A plasticity model and algorithm for mode-I cracking in concrete

A class of plasticity models which utilize Rankine's (principal stress) yield locus is formulated to simulate cracking in concrete and rock under monotonic loading conditions. The formulation encompasses isotropic and kinematic hardening/softening rules, and incremental (flow theory) as well as total (deformation theory) formats are considered. An Euler backward algorithm is used to integrate the stresses and internal variables over a finite loading step and an explicit expression is derived for a consistently linearized tangent stiffness matrix associated with the Euler backward scheme. Particular attention is paid to the corner regime, that is when the two major principal stresses become equal. A detailed comparison has been made of the proposed plasticity-based crack formulations and the traditional fixed and rotating smeared-crack models for a homogeneously stressed sample under a non-proportional loading path. A comparison between the flow-theory-based plasticity crack models and experimental data has been made for a Single Edge Notched plain concrete specimen under mixed-mode loading conditions.     

Stress‐based finite element analysis of plane plasticity problems

A stress‐based model of the finite element method is evolved for two‐dimensional quasi‐static plasticity problems. The self‐equilibrating fields of stresses are constructed by means of the Airy stress function, which is approximated by three types of elements: the Bogner–Fox–Schmit rectangle, the Hsieh–Clough–Tocher triangle and its reduced variant. Traction boundary conditions are imposed by the use of the Lagrange multiplier method which gives the possibility of calculation of displacements for boundary points. The concept of multi‐point‐constraints elements is applied in order to facilitate the application of this technique. The iterative algorithm, analogous to the closest‐point‐projection method commonly used in the displacement‐based finite element model, is proposed for solving non‐linear equations for each load increment. Two numerical examples with stress‐ and displacement‐controlled load are considered. The results are compared with those obtained by the displacement model of FEM. Bounds for limit loads are obtained. Copyright © 1999 John Wiley & Sons, Ltd.     

钢筋混凝土微平面本构模型及其算法研究

阐述文献[1]的第二部分。第一部分在Ba ant Z.P.等人提出的混凝土微平面模型的基础上引入钢筋的影响提出了一个适用于配筋混凝土的微平面动态本构模型。混凝土模型采用能够反映各种复杂受力行为并被试验充分验证的微平面模型,钢筋采用Cowper-Symonds型率相关的双线性模型。该模型可用于钢筋混凝土的静力和动力显式分析。这一部分将给出模型的显式算法和试验验证。     

A plane stress softening plasticity model for orthotropic materials

A plane stress model has been developed for quasi-brittle orthotropic materials. The theory of plasticity, which is adopted to describe the inelastic behaviour, utilizes modern algorithmic concepts, including an implicit Euler backward return mapping scheme, a local Newton–Raphson method and a consistent tangential stiffness matrix. The model is capable of predicting independent responses along the material axes. It features a tensile fracture energy and a compressive fracture energy, which are different for each material axis. A comparison between calculated and experimental results in masonry shear walls shows that a successful implementation has been achieved. © 1997 John Wiley & Sons, Ltd.     

A finite element for the analysis of reinforced concrete structures

Formulation of a four-node isoparametric element suitable for modelling cracks in reinforced concrete structures is presented. The standard isoparametric element is known to give spurious shear stresses. The conventional remedy of selective integration breaks down in a ‘cracked’ element. It is shown that the proposed formulation gives superior results as compared to both the standard isoparametric element and the conventional selectively integrated element.     

An adaptive domain decomposition coupled finite element–boundary element method for solving problems in elasto‐plasticity

The purpose of this paper is to present an adaptive finite element–boundary element method (FEM–BEM) coupling method that is valid for both two‐ and three‐dimensional elasto‐plastic analyses. The method takes care of the evolution of the elastic and plastic regions. It eliminates the cumbersome of a trial and error process in the identification of the FEM and BEM sub‐domains in the standard FEM–BEM coupling approaches. The method estimates the FEM and BEM sub‐domains and automatically generates/adapts the FEM and BEM meshes/sub‐domains, according to the state of computation. The results for two‐ and three‐dimensional applications in elasto‐plasticity show the practicality and the efficiency of the adaptive FEM–BEM coupling method. Copyright © 2009 John Wiley & Sons, Ltd.     

