Strain energy release rate for interfacial cracks in hybrid beams

The finite element modeling and fracture mechanics concept were used to study the interfacial fracture of a FRP-concrete hybrid structure. The strain energy release rate of the interfacial crack was calculated by the virtual crack extension method. It is shown that the crack growth has three phases, namely, cracking initiation, stable crack growth and unstable crack propagation. The effects of geometric and physical parameters of the hybrid beam on the energy release rate were considered. These parameters include Young’s moduli of the FRP, the concrete and the adhesive, thickness of the FRP plate and adhesive, and the distance of FRP plate end from the beam end. The numerical results show that the energy release rate of the interfacial crack is influenced considerably by these parameters. The present investigation can contribute to the mechanism understanding and engineering design of the hybrid structures.     

Cohesive fracture simulation and failure modes of FRP–concrete bonded interfaces

A work-of-fracture method using three-point bend beam (3PBB) specimen, commonly employed to determine the fracture energy of concrete, is adapted to evaluate the mode-I cohesive fracture of fiber reinforced plastic (FRP) composite–concrete adhesively bonded interfaces. In this study, a bilinear damage cohesive zone model (CZM) is used to simulate cohesive fracture of FRP–concrete bonded interfaces. The interface cohesive process damage model is proposed to simulate the adhesive–concrete interface debonding; while a tensile plastic damage model is used to account for the cohesive cracking of concrete near the bond line. The influences of the important interface parameters, such as the interface cohesive strength, concrete tensile strength, critical interface energy, and concrete fracture energy, on the interface failure modes and load-carrying capacity are discussed in detail through a numerical finite element parametric study. The results of numerical simulations indicate that there is a transition of the failure modes controlling the interface fracture process. Three failure modes in the mode-I fracture of FRP–concrete interface bond are identified: (1) complete adhesive–concrete interface debonding (a weak bond), (2) complete concrete cohesive cracking near the bond line (a strong bond), and (3) a combined failure of interface debonding and concrete cohesive cracking. With the change of interface parameters, the transition of failure modes from interface debonding to concrete cohesive cracking is captured, and such a transition cannot be revealed by using a conventional fracture mechanics-based approach, in which only an energy criterion for fracture is employed. The proposed cohesive damage models for the interface and concrete combined with the numerical finite element simulation can be used to analyze the interface fracture process, predict the load-carrying capacity and ductility, and optimize the interface design, and they can further shed new light on the interface failure modes and transition mechanism which emulate the practical application.     

钢筋混凝土开孔深梁有限元分析与设计研究Finite element analysis of RC deep beams with openings and researching of the design method

钢筋混凝土深梁受力不同于浅梁,梁腹开孔后受力更趋复杂。现有的设计方法对深梁行为的解释不够完备,设计结果的适用性难以判断,设计规范也没有给出开孔深梁的设计条文。为研究深梁设计方法的有效性,本文采用了非线性有限元分析方法,引入适合混凝土结构非线性分析的断裂塑性模型,并考虑钢筋粘结滑移效应,对一系列开双孔或偏孔钢筋混凝土深梁试验进行仿真分析,所得结果与试验结果吻合良好,能够准确预测深梁在裂缝、破坏形态及承载力等方面的受力特征。研究表明现有的深梁设计方法中,压拉杆模型方法相较内力法和应力图形法更加经济有效。在仿真分析的基础上,提出了一种对开孔深梁具有普遍适用性的非线性设计方法,其设计结果具有高承载力、较好延性、经济的配筋量和充分的材料利用率的优点。     

钢板-混凝土组合加固钢筋混凝土梁的非线性有限元分析

以10根采用钢板-混凝土组合加固技术加固的钢筋混凝土梁的试验为基础,建立了钢板-混凝土组合加固钢筋混凝土梁的非线性有限元模型.沿用了钢板-混凝土组合梁有限元分析中栓钉的荷载-滑移曲线及断裂模型,提出了新老混凝土界面的剪切-滑移模型,可以较好地模拟界面受力性能.采用有限元软件ABAQUS,模拟了一次加固、不同损伤加固及持载加固等加载情况下加固构件受力全过程和受弯破坏以及新老混凝土剥离破坏等破坏形态下加固试件的受力性能.在验证了有限元模型的准确性后,分析了钢板厚度、加固部分高度及长度等参数对加固构件承载能力及刚度的影响.最后提出了几点对钢板-混凝土组合加固RC梁的设计建议.     

