condition this is a well understood phenomenon particularly in the context of the incompressible and nearly incompressible problem in solid and fluid mechanics e g see l 22 25 for a review recently augmented lagrangian procedures have been proposed as a promising way to partially overcome these difficulties and regularize the penalty formulation e g see the survey in 7 8 within the framework of zinearited e u c it is possible to restrict the finite element formulation of contact problems by assuming that node to node contact occurs this is in fact the case often considered in the literature l 2 4 6 12 20 211 in the general context of fully

a consistent tangent stiffness matrix for three dimensional non linear contact analysis a consistent tangent stiffness matrix for the analysis of non linear contact problems is presented the associated element has three or four nodes and establishes contact between three dimensional structures like solids and shells it accounts for the non linear kinematics of large deformation analysis and guarantees a quadratic convergence rate two formulations the penalty method and the lagrange multiplier method are investigated

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

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

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

the convected description in large deformation frictional contact problems abstract the converted description is introduced for finite deformation frictional contact problems such that both coulomb and more general friction criteria can be conveniently and reliably numerically implemented in lagrangian finite element calculations the discussion includes careful definition of the convected frame from the standpoint of differential geometry complete with physical interpretations of the frame and the associated slip and traction rate measures as demonstrated use of these measures enables prescription of frictional constitutive relationships with virtually no more complexity than is required by the kinematically linear theory while ensuring the required frame indifference of the description as a result the work provides a sound mathematical and continuum mechanical foundation for future implementations of general friction laws in large deformation solid mechanics computing architectures

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

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

a framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition part ii computational aspects computational aspects of the formulation of elastoplasticity proposed in part i of this work employing a multiplicative decomposition and based on the principle of maximum plastic dissipation are examined in detail in particular the implementation of the proposed hyperelastic j2 flow theory is shown to reduce to a trivial modification of the classical radial return algorithm which is amenable to exact linearization this results in a closed form expression for the consistent elastoplastic tangent moduli the algorithmic treatment of the general case is considered subsequently it is emphasized that objective rates and incrementally objective algorithms play no role in the present approach a number of numerical experiments are presented that illustrate the excellent performance of the proposed formulation

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