Two-dimensional modeling of material failure in reinforced concrete by means of a continuum strong discontinuity approach

The paper presents a new methodology to model material failure, in two-dimensional reinforced concrete members, using the Continuum Strong Discontinuity Approach (CSDA). The mixture theory is used as the methodological approach to model reinforced concrete as a composite material, constituted by a plain concrete matrix reinforced with two embedded orthogonal long fiber bundles (rebars). Matrix failure is modeled on the basis of a continuum damage model, equipped with strain softening, whereas the rebars effects are modeled by means of phenomenological constitutive models devised to reproduce the axial non-linear behavior, as well as the bond-slip and dowel effects. The proposed methodology extends the fundamental ingredients of the standard Strong Discontinuity Approach, and the embedded discontinuity finite element formulations, in homogeneous materials, to matrix/fiber composite materials, as reinforced concrete. The specific aspects of the material failure modeling for those composites are also addressed. A number of available experimental tests are reproduced in order to illustrate the feasibility of the proposed methodology.     

An approach for modelling concrete spalling in finite strains

A new approach for modelling concrete spalling process is here proposed, taking into account a fully nonlinear-displacement/strain theory able to catch complex interactions between pressure, thermal and mechanical fields. The micro-structural modelling of concrete under fire conditions is derived from a mechanical and thermodynamic consistent theory and it is strictly related to a self-consistent, carefully extracted set of experimental data, in order to make a correct validation and calibration of the numerical F.E. procedures and codes. Even if appearing as a first but successful example, it is shown that a procedure accounting for coupled material and geometric nonlinearities is able to attain valuable and realistic numerical results concerning spalling process in concrete.     

A separation of scales homogenization analysis for the modelling of calcium leaching in concrete

Calcium leaching in concrete is highly influenced by the presence of aggregates. We present in this work a modelling framework of calcium leaching which accounts for this fact. Starting from the microscopic point of view, the method consists of the derivation of the macroscopic equation governing the average concentration field in the equivalent medium as well as the determination of the macroscopic transport parameters. In fact, the homogenization method used in this work is based on a separation of scales approach and allows to estimate the diffusion and the tortuosity tensors to be introduced in the macroscopic formulation of the mass conservation of calcium in the liquid phase. In this first attempt, we show that these estimates depend strongly on the morphological parameters of the microstructure which represent the geometry of the domain occupied by the phase in which the diffusion process takes place. The problem of numerically integrating the equations at hand is addressed within the context of the finite element method. Finally, numerical simulations are compared with our experimental results on cement paste, mortar and concrete.     

An efficient generation method of embedded reinforcement in hexahedral elements for reinforced concrete simulations

In this paper, an automatic procedure for the generation of embedded steel reinforcement inside hexahedral finite elements is presented. The automatic mapping of the entire reinforcement network inside the concrete hexahedral finite elements is performed using the end-point coordinates of the rebar reinforcement macro-elements. By introducing a geometrical constraint, this procedure decreases significantly the computational effort for generating the input data of the embedded rebar elements in three-dimensional finite-element analysis, particularly when dealing with relatively large-scale reinforced concrete models. The computational robustness and efficiency of the proposed mesh generation method are demonstrated through numerical experiments.     

Numerical analysis of the early age behavior of concrete structures with a hydration based microplane model

To simulate the early age behavior of concrete structures composed of young concrete, a finite element analysis (FEA) was implemented with the hydration based microplane model. Structural behaviors were investigated with concrete age for a massive concrete wall and slab. From FEA, it was found that surface cracking at early age occurred via different crack driving mechanisms. In the case of combined hydration heat and shrinkage, later surface cracking was produced by differential drying shrinkage. A numerical analysis performed with the hydration based microplane model successfully simulated the typical cracking patterns due to edge restraint in the concrete slab.     

Mesoscale modeling of concrete: Geometry and numerics

Mesoscale analysis is a promising discipline for concrete mix design and damage prediction. Besides many other aspects, its success crucially depends on accurate modeling of the mesoscale geometry and efficient numerical analysis of high resolution, to both of which this article contributes. Mesoscale models of concrete include aggregates, cement stone and, optionally, interfacial transition zones. The present paper establishes transparent formulas for consistent numerical generation of aggregate sizes. Fast separation checks are applied to place ellipsoidal and in particular arbitrary shaped particles. The multigrid method enables efficient computation of very large heterogeneous mesoscale models. This is exemplified by linear finite element analysis of two-dimensional models. Corresponding results are confirmed by experiments and analytical models from literature. The influence of concrete mix parameters on effective elastic properties is studied.     