Green’s functions for bending problem of a thin anisotropic plate with an elliptic hole

The Green’s functions have not been studied in open literatures for the bending problem of an anisotropic plate with an elliptic hole subjected to a normal concentrated force and a concentrated moment. In this paper, the problem is investigated and the Green’s functions are first obtained by using the complex potential approach. The techniques of conformal mapping transformation and analytic continuation are used to derive the closed-form complex stress functions. The Green’s functions obtained have some potential applications in the analysis of composite structures such as the modification of the displacement compatibility model for notched stiffened composite panels and the formulation of a new method for interlaminar stress analysis around holes of laminates.     

Existence of the detonation cellular structure in two-phase hybrid mixtures

The cellular detonation structure has been recorded for hybrid hydrogen/air/aluminium mixtures on 1.0 m 0.110 m soot plates. Addition of aluminium particles to the gaseous mixture changes its detonation velocity. For very fine particles and flakes, the detonation velocity is augmented and, in the same time, the cell width diminishes as compared with the characteristic cell size of the mixture without particles. On the contrary, for large particles, the detonation velocity decreases and the cell size becomes larger than . It appears that the correlation law between the cell size and the detonation velocity in the hybrid mixture is similar to the correlation between the cell size and the rate of detonation overdrive displayed for homogeneous gaseous mixtures. Moreover, this correlation law remains valid in hybrid mixtures for detonation velocities smaller than the value D of the mixture without particles. Received 10 May 2001 / Accepted 12 August 2002 Published online 19 December 2002 Correspondence to: B. Veyssiere (e-mail: veyssiere@lcd.ensma.fr)     

Outflow boundary conditions for one-dimensional finite element modeling of blood flow and pressure waves in arteries

Flow and pressure waves, originating due to the contraction of the heart, propagate along the deformable vessels and reflect due to tapering, branching, and other discontinuities. The size and complexity of the cardiovascular system necessitate a “multiscale” approach, with “upstream” regions of interest (large arteries) coupled to reduced-order models of “downstream” vessels. Previous efforts to couple upstream and downstream domains have included specifying resistance and impedance outflow boundary conditions for the nonlinear one-dimensional wave propagation equations and iterative coupling between three-dimensional and one-dimensional numerical methods. We have developed a new approach to solve the one-dimensional nonlinear equations of blood flow in elastic vessels utilizing a space-time finite element method with GLS-stabilization for the upstream domain, and a boundary term to couple to the downstream domain. The outflow boundary conditions are derived following an approach analogous to the Dirichlet-to-Neumann (DtN) method. In the downstream domain, we solve simplified zero/one-dimensional equations to derive relationships between pressure and flow accommodating periodic and transient phenomena with a consistent formulation for different boundary condition types. In this paper, we also present a new boundary condition that accommodates transient phenomena based on a Green’s function solution of the linear, damped wave equation in the downstream domain.     

Structural–acoustic sensitivity analysis of radiated sound power using a finite element/ discontinuous fast multipole boundary element scheme

The complete interaction between the structural domain and the acoustic domain needs to be considered in many engineering problems, especially for the acoustic analysis concerning thin structures immersed in water. This study employs the finite element method to model the structural parts and the fast multipole boundary element method to model the exterior acoustic domain. Discontinuous higher‐order boundary elements are developed for the acoustic domain to achieve higher accuracy in the coupling analysis. Structural–acoustic design sensitivity analysis can provide insights into the effects of design variables on radiated acoustic performance and thus is important to the structural–acoustic design and optimization processes. This study is the first to formulate equations for sound power sensitivity on structural surfaces based on an adjoint operator approach and equations for sound power sensitivity on arbitrary closed surfaces around the radiator based on the direct differentiation approach. The design variables include fluid density, structural density, Poisson's ratio, Young's modulus, and structural shape/size. A numerical example is presented to demonstrate the accuracy and validity of the proposed algorithm. Different types of coupled continuous and discontinuous boundary elements with finite elements are used for the numerical solution, and the performances of the different types of finite element/continuous and discontinuous boundary element coupling are presented and compared in detail. Copyright © 2016 John Wiley & Sons, Ltd.     

