Analytical integration of elasto‐plastic uniaxial constitutive laws over arbitrary sections.

We present the preliminary results of a novel approach to the state determination of polygonal sections of arbitrary shape endowed with elasto‐plastic uniaxial constitutive laws. By means of a suitable application of Gauss theorem, we prove that the normal stress resultants can be computed analytically as sum of finite quantities evaluated solely at the vertices of the section. For this reason, the proposed approach has been termed fiber‐free to emphasize the fact that it does not require any subdivision of the section in fibers. Numerical results show that the fiber approach is grossly inaccurate and that the number of fibers required to achieve a degree of accuracy comparable with that entailed by the fiber‐free approach is at least one order of magnitude greater than the one commonly suggested in commercial software for nonlinear frame analysis. Copyright © 2012 John Wiley & Sons, Ltd.     

The boundary element‐free method for elastoplastic implicit analysis

A meshless procedure, based on boundary integral equations, is proposed to analyze elastoplastic problems. To cope with non‐linear problems, the usual boundary element method introduces domain discretization cells, often considered a ‘drawback’ of the method. Here, to get rid of the standard element and cell, i.e. boundary and domain discretization, the orthogonal moving least squares (also known as improved moving least squares) method is used. The algorithm adopted to solve these particular inelastic non‐linear problems is a well‐established, criterion‐independent implicit procedure, previously developed by the authors. Comparative results are presented at the end to illustrate the effectiveness of the proposed techniques. Copyright © 2008 John Wiley & Sons, Ltd.     

Interface dynamic stiffness matrix approach for three‐dimensional transient multi‐region boundary element analysis

A novel substructuring method is developed for the coupling of boundary element and finite element subdomains in order to model three‐dimensional multi‐region elastodynamic problems in the time domain. The proposed procedure is based on the interface stiffness matrix approach for static multi‐region problems using variational principles together with the concept of Duhamel integrals. Unit impulses are applied at the boundary of each region in order to evaluate the impulse response matrices of the Duhamel (convolution) integrals. Although the method is not restricted to a special discretization technique, the regions are discretized using the boundary element method combined with the convolution quadrature method. This results in a time‐domain methodology with the advantages of performing computations in the Laplace domain, which produces very accurate and stable results as verified on test examples. In addition, the assembly of the boundary element regions and the coupling to finite elements are greatly simplified and more efficient. Finally, practical applications in the area of soil–structure interaction and tunneling problems are shown. Copyright © 2009 John Wiley & Sons, Ltd.     

Finite element implementation of non‐linear elastoplastic constitutive laws using local and global explicit algorithms with automatic error control

Implicit stress integration algorithms have been demonstrated to provide a robust formulation for finite element analyses in computational mechanics, but are difficult and impractical to apply to increasingly complex non‐linear constitutive laws. This paper discusses the performance of fully explicit local and global algorithms with automatic error control used to integrate general non‐linear constitutive laws into a non‐linear finite element computer code. The local explicit stress integration procedure falls under the category of return mapping algorithm with standard operator split and does not require the determination of initial yield or the use of any form of stress adjustment to prevent drift from the yield surface. The global equations are solved using an explicit load stepping with automatic error control algorithm in which the convergence criterion is used to compute automatically the coarse load increment size. The proposed numerical procedure is illustrated here through the implementation of a set of elastoplastic constitutive relations including isotropic and kinematic hardening as well as small strain hysteretic non‐linearity. A series of numerical simulations confirm the robustness, accuracy and efficiency of the algorithms at the local and global level. Published in 2001 by John Wiley & Sons, Ltd.     

An isogeometric locking‐free NURBS‐based solid‐shell element for geometrically nonlinear analysis

In this work, we develop an isogeometric non‐uniform rational B‐spline (NURBS)‐based solid‐shell element for the geometrically nonlinear static analysis of elastic shell structures. A single layer of continuous 3D elements through the thickness of the shell is considered, and the order of approximation in that direction is chosen to be equal to two. A complete 3D constitutive relation is assumed. The objective is to develop a highly accurate low‐order element for coarse meshes. We propose an extension of the mixed method of Bouclier et al. [11] to deal with locking in the context of large rotations and large displacements. The main idea is to modify the interpolation of the average through the thickness of the stress components. It is also necessary to stabilize the element in order to avoid the occurrence of spurious zero‐energy modes. This was achieved, for the quadratic version, through the adjunction of artificial elementary stabilization stiffnesses. The result is an element of order 2, which is at least as accurate as standard NURBS shell elements of order 4. Linear and nonlinear test calculations have been carried out along with comparisons with other published NURBS and classical techniques in order to assess the performance of the element. Copyright © 2014 John Wiley & Sons, Ltd.     