Nonlinear finite element analysis of reinforced concrete beams strengthened by fiber-reinforced plastics

Numerical analyses are performed using the ABAQUS finite element program to predict the ultimate loading capacity of rectangular reinforced concrete beams strengthened by fiber-reinforced plastics applied at the bottom or on both sides of these beams. Nonlinear material behavior, as it relates to steel reinforcing bars, plain concrete, and fiber-reinforced plastics is simulated using appropriate constitutive models. The influences of fiber orientation, beam length and reinforcement ratios on the ultimate strength of the beams are investigated. It has been shown that the use of fiber-reinforced plastics can significantly increase the stiffnesses as well as the ultimate strengths of reinforced concrete beams. In addition, with the same fiber-reinforced plastics layer numbers, the ultimate strengths of beams strengthened by fiber-reinforced plastics at the bottom of the beams are much higher than those strengthened by fiber-reinforced plastics on both sides of the beams.     

Durability model for AR-glass fibres in textile reinforced concrete

Textile reinforced concrete (TRC) is an innovative material for thin-walled, structural elements with a high load-bearing capacity. For a safe design of TRC load bearing structures comprehensive investigations were carried out to predict the time-dependent loss in strength of the AR-glass reinforcement embedded in fine grained concrete as a consequence of weathering. The present work describes two different approaches to calculate the amount of strength loss of the reinforcement as a function of material, humidity and temperature. Both models, however, do not take into account outdoor weathering of TRC components which leads to a strength loss that is too high to be realistic. One of these approaches is combined with the component temperature and humidity constantly measured during outdoor weathering to derive a basis for a durability model which can take into account arbitrarily complex weathering. Consequently, this work presents the basis for a quantitative prognosis of the loss in strength of AR-glass reinforcement in TRC adapted to the respective material and weathering conditions.     

A computational model for failure analysis of fibre reinforced concrete with discrete treatment of fibres

Failure patterns and mechanical behaviour of high-performance fibre reinforced cementitious composites depend on the distribution of fibres within a specimen. In this contribution, we propose a novel computational approach to describe failure processes in fibre reinforced concrete. A discrete treatment of fibres enables us to study the influence of various fibre distributions on the mechanical properties of the material. To ensure numerical efficiency, fibres are not explicitly discretized but they are modelled by applying discrete forces to a background mesh. The background mesh represents the matrix while the discrete forces represent the interaction between fibres and matrix. These forces are assumed to be equal to fibre pull-out forces. With this approach experimental data or micro mechanical models, including detailed information about the fibre-matrix interface, can be directly incorporated into the model.     

Constitutive model for fibre reinforced concrete based on the Barcelona test

Several constitutive models for fibre reinforced concrete (FRC) have been reported in the past years based on the flexural performance obtained in a bending test. The Barcelona test was presented as an alternative to characterise the tensile properties of FRC; however, no constitutive model was derived from it. In this article, a formulation to predict the tensile behaviour of FRC is developed based on the results of the Barcelona test. The constitutive model proposed is validated by simulating the results of an experimental program involving different types of fibres and fibre contents by means of finite element software. Moreover, the simplified formulation proposed is compared with constitutive models from European codes and guidelines.     

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.     

Explicit finite element modeling of static crack propagation in reinforced concrete

We propose a methodology to model complex fracture processes in reinforced concrete beams subjected to static loading. The discrete cohesive approach, accompanied by an insertion algorithm, is adopted and a modified dynamic relaxation method is chosen as an alternative solver. The concrete matrix and steel re-bars are modeled explicitly; the connection in between is represented by means of interface elements. Such elements allow for slip of re-bars and transmit forces to the matrix that may generate secondary cracking around the reinforcement. The methodology is validated against three-point bending tests on lightly reinforced concrete (LRC) beams.     

