Implicit J2‐bounding surface plasticity using Prager's translation rule

A bounding surface J₂‐plasticity model that uses Prager's translation rule is presented. The model preserves Masing's rules and is developed from the same ideas as classical infinitesimal J₂‐plasticity, resulting in the same formulation with the exception of the algorithm for the computation of the hardening function. Instead of utilizing a loading surface as in a previous formulation, hardening surfaces are introduced; the formulation is similar to that of multilayer plasticity using Prager's rule, presented in previous work. An implicit algorithm based on the radial return concept is used, and the consistent elastoplastic tangent is also developed in closed form. Examples illustrating anisotropic behaviour are presented and compared to that predicted by a multilayer J₂‐plasticity model. The model is also applied to a soil dynamics problem to show the robustness of the algorithm and its applicability to complex loading. Copyright © 2002 John Wiley & Sons, Ltd.     

Elasto‐plasticity revisited: numerical analysis via reproducing kernel particle method and parametric quadratic programming

Aiming to simplify the solution process of elasto‐plastic problems, this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto‐plasticity. The parametric quadratic programming theory is useful and effective for the assessment of certain features of structural elasto‐plastic behaviour and can also be exploited for numerical iteration. Examples are presented to illustrate the essential aspects of the behaviour of the model proposed and the flexibility of the coupled parametric quadratic programming formulations with the reproducing kernel particle method. Copyright © 2002 John Wiley & Sons, Ltd.     

Curved Mindlin beam and axi-symmetric shell elements—A new approach

Two sets of strain definitions for analysis of curved Mindlin beams and axi-symmetric shells are examined. Their conventional finite element implementations are shown to be unsuitable. The parameter used as a nodal degree of freedom in the first conventional method to describe the cross section rotation is in general a discontinuous function and has no clear physical meaning. The second conventional method has relied on an incorrect differentiation for its successful use in finite element analysis. A new approach which overcomes these problems is presented. Examples are given to illustrate the incorrect results that can be obtained from the two conventional methods and to show that the new approach provides accurate solutions to general curved beam and axi-symmetric shell problems.     

Implicit plane stress algorithm for multilayer J2‐plasticity using the Prager–Ziegler translation rule

A totally implicit algorithm for plane stress multilayer plasticity is presented. The algorithm presents the plane stress version of the 3D/plane strain model for multilayer plasticity presented in a previous work. As in the 3D/plane strain case, the model is consistent with the principle of maximum dissipation and it may be considered as an extension of classical J₂‐plasticity for anisotropic non‐linear kinematic behaviour preserving Masing's rules. In order to obtain the asymptotic second‐order convergence of the Newton algorithm, the consistent tangent moduli are also given. Copyright © 2003 John Wiley & Sons, Ltd.     

An integration procedure based on multi‐surface plasticity for plane stress plasticity: Theoretical formulation and application

An integration procedure designed to satisfy plane stress conditions for any constitutive law initially described in 3D and based on classical plasticity theory is presented herein. This method relies on multi‐surface plasticity, which allows associating in series various mechanisms. Three mechanisms have ultimately been used and added to the first one to satisfy the plane stress conditions. They are chosen to generate a plastic flow in the 3 out‐of‐plane directions, whose stresses must be canceled (σ₃₃,σ₁₃, and σ₂₃). The advantage of this method lies in its ease of use for every plastic constitutive law (in the general case of the non‐associated flow rule and with both nonlinear kinematic and isotropic hardening). Method implementation using a cutting plane algorithm is presented in its general framework and then illustrated by the example of a J2‐plasticity material model considering linear kinematic and isotropic hardening. The approach is compared with the same J2‐plasticity model that has been directly derived from a projection of its equations onto the plane stress subspace. The performance of the multi‐surface plasticity method is shown through the comparison of iso‐error and iso‐step contours in both formulations, and lastly with a case study considering a hollow plate subjected to tension. Copyright © 2014 John Wiley & Sons, Ltd.     

Efficient visualization of high‐order finite elements

A general method for the post‐processing treatment of high‐order finite element fields is presented. The method applies to general polynomial fields, including discontinuous finite element fields. The technique uses error estimation and h‐refinement to provide an optimal visualization grid. Some filtering is added to the algorithm in order to focus the refinement on a visualization plane or on the computation of one single iso‐zero surface. 2D and 3D examples are provided that illustrate the power of the technique. In addition, schemes and algorithms that are discussed in the paper are readily available as part of an open source project that is developed by the authors, namely Gmsh. Copyright © 2006 John Wiley & Sons, Ltd.     