Elastic–plastic-hydrodynamic analysis of crater blasting in steel fiber reinforced concrete

This paper presents a numerical analysis of crater blasting in steel fiber reinforced concrete (SFRC). In order to model the nonlinear damage-softening behavior of SFRC, the effective stress and effective plastic strain curve is tabulated and used as input for the material Type10 (MAT_ELASTIC_PLASTIC_HYDRO) available in LS-DYNA. The Gruneisen equation of state (EOS) is used to model the pressure volume relationship. With the two erosion criteria namely tensile cut-off and failure strain incorporated, the crater blasting in SFRC is simulated. Numerical results show that the adopted model and high-pressure EOS can well capture the main characteristics and failure process of SFRC under blast loading, and the related parameters can be determined conveniently. In addition, the volume fraction of fibers exerts a significant influence on the dimension of blast-induced crater.     

Hysteresis loops predicted by isoenergy density theory for polycrystals. Part I: fundamentals of non-equilibrium thermal–mechanical coupling effects

When a polycrystal is stressed or strained at fifty percent of the corresponding yield value, damage will be inflicted non-homogeneously in the material due to the fact that the stress and/or strain distribution is non-uniform even if isotropy and homogeneity are assumed for the initial microstructure. This effect will be cumulated for each cycle of the load if the applied stress or strain is repeated continuously. Nucleation of microcracks can eventually lead to the propagation of a macrocrack.The process of damage accumulation in fatigue is defined to be sufficiently slow such that inhomogeneity of material behavior created by loading is a significant factor that can not be arbitrarily dismissed without a good reason. What this means specifically is that the difference of the stress and strain behavior at each point in a fatigue specimen must be accounted for in the analytical model in order to predict the correct cumulative effect. Such a requirement translates into a non-equilibrium formulation where the constitutive relations for each point and loading cycle must be determined separately. In this sense, the true problem of fatigue cannot be completely treated by the classical continuum mechanics approach that is limited to equilibrium mechanics for a closed system. Having said this, the isoenergy density theory will be applied to estimate the hysteresis loops of a hour-glass profile cylindrical bar specimen as recommended by the American Society for Testing and Materials (ASTM) for low-cycle fatigue.The work will be divided into two parts. Part I will cover the fundamentals of a non-equilibrium theory where the continuum elements are finite in size; they do not vanish in the limit. Therefore, size effects are immediately encountered as a function of time. General expressions for the rate change of volume of these elements with surface area are derived such that they can be computed from the nine displacement gradients. These elements can differ in size and must fit together without discontinuities or gaps to form the continuum. The condition of isoenergy energy density is invoked such that the size of these individual elements under large and finite deformation and rotation can be determined without loss in generality. The existence of such a space having the property of the same isoenergy density in all directions is thus proved. This enables the establishment of the one dimensional energy state with that in three dimensions without restriction, the absence of which has prevented the development of a complete non-linear theory of mechanics that can be solved in a direct fashion in contrast to the inverse method of assuming the displacement field. Illustration is provided for deriving the constitutive relation incrementally for a given location for the hour-glass specimen made of 6061-T6 aluminum. Once the specimen is loaded, each material point will follow a different stress and strain curve according to the local displacement rate. Hence, the method applies to material with non-homogeneous microstructure if their individual expressions can be assessed and fed into the computer.Part II computes for the non-equilibrium temperature and an entropy-like quantity that can be positive and negative. This implies that the system can absorb or dissipate energy with reference to the surrounding. Additional data for hysteresis loops are given for 6061-T6 aluminum, SAE 4340 steel and Ti–8Al–1Mo–1V titanium. Accumulation of the local hysteresis energy per cycle is found to be the highest near the surface of the uniaxial specimen where load symmetry prevails. This is a consequence of the difference in accumulation of the energy density due to distortion in contrast to dilatation at the specimen center. This is why fatigue cracks tend to nucleate near the specimen surface, at a small distance towards the interior. Another distinct feature of fatigue is that the non-equilibrium temperature is found to oscillate about the ambient temperature while the local stress states fluctuate between tension and compression. This temperature reversal behavior is typical of non-equilibrium behavior and also occurs under monotonic loading. The space and time variations of the dissipated energy density for different materials are found to be related to the initial monotonic energy density or area under the true stress and true strain curve.What will be demonstrated is that no special consideration need to be made when applying the isoenergy density theory for analyzing the nucleation of micro and macrocracks in addition to failure of the specimen. Crack nucleation under fatigue is assumed to occur when the total hysteresis energy reaches a critical value. It is possible to establish a relation between the average hysteresis energy per cycle and the number of cycles to failure. The proposed method requires only a knowledge of the initial monotonic energy density curve for a given material. Predicted results for the fatigue of cylindrical bar specimens with hour-glass profile are given and