Two‐scale finite element modelling of reinforced concrete structures: Effective response and subscale fracture development

A two‐scale model is derived from a fully resolved model where the response of concrete, steel reinforcement, and bond between them are considered. The pertinent “effective” large‐scale problem is derived from selective homogenisation in terms of the equilibrium of reinforced concrete considered as a single‐phase solid. Variational formulations of the representative volume element problem are established in terms of the subscale displacement fields for the plain concrete continuum and the reinforcement bars. Dirichlet and Neumann boundary conditions (BCs) are imposed on the concrete (pertaining to uniform boundary displacement and constant boundary traction, respectively) and on the reinforcement bars (pertaining to prescribed boundary displacement and vanishing sectional forces, respectively). Different representative volume element sizes and combinations of BCs were used in FE² analyses of a deep beam subjected to four‐point bending. Results were compared with those of full resolution (single‐scale). The most reliable response was obtained for the case of Dirichlet‐Dirichlet BCs, with a good match between the models in terms of the deformed shape, force‐deflection relation, and average strain. Even though the maximum crack widths were underestimated, the Dirichlet‐Dirichlet combination provided an approximate upper bound on the structural stiffness.     

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.     

Conceptual design of reinforced concrete structures using topology optimization with elastoplastic material modeling

Design of reinforced concrete structures is governed by the nonlinear behavior of concrete and by its different strengths in tension and compression. The purpose of this article is to present a computational procedure for optimal conceptual design of reinforced concrete structures on the basis of topology optimization with elastoplastic material modeling. Concrete and steel are both considered as elastoplastic materials, including the appropriate yield criteria and post‐yielding response. The same approach can be applied also for topology optimization of other material compositions where nonlinear response must be considered. Optimized distribution of materials is achieved by introducing interpolation rules for both elastic and plastic material properties. Several numerical examples illustrate the capability and potential of the proposed procedure. Copyright © 2012 John Wiley & Sons, Ltd.     

自适应降噪麦克风壳体声学有限元分析与设计

基于DSP技术的自适应主动降噪麦克风是近年来适应超高噪声下通讯应用而发展起来的麦克风技术。该技术依靠两个独立的无指向型传声元件实现降噪。这两个传声元件通常背靠背地封装在一起。根据自适应滤波理论,系统的降噪性能与这两个元件间对应背景噪声的空间相干函数及对应近场语音的传递函数有关。这两个函数又与麦克风封装壳体的几何设计直接相关。为优化降噪性能,建立了一个以有限元声学仿真为基础的,考虑声场特性及麦克风壳体几何形状的主动降噪性能的模型。依据此模型,提出了新型附加反射板的壳体设计方案。仿真和实验结果显示,相对传统壳体设计,有限元优化后的新方案可以提高麦克风降噪性能大于15dB,提高输出信噪比大于10dB。     

Simulating small crack growth behaviour using crystal plasticity theory and finite element analysis

Predictions of small crack growth under cyclic loading in aluminium alloy 7075 are performed using finite element analysis (FEA), and results are compared with published experimental data. A double‐slip crystal plasticity model is implemented within the analyses to enable the anisotropic nature of individual grains to be approximated. Small edge‐cracks in a single grain with a starting length of 6 μm are incrementally grown following a node‐release scheme. Crack‐tip opening displacements (CTOD) and crack opening stresses are calculated during the simulated crack growth, and da/dN against ΔK diagrams are computed. Interactions between the crack tip and a grain boundary are also considered. The computations are shown to accurately capture the magnitude and the variability normally observed in small crack fatigue data.     

一种采用自适应遗传算法的模糊自整定控制器

针对模糊自整定控制器参数寻优能力差的不足,研究了采用自适应交叉概率与变异概率的遗传算法,提出了用这种自适应遗传算法改善模糊自整定控制器性能的方法。对采用自适应遗传算法的模糊自整定控制器与一般的模糊自适应控制器作了仿真对比研究,说明了前者的优越性。