Automatic mesh generation and adaptation by using contours

A general and efficient remeshing algorithm is presented for the discretization of arbitrary planar domains into triangular elements in consistency with the given node spacing function. The contour lines of the node spacing function at suitable calculated levels provide the natural lines of division of the problem domain into subregions, where finite element meshes of different element sizes are generated using the available general-purpose mesh generators.^{1, 2} Examples of remeshing for various node spacing functions are given to illustrate that high-quality gradation meshes can be generated automatically without any user's intervention by this simple contour line method.     

The Asymptotic Expansion Load Decomposition elastoplastic beam model

A new higher‐order elastoplastic beam model is derived and implemented in this paper. The reduced kinematic approximation is based on a higher‐order elastic beam model using the asymptotic expansion method. This model introduces new degrees of freedom associated to arbitrary loads as well as eigenstrains applied to the beam. In order to capture the effect of plasticity on the structure, the present elastoplastic model considers the plastic strain as an eigenstrain imposed on the structure, and new degrees of freedom are added on the fly into the kinematics during the incremental‐iterative process. The radial return algorithm of J₂ plastic flow is used. Because of the constant evolution of beam kinematics, the Newton‐Raphson algorithm for satisfying the global equilibrium is modified. An application to a cantilever beam loaded at its free extremity is presented and compared to a three‐dimensional reference solution. The beam model shows satisfying results even at a local scale and for a significantly reduced computation time.     

Statistical approach to roughness-induced shielding effects

A new theoretical concept is introduced to describe the roughness‐induced shielding effects in metallic materials. This approach is based on the statistics of the local ratio between the characteristic microstuctural distance and the plastic zone size. A general equation involving both the crack branching and the crack closure phenomena is derived in the frame of linear elastic fracture mechanics under the assumption of remote mode I loading. It enables the determination of the intrinsic values of both the fracture toughness and the fatigue crack growth threshold. Moreover, the roughness‐induced component can be separated from other closure components, such as the plasticity or oxide‐induced closure. In order to estimate the total roughness‐induced shielding effect only standard materials data such as the yield stress, the mean grain size, the surface roughness and the fracture mode are necessary. Examples of applications concerning static fracture and fatigue are presented for selected metallic materials.     

Implementation of an algorithm for general material behavior of steel taking interaction between plasticity and transformation‐induced plasticity into account

In this article a semi‐implicit algorithm (predictor–corrector approach) for incorporating the interaction between plasticity and transformation‐induced plasticity (TRIP) in steel is developed. Contrary to the usual elasto‐plasticity, the underlying model of material behavior of steel is far more complex. The interaction between plasticity and TRIP requires extensions of algorithms developed in Doghri (Int. J. Numer. Meth. Engng 1993; 36 :3915–3932) and in Mahnken (Commun. Numer. Meth. Engng 1999; 15 :745–754). A particular feature of the algorithm is that the inner iteration can be reduced to a single scalar equation. Numerical examples illustrate the algorithm's capabilities. Copyright © 2011 John Wiley & Sons, Ltd.     

Post‐buckling analysis of imperfect laminates using finite strips based on a higher‐order plate theory

A finite strip procedure has been developed for the post‐buckling analysis of composite laminates when subjected to progressive end shortening. The finite strips are developed based on a higher‐order shear deformation plate theory and there are nine variables at each nodal line. Initial imperfection expressed in the form of suitable trigonometric function is allowed. Examples including isotropic plates and laminates with arbitrary lay‐up arrangement are presented. Numerical results for laminates with and without initial imperfection are used to illustrate the effect of imperfection. Copyright © 2003 John Wiley & Sons, Ltd.     

Apodization of multilayer bulk-wave transducers

Recent experiments have demonstrated the use of superlattice transducers for bulk acoustic waves in the gigahertz frequency range. The transducers consisted of multilayers of ZnO or LiNbO(3) with alternating crystal orientations or polarizations. A procedure for calculating the electromechanical characteristics of general multilayer transducers in which the individual layers are anisotropic and piezoelectric and have arbitrary crystal orientation is described. The algorithm used is numerically stable and easily implemented for use on a personal computer using commercial software. A network model is also derived to provide both an approximate analysis of multilayer transducer performance and an insight into synthesis procedures. Examples are used to compare the two approaches and illustrate an initial design procedure for broadband transducers.     