Confinement-shear lattice CSL model for fracture propagation in concrete

A previously developed lattice model is improved and then applied to simulations of mixed-mode crack propagation in concrete. The concrete meso-structure is simulated by a three-dimensional lattice system connecting nodes which represent the centers of aggregate particles. These nodes are generated randomly according to the given grain size distribution. Only coarse aggregates are taken into account. Three-dimensional Delaunay triangulation is used to determine the lattice connections. The effective cross-section areas of connecting struts are defined by performing a three-dimensional domain tessellation partly similar to Voronoi tessellation. The deformations of each link connecting two adjacent aggregate pieces are defined in the classical manner of Zubelewicz and Ba?ant in which rigid body kinematics is assumed to characterize the displacement and rotation vectors at the lattice nodes. Each strut connecting adjacent particles can transmit both axial and shear forces. The adopted constitutive law simulates fracture, friction and cohesion at the meso-level. The behavior in tension and shear is made dependent on the transversal confining strain, which is computed assuming a linear displacement field within each tetrahedron of Delaunay triangulation, and neglecting the effect of the particle rotations. A mid-point explicit scheme is used to integrate the governing equations of the problems. General procedures to handle the boundary conditions and to couple the lattice mesh to the usual elastic finite element mesh are also formulated. Numerical simulations of mixed-mode fracture test data are used to demonstrate that the model is capable of accurately predicting complex crack paths and the corresponding load-deflection responses observed in experiments.     

An elastic plastic damage formulation for concrete: Application to elementary tests and comparison with an isotropic damage model

Pure elastic damage models or pure elastic plastic constitutive laws are not totally satisfactory to describe the behaviour of concrete. They indeed fail to reproduce the unloading slopes during cyclic loading which define experimentally the value of the damage in the material. When coupled effects are considered, in particular in hydro-mechanical problems, the capability of numerical models to reproduce the unloading behaviour is essential, because an accurate value of the damage, which controls the material permeability, is needed. In the context of very large size calculations that are needed for 3D massive structures heavily reinforced and pre-stressed (such as containment vessels), constitutive relations ought also to be as simple as possible. Here an elastic plastic damage formulation is proposed to circumvent the disadvantages of pure plastic and pure damage approaches. It is based on an isotropic damage model combined with a hardening yield plastic surface in order to reach a compromise as far as simplicity is concerned. Three elementary tests are first considered for validation. A tension test, a cyclic compression test and triaxial tests illustrate the improvements achieved by the coupled law compared to a simple damage model (plastic strains, change of volumetric behaviour, decrease in the elastic slope under hydrostatic pressures). Finally, one structural application is also considered: a concrete column wrapped in a steel tube.     

钢筋混凝土结构有限元网格剖分的一种方法

本文将选用２分离式模型对钢筋混凝土平面结构进行有限元网格剖分,其中对混凝土结构采用四边形网格的自动剖分方法,对钢筋则采用一维杆单元的生成方法。本文所述方法能保证所产生网格的质量,有利于钢筋混凝土有限元分析。     

Refined sandwich model for the vibration of beams with embedded shear piezoelectric actuators and sensors

This work extends a previously presented refined sandwich beam finite element (FE) model to vibration analysis, including dynamic piezoelectric actuation and sensing. The mechanical model is a refinement of the classical sandwich theory (CST), for which the core is modelled with a third-order shear deformation theory (TSDT). The FE model is developed considering, through the beam length, electrically: constant voltage for piezoelectric layers and quadratic third-order variable of the electric potential in the core, while mechanically: linear axial displacement, quadratic bending rotation of the core and cubic transverse displacement of the sandwich beam. Despite the refinement of mechanical and electric behaviours of the piezoelectric core, the model leads to the same number of degrees of freedom as the previous CST one due to a two-step static condensation of the internal dof (bending rotation and core electric potential third-order variable). The results obtained with the proposed FE model are compared to available numerical, analytical and experimental ones. Results confirm that the TSDT and the induced cubic electric potential yield an extra stiffness to the sandwich beam.     

Comparison of non-orthogonal smeared crack and plasticity models for dynamic analysis of concrete arch dams

A special three-dimensional finite element program is developed to study the seismic response of concrete arch dams. Two types of continuum mechanics non-linear techniques are incorporated in the program, i.e. non-orthogonal smeared crack and elasto-plastic models. The formulation is presented initially and accuracy of the models and their correct implementations are verified by analyzing a notched beam and comparing its results with available experimental data. Following the satisfactory results of the beam analysis, the program is applied to a practical problem, viz. the non-linear behavior of the 130 m high Shahid Rajaee arch dam in Iran, subjected to the Friuli-Tolmezzo earthquake. Two cases of non-orthogonal smeared crack model are implemented for the dam, namely, ordinary and fictitious approaches. Meanwhile, an elastic-perfectly plastic model for mass concrete is also applied. The results are compared with those obtained from a linear elastic analysis under the same excitation. Based on the results, it is concluded that the non-orthogonal smeared crack approach can redistribute the state of stresses and produces a more realistic profile of stresses in the dam. Further, the elasto-plastic model could reduce significantly the high amount of overstressing noticed in the linear analysis. However, the elasto-plastic model is not perceptibly activated in the compressive state of stresses. It is also observed that a drift in the crest displacements is the prominent consequence of cracking or plasticity of the dam.     