Two‐point constitutive equations and integration algorithms for isotropic‐hardening rate‐independent elastoplastic materials in large deformation

This paper presents alternative forms of hyperelastic–plastic constitutive equations and their integration algorithms for isotropic‐hardening materials at large strain, which are established in two‐point tensor field, namely between the first Piola–Kirchhoff stress tensor and deformation gradient. The eigenvalue problems for symmetric and non‐symmetric tensors are applied to kinematics of multiplicative plasticity, which imply the transformation relationships of eigenvectors in current, intermediate and initial configurations. Based on the principle of plastic maximum dissipation, the two‐point hyperelastic stress–strain relationships and the evolution equations are achieved, in which it is considered that the plastic spin vanishes for isotropic plasticity. On the computational side, the exponential algorithm is used to integrate the plastic evolution equation. The return‐mapping procedure in principal axes, with respect to logarithmic elastic strain, possesses the same structure as infinitesimal deformation theory. Then, the theory of derivatives of non‐symmetric tensor functions is applied to derive the two‐point closed‐form consistent tangent modulus, which is useful for Newton's iterative solution of boundary value problem. Finally, the numerical simulation illustrates the application of the proposed formulations. Copyright © 2008 John Wiley & Sons, Ltd.     

Corrosion Process and Mechanisms of Corrosion‐Induced Cracks in Reinforced Concrete identified by AE Analysis

Abstract: Concrete structures could suffer from the corrosion of reinforcing steel bars (rebars) because of the penetration of chloride ions. For crack detection and damage evaluation in concrete, acoustic emission (AE) techniques have been extensively applied to concrete and concrete structures. In the corrosion process of reinforced concrete, it is demonstrated that continuous AE monitoring is available to identify the onset of corrosion and the nucleation of concrete cracking because of the expansion of corrosion products. At the latter stage, the expansion of corrosion products generates corrosion‐induced cracks in concrete. The generating mechanisms of these cracks are studied in accelerated corrosion tests of reinforced concrete beams. Kinematics of microcracks are identified by SiGMA (Simplified Green’s functions for Moment tensor Analysis) analysis of AE. It is demonstrated that AE activity at the onset of corrosion and at the nucleation of corrosion‐induced cracks is in remarkable agreement with the phenomenological model of the corrosion process in steel. Then, mechanisms of corrosion‐induced cracks are visually and quantitatively investigated by the SiGMA analysis.     

A general procedure for deriving symmetric expressions for the secant and tangent stiffness matrices in finite element analysis

The paper presents a general and straightforward procedure based on the use of the strain energy density for deriving symmetric expressions of the secant and tangent stiffness matrices for finite element analysis of geometrically non-linear structural problems. The analogy with previously proposed methods for deriving secant and tangent matrices is detailed. The simplicity of the approach is shown in an example of application. © 1998 John Wiley & Sons, Ltd.     

Assessment of the Effectiveness of the Embedded Through‐Section Technique for the Shear Strengthening of Reinforced Concrete Beams

Abstract: Embedded Through‐Section (ETS) technique is a relatively recent shear strengthening strategy for reinforced concrete (RC) beams and consists of opening holes across the depth of the beam’s cross‐section, with the desired inclinations, where bars are introduced and are bonded to the concrete substrate with adhesive materials. To assess the effectiveness of this technique, a comprehensive experimental program composed of 14 RC beams was carried out, and the obtained results confirm the feasibility of the ETS method and revealed that: (i) inclined ETS strengthening bars were more effective than vertical ETS bars, and the shear capacity of the beams has increased with the decrease of the spacing between bars; (ii) brittle shear failure was converted in ductile flexural failure, and (iii) the contribution of the ETS strengthening bars for the beam shear resistance was limited by the concrete crushing or due to the yielding of the longitudinal reinforcement. The applicability of the ACI 318 (2008) and Eurocode 2 (2004) standard specifications for shear resistance was examined, and a good agreement between the experimental and analytical results was obtained.     

Modeling steel fiber reinforced concrete: numerical immersed boundary approach and a phenomenological mesomodel for concrete‐fiber interaction

Steel fiber reinforced concrete (SFRC) allows overcoming brittleness and weakness under tension, the main drawbacks of plain concrete. The influence of the fibers on the behavior of SFRC depends on their shape, length, slenderness, and also on their orientation and distribution into the plain concrete. The goal of this paper is to develop an ad hoc numerical strategy to account for the contribution of the fibers in the simulation of the mechanical response of SFRC. In the model presented, the individual fibers immersed in the concrete bulk are accounted for in their actual location and orientation. The selected approach is based on the ideas introduced in the immersed boundary (IB) methods. These methods were developed to account for 1D (or 2D) solids immersed in 2D (or 3D) fluids. Here, the concrete bulk is playing the role of the fluid and the cloud of steel fibers is acting as the immerse boundary (that is, a 1D structure in a 2D or 3D continuous). Thus, the philosophy of the IB methodology is used to couple the behavior of the two systems, the concrete bulk and fiber cloud, precluding the need of matching finite element meshes. Note that, considering the different size scales and the intricate geometry of the fiber cloud, the conformal matching of the meshes would be a restriction resulting in a practically unaffordable mesh. In the proposed approach, the meshes of the concrete bulk and fiber cloud are independent, and the models are coupled imposing displacement compatibility and equilibrium of the two systems. In the applications presented here, the concrete bulk is modeled using a standard nonlinear damage model. The constitutive model for the fibers is designed to account for the complex interaction between fibers and concrete. The fiber models are based on the previous investigations describing the concrete‐fiber interaction and its dependence on the factors identified to be relevant: shape of the fiber (straight or hooked) and angle between the fiber and crack plane. Copyright © 2011 John Wiley & Sons, Ltd.     

The geometric stiffness of thick shell triangular finite elements for large rotations

This paper is concerned with the development of the geometric stiffness matrix of thick shell finite elements for geometrically nonlinear analysis of the Newton type. A linear shell element that is comprised of the constant stress triangular membrane element and the triangular discrete Kirchhoff Mindlin theory (DKMT) plate element is ‘upgraded’ to become a geometrically nonlinear thick shell finite element. Perturbation methods are used to derive the geometric stiffness matrix from the gradient, in global coordinates, of the nodal force vector when stresses are kept fixed. The present approach follows earlier works associated with trusses, space frames and thin shells. It has the advantage of explicitness and clear physical insight. A special procedure, tailored to triangular elements is used to isolate pure rotations to enable stress recovery via linear elastic constitutive relations. Several examples are solved. The results compare well with those available in the literature. Copyright © 2005 John Wiley & Sons, Ltd.     

A constitutive relation error estimator based on traction‐free recovery of the equilibrated stress

A new methodology for recovering equilibrated stress fields is presented, which is based on traction‐free subdomains' computations. It allows a rather simple implementation in a standard finite element code compared with the standard technique for recovering equilibrated tractions. These equilibrated stresses are used to compute a constitutive relation error estimator for a finite element model in 2D linear elasticity. A lower bound and an upper bound for the discretization error are derived from the error in the constitutive relation. These bounds in the discretization error are used to build lower and upper bounds for local quantities of interest. Copyright © 2008 John Wiley & Sons, Ltd.     

On semi‐analytical probabilistic finite element method for homogenization of the periodic fiber‐reinforced composites

The main aim of this paper is a development of the semi‐analytical probabilistic version of the finite element method (FEM) related to the homogenization problem. This approach is based on the global version of the response function method and symbolic integral calculation of basic probabilistic moments of the homogenized tensor and is applied in conjunction with the effective modules method. It originates from the generalized stochastic perturbation‐based FEM, where Taylor expansion with random parameters is not necessary now and is simply replaced with the integration of the response functions. The hybrid computational implementation of the system MAPLE with homogenization‐oriented FEM code MCCEFF is invented to provide probabilistic analysis of the homogenized elasticity tensor for the periodic fiber‐reinforced composites. Although numerical illustration deals with a homogenization of a composite with material properties defined as Gaussian random variables, other composite parameters as well as other probabilistic distributions may be taken into account. The methodology is independent of the boundary value problem considered and may be useful for general numerical solutions using finite or boundary elements, finite differences or volumes as well as for meshless numerical strategies. Copyright © 2011 John Wiley & Sons, Ltd.     

Determination of the bilinear stress‐crack opening curve for normal‐ and high‐strength concrete

An improved version of the method proposed to ACI committee 446 and to RILEM TC 187‐SOC to determine the fracture parameters of concrete is applied in this study to several mixtures of normal and high‐strength concretes. The results are processed with a C++ program developed by the authors to automatise the mathematical operations required to obtain the bilinear softening curve of concrete from the experimental results. Numerical simulations of the tests are also carried out using finite elements with an embedded cohesive crack. The comparison between numerical and experimental results confirms that the experimental and numerical procedures are appropiate for normal‐strength concretes and high‐strength concretes.     