An implicit BEM formulation for gradient plasticity and localization phenomena

The aim of this paper is to discuss a boundary element formulation for non‐linear structural problems involving localization phenomena. In order to overcome the well‐known mesh dependency observed in local plasticity, a gradient plasticity model is used. An implicit boundary element formulation is proposed and the underlying consistent tangent operator defined. This formulation is based on the classical displacement and strain integral representations combined with an integral representation of the plastic multiplier. First numerical examples are presented to illustrate the application of the method. Copyright © 2001 John Wiley & Sons, Ltd.     

Efficient computation of order and mode of corner singularities in 3D‐elasticity

A general numerical procedure is presented for the efficient computation of corner singularities, which appear in the case of non‐smooth domains in three‐dimensional linear elasticity. For obtaining the order and mode of singularity, a neighbourhood of the singular point is considered with only local boundary conditions. The weak formulation of the problem is approximated by a Galerkin–Petrov finite element method. A quadratic eigenvalue problem ( P +λ Q +λ² R ) u = 0 is obtained, with explicitly analytically defined matrices P , Q , R . Moreover, the three matrices are found to have optimal structure, so that P , R are symmetric and Q is skew symmetric, which can serve as an advantage in the following solution process. On this foundation a powerful iterative solution technique based on the Arnoldi method is submitted. For not too large systems this technique needs only one direct factorization of the banded matrix P for finding all eigenvalues in the interval ?e(λ)∈(?0.5,1.0) (no eigenpairs can be ‘lost’) as well as the corresponding eigenvectors, which is a great improvement in comparison with the normally used determinant method. For large systems a variant of the algorithm with an incomplete factorization of P is implemented to avoid the appearance of too much fill‐in. To illustrate the effectiveness of the present method several new numerical results are presented. In general, they show the dependence of the singular exponent on different geometrical parameters and the material properties. Copyright © 2001 John Wiley & Sons, Ltd.     

Neuro‐genetic algorithm for non‐linear active control of structures

In a companion paper, a new non‐linear control model was presented for active control of three‐dimensional (3D) building structures including geometrical and material non‐linearities, coupling action between lateral and torsional motions, and actuator dynamics (Int. J. Numer. Meth. Engng; DOI: 10.1002/nme.2195 ). A dynamic fuzzy wavelet neuroemulator was presented for predicting the structural response in future time steps. In this paper, a new neuro‐genetic algorithm or controller is presented for finding the optimal control forces. The control algorithm does not need the pre‐training required in a neural network‐based controller, which improves the efficiency of the general control methodology significantly. Two 3D steel building structures, a 12‐story structure with vertical setbacks and an 8‐story structure with plan irregularity, are used to validate the neuro‐genetic control algorithm under three different seismic excitations. Numerical validations demonstrate that the new control methodology significantly reduces the displacements of buildings subjected to various seismic excitations including structures with plan and elevation irregularities. Copyright © 2008 John Wiley & Sons, Ltd.     

A three‐invariant hardening plasticity for numerical simulation of powder forming processes via the arbitrary Lagrangian–Eulerian FE model

In this paper, a three‐invariant cap plasticity model with an isotropic hardening rule is presented for numerical simulation of powder compaction processes. A general form is developed for single‐cap plasticity which can be compared with some common double‐surface plasticity models proposed for powders in literature. The constitutive elasto‐plastic matrix and its components are derived based on the definition of yield surface, hardening parameter and non‐linear elastic behaviour, as function of relative density of powder. Different aspects of the new single plasticity are illustrated by generating the classical plasticity models as special cases of the proposed model. The procedure for determination of powder parameters is described by fitting the model to reproduce data from triaxial compression and confining pressure experiments. The three‐invariant cap plasticity is performed within the framework of an arbitrary Lagrangian–Eulerian formulation, in order to predict the non‐uniform relative density distribution during large deformation of powder die pressing. In ALE formulation, the reference configuration is used for describing the motion, instead of material configuration in Lagrangian, and spatial configuration in Eulerian formulation. This formulation introduces some convective terms in the finite element equations and consists of two phases. Each time step is analysed according to Lagrangian phase until required convergence is attained. Then, the Eulerian phase is applied to keep mesh configuration regular. Because of relative displacement between mesh and material, all dependent variables such as stress and strain are converted through the Eulerian phase. Finally, the numerical schemes are examined for efficiency and accuracy in the modelling of a rotational flanged component, an automotive component, a conical shaped‐charge liner and a connecting‐rod. Copyright © 2005 John Wiley & Sons, Ltd.     