Evaluation of cracking potential for concrete arch dam based on simulation feedback analysis

It is still very difficult for researchers and engineers to implement the simulation analysis including a complete process and a full model with the complicated arch dam and the foundation, and to evaluate the cracking potential in the construction and service periods. To take Xiaowan project of China for an example, a practical system of simulation feedback analysis, a specific cracking criterion, and a resolution for the conflicting requirements of temperature and stress/strain simulation are presented, w...     

Nonlinear finite element analysis of concrete structures using new constitutive models

Nonlinear finite element analysis was applied to various types of reinforced concrete structures using a new set of constitutive models established in the fixed-angle softened-truss model (FA-STM). A computer code FEAPRC was developed specifically for application to reinforced concrete structures by modifying the general-purpose program FEAP. FEAPRC can take care of the four important characteristics of cracked reinforced concrete: (1) the softening effect of concrete in compression, (2) the tension-stiffening effect by concrete in tension, (3) the average (or smeared) stress–strain curve of steel bars embedded in concrete, and (4) the new, rational shear modulus of concrete. The predictions made by FEAPRC are in good agreement with the experimental results of beams, panels, and framed shear walls.     

Inelastic dynamic response of reinforced concrete infilled frames

An inelastic finite element model to simulate the behaviour of reinforced concrete frames infilled with masonry panels subjected to static load and earthquake excitation has been presented. Under the loads, the mortar may crack causing sliding and separation at the interface between the frame and the infill. Further, the infill may get cracked and/or crushed which changes its structural behaviour and may render the infill ineffective, leaving the bare frame to take all the load which may lead to the failure of the framing system itself. In this study, a mathematical model to incorporate this behaviour has been presented.     

Finite element methods for the time-dependent Ginzburg-Landau model of superconductivity

The initial-boundary value problem for the time-dependent Ginzburg-Landau equations that model the macroscopic behavior of superconductors is considered. The convergence of finite-dimensional, semidiscrete Galerkin approximations is studied as is a fully-discrete scheme. The results of some computational experiments are presented.     

A three-dimensional model for the study of the cooling system of submersible electric pumps

We study the cooling system for submersible electric pumps. This study aims to provide some guidelines to improve the existing cooling system of these electric pumps when they work partially or totally not immersed in the service fluid. Note that inefficient cooling systems cannot prevent the rise in temperature of the alternating current (AC) motor of the pump, and the consequent reduction of the service factor.     

CDM based finite element code for concrete in 3-D

This paper presents a three dimensional finite element code DAMAG3D for nonlinear analysis of concrete type materials modeled as elastic-damage. The CDM model adopted is the one as proposed by SUARIS W, OUYANG C, FERNANDO V. M. Damage model for cyclic loading of concrete. J Engng Mech, American Society of Civil Engineers 1990; 116(5): 1020-35. for monotonic and cyclic loading of concrete structures. Code DAMAG3D is applied to simulate response of concrete under monotonically increasing load paths of uniaxial compression, Brazilian test, strip loading and patch loading, with reasonable correlation established with experimental results and results from other nonlinear constitutive models.     

Development of a methodology for a simplified finite element model and optimum design

As computer power is increased, refined finite element models are employed for structural analysis and design. However, it is still difficult and expensive to make and use refined finite element models in the design stage. The refined models usually cause problems in the preliminary design where the design is frequently changed. Therefore, the development of a simplified finite element model is desirable for use in the preliminary design stage. This paper describes the methodology for the simplified model and its optimum design. A Goal programming algorithm is used for system identification to make the simplified model. The developed methodology consists of three phases such as simplification, design, and inverse process. The simplified finite element model is used for the design change and the changed design is recovered onto the original design. The presented methodology is verified through a few examples.     

Analysis and approximation of a fractional Laplacian-based closure model for turbulent flows and its connection to Richardson pair dispersion

We study a turbulence closure model in which the fractional Laplacian ${(?\Delta )}^{\alpha }$ of the velocity field represents the turbulence diffusivity. We investigate the energy spectrum of the model by applying Pao’s energy transfer theory. For the case $\alpha =1∕3$, the corresponding power law of the energy spectrum in the inertial range has a correction exponent on the regular Kolmogorov $?5∕3$ scaling exponent. For this case, this model represents Richardson’s particle pair-distance superdiffusion of a fully developed homogeneous turbulent flow as well as Lévy jumps that lead to the superdiffusion. For other values of $\alpha$, the power law of the energy spectrum is consistent with the regular Kolmogorov $?5∕3$ scaling exponent. We also propose and study a modular time-stepping algorithm in semi-discretized form. The algorithm is minimally intrusive to a given legacy code for solving Navier–Stokes equations by decoupling the local part and nonlocal part of the equations for the unknowns. We prove the algorithm is first-order accurate and unconditionally stable. We also derive error estimates for full discretizations of the model which, in addition to the time stepping algorithm, involves a finite element spatial discretization and a domain truncation approximation to the range of the fractional Laplacian.