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.     

Analytical and numerical investigation of the stiffness matrix for edge‐cracked circular shafts

This paper examines two engineering methods of evaluating the stress intensity factors for cracked beams and bars subjected to a combined loading and proposes innovative formulations, as far as the circular cross section is concerned. Based on the definition of the stress intensity factors, the compliance matrix is determined as the inverse of the stiffness matrix, modelling the cracked section of a beam through a line‐spring approximation with interactive forces computed within fracture mechanics. A comparative evaluation of numerical predictions based on the proposed methods is also performed with methods available from the literature. Results for free vibration analyses of beams with transverse non‐propagating open cracks are presented and compared in order to estimate the accuracy and efficiency of the proposed methods, where a good agreement is generally found. More specifically, two different coupling effects are herein analysed for circular beams subjected to a combined bending, axial and shear loading, first, and a combined bending, shear and torsion loading, subsequently.     

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.     

Computational electro‐elasticity and magneto‐elasticity for quasi‐incompressible media immersed in free space

In this work, a mixed variational formulation to simulate quasi‐incompressible electro‐active or magneto‐active polymers immersed in the surrounding free space is presented. A novel domain decomposition is used to disconnect the primary coupled problem and the arbitrary free‐space mesh update problem. Exploiting this decomposition, we describe a block‐iterative approach to solving the linearised multiphysics problem, and a physically and geometrically based, three‐parameter method to update the free space mesh. Several application‐driven example problems are implemented to demonstrate the robustness of the mixed formulation for both electro‐elastic and magneto‐elastic problems involving both finite deformations and quasi‐incompressible media. Copyright © 2016 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.     

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.     

A refined diffuse cohesive approach for the failure analysis in quasibrittle materials—part II: Application to plain and reinforced concrete structures

This work presents the numerical application of the diffuse cohesive interface model introduced in the Part I paper to the failure analysis of plain and reinforced concrete structures, subjected to complex loading conditions, inducing mixed‐mode fracture initiation and propagation. With the aim of capturing the interaction between concrete and steel reinforcements, the adopted fracture model is incorporated in a novel, more general numerical framework for the nonlinear analysis of reinforced concrete structures. Such a framework includes a newly proposed embedded truss model for the reinforcing bars, allowing them to be crossed by the neighboring propagating cracks. Comparisons with available experimental results are provided, assessing the reliability and the numerical accuracy of the proposed concrete model, with reference to plain specimens subjected to single‐crack propagation as well as to reinforced elements subjected to multiple cracking.     

拉压异性纤维增强树脂基复合材料弹塑性问题的有限元分析

为了对复杂的非线性问题进行便捷求解,首先提出了考虑拉压异性的纤维增强树脂基复合材料统一非线性本构模型;然后,在此基础上进一步导出了本构模型的三维表现形式,以适用于非线性有限元分析工具的开发;随后,利用有限元软件ABAQUS提供的用户自定义子程序UMAT,自编了在二维和三维情况下的弹塑性应力分析程序;最后,应用程序对复合材料单向板和复合材料斜交板在偏轴拉伸/压缩下应力-应变曲线的预测与测试结果进行了比较,探讨了复合材料悬臂梁的弹塑性问题,并分析和比较了有无考虑拉压异性情况下应力分布和挠度响应的差异。结果表明:运用所提出的本构模型对考虑拉压不对称问题的弹塑性变形分析十分有效,这一本构模型有望成为实用数值分析工具,进而指导工程实践。     

Insight into the tension stiffening behavior of reinforced concrete tension members revealed by finite element modeling

Abstract

The disasters happened in recent past pointed out the need of design criteria, ensuring adequate safety levels against progressive collapse. The attention was focused on the behavior of composite beam-to-column joint components in the field of large displacements. This article presents the experimental and numerical study enabling the simulation of the RC elements under tension. This has helped in understanding the non-negligible contribution of concrete in tension stiffening response up to failure especially in the case of discontinuous geometry marked in composite structures. The finite element model proposed may be considered a mid-way between smeared and discrete crack modeling approaches.     

Non‐proportional size scaling of strength of concrete in uniaxial and biaxial loading conditions

A procedure for non‐proportional size scaling of the strength of concrete based on the weakest‐link statistics is proposed to synchronize strength data from specimens of different geometries and different loading modes. The procedure relies on proportional size scaling of strength to determine the parameters of the statistical model and often on finite element analysis to calculate the coefficient of the equivalent strength. The approach for non‐proportional size scaling is capable to synchronize the uniaxial strength data of concrete from uniaxial tensile specimens and 3‐point bending specimens, or the biaxial tensile strength data of circular plates in different loading mode. The non‐transference of the uniaxial strength data to the biaxial strength data is unclear in its mechanism but possibly due to the variation of statistical distribution of microcracks with stress states in different specimens.