An unconditionally convergent algorithm for the evaluation of the ultimate limit state of RC sections subject to axial force and biaxial bending

We present a numerical procedure, based upon a tangent approach, for evaluating the ultimate limit state (ULS) of reinforced concrete (RC) sections subject to axial force and biaxial bending. The RC sections are assumed to be of arbitrary polygonal shape and degree of connection; furthermore, it is possible to keep fixed a given amount of the total load and to find the ULS associated only with the remaining part which can be increased by means of a load multiplier. The solution procedure adopts two nested iterative schemes which, in turn, update the current value of the tentative ultimate load and the associated strain parameters. In this second scheme an effective integration procedure is used for evaluating in closed form, as explicit functions of the position vectors of the vertices of the section, the domain integrals appearing in the definition of the tangent matrix and of the stress resultants. Under mild hypotheses, which are practically satisfied for all cases of engineering interest, the existence and uniqueness of the ULS load multiplier is ensured and the global convergence of the proposed solution algorithm to such value is proved. An extensive set of numerical tests, carried out for rectangular, L‐shaped and multicell sections shows the effectiveness of the proposed solution procedure. Copyright © 2007 John Wiley & Sons, Ltd.     

Extension of the ‘solid‐shell’ concept for application to large elastic and large elastoplastic deformations

In the present contribution we extend a previously proposed so‐called solid–shell concept which incorporates only displacement degrees of freedom to the simulation of large elastic and large elastoplastic deformations of shells. Therefore, the modifications necessary for hyper‐elastic or elastoplastic material laws are discussed. These modifications concern the right Cauchy–Green tensor for large elastic deformations, respectively, the deformation gradient for elastoplasticity which then are consistent to the modified Green–Lagrange strains that are necessary for transverse shear and membrane locking free solid–shell element formulations. However, in addition to the locking mentioned above especially in the range of plasticity incompressibility locking becomes important. Thus, the second major aspect of this contribution is the discussion of several ways to avoid incompressibility locking also including the investigation of eigenmodes. Finally, a selective reduced integration scheme with reduced integration for the volumetric term is employed and described in detail, although it is limited to material laws which allow the decomposition into a volumetric and a deviatoric part. Some numerical examples show the range of application for the proposed elements. Copyright © 2000 John Wiley & Sons, Ltd.     

Exact dynamic stiffness matrix for a thin‐walled beam of doubly asymmetric cross‐section filled with shear sensitive material

An exact dynamic stiffness matrix is developed for the flexural motion of a three‐dimensional, bi‐material beam of doubly asymmetric cross‐section. The beam comprises a thin walled outer layer that encloses and works compositely with its shear sensitive core material. The outer layer may have the form of an open or closed section and provides flexural, warping and Saint‐Venant rigidity, while the core material provides Saint‐Venant and shear rigidity. The uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick–Williams algorithm, which enables the required natural frequencies to be converged upon to any required accuracy with the certain knowledge that none have been missed. Such a formulation enables the powerful modelling features associated with the finite element technique to be utilized when establishing structural models. Three examples are included to validate and illustrate the method. The work also holds considerable potential in its application to the approximate analysis of asymmetric, multi‐storey, three‐dimensional wall‐frame structures. Copyright © 2006 John Wiley & Sons, Ltd.     

An evaluation of limited‐memory sparse linear solvers for thermo‐mechanical applications

We consider the performance of sparse linear solvers for problems that arise from thermo‐mechanical applications. Such problems have been solved using sparse direct schemes that enable robust solution at the expense of memory requirements that grow non‐linearly with the dimension of the coefficient matrix. In this paper, we consider a class of preconditioned iterative solvers as a limited‐memory alternative to direct solution schemes. However, such preconditioned iterative solvers typically exhibit complex trade‐offs between reliability and performance. We therefore characterize such trade‐offs for systems from thermo‐mechanical problems by considering several preconditioning schemes including multilevel methods and those based on sparse approximate inversion and incomplete matrix factorization. We provide an analysis of computational costs and memory requirements for model thermo‐mechanical problems, indicating that certain incomplete factorization schemes can achieve good performance. We also provide empirical evaluations that corroborate our analysis and indicate the relative effectiveness of different solution schemes. Our results indicate that our drop‐threshold incomplete Cholesky preconditioning is more robust, efficient and flexible than other popular preconditioning schemes. In addition, we propose preconditioner reuse to amortize preconditioner construction cost over a sequence of linear systems that arise from non‐linear solutions in a plastic regime. Copyright © 2007 John Wiley & Sons, Ltd.