Smooth finite strain plasticity with non‐local pressure support

The aim of this work is to introduce an alternative framework to solve problems of finite strain elastoplasticity including anisotropy and kinematic hardening coupled with any isotropic hyperelastic law. After deriving the constitutive equations and inequalities without any of the customary simplifications, we arrive at a new general elasto‐plastic system. We integrate the elasto‐plastic algebraico‐differential system and replace the loading–unloading condition by a Chen–Mangasarian smooth function to obtain a non‐linear system solved by a trust region method. Despite being non‐standard, this approach is advantageous, since quadratic convergence is always obtained by the non‐linear solver and very large steps can be used with negligible effect in the results. Discretized equilibrium is, in contrast with traditional approaches, smooth and well behaved. In addition, since no return mapping algorithm is used, there is no need to use a predictor. The work follows our previous studies of element technology and highly non‐linear visco‐elasticity. From a general framework, with exact linearization, systematic particularization is made to prototype constitutive models shown as examples. Our element with non‐local pressure support is used. Examples illustrating the generality of the method are presented with excellent results. Copyright © 2009 John Wiley & Sons, Ltd.     

Associated computational plasticity schemes for nonassociated frictional materials

A new methodology for computational plasticity of nonassociated frictional materials is presented. The new approach is inspired by the micromechanical origins of friction and results in a set of governing equations similar to those of standard associated plasticity. As such, procedures previously developed for associated plasticity are applicable with minor modification. This is illustrated by adaptation of the standard implicit scheme. Moreover, the governing equations can be cast in terms of a variational principle, which after discretization is solved by means of a newly developed second‐order cone programming algorithm. The effects of nonassociativity are discussed with reference to localization of deformations and illustrated by means of a comprehensive set of examples. Copyright © 2012 John Wiley & Sons, Ltd.     

Locking‐free continuum displacement finite elements with nodal integration

An assumed‐strain finite element technique is presented for linear, elastic small‐deformation models. Weighted residual method (reminiscent of the strain–displacement functional) is used to weakly enforce the balance equation with the natural boundary condition and the kinematic equation (the strain–displacement relationship). A priori satisfaction of the kinematic weighted residual serves as a condition from which strain–displacement operators are derived via nodal integration. A variety of element shapes is treated: linear triangles, quadrilaterals, tetrahedra, hexahedra, and quadratic (six‐node) triangles and (27‐node) hexahedra. The degrees of freedom are only the primitive variables (displacements at the nodes). The formulation allows for general anisotropic materials. A straightforward constraint count can partially explain the insensitivity of the resulting finite element models to locking in the incompressible limit. Furthermore, the numerical inf–sup test is applied in select problems and several variants of the proposed formulations (linear triangles, quadrilaterals, tetrahedra, hexahedra, and 27‐node hexahedra) pass the test. Examples are used to illustrate the performance with respect to sensitivity to shape distortion and the ability to resist volumetric locking. Copyright © 2008 John Wiley & Sons, Ltd.     

Acoustic boundary element eigenproblem with sound absorption and its solution using Lanczos algorithm

A damped system eigenvalue analysis of acoustical cavities using the boundary element method is presented. The acoustic boundary element eigenproblem formulation found in the literature is extended to include sound absorption in acoustical cavities. A dissipative term is included in the eigenvalue matrix equation to account for boundary absorption. The resulting damped system eigenvalue problem is solved using a new Lanczos subspace algorithm for quadratic eigenproblems. Since the boundary element matrices are unsym-metric, the Lanczos algorithm presented is in its most general form for unsymmetric quadratic eigenprob-lems. Examples are presented to show the application of the method in computing the eigenfrequencies of acoustic cavities with sound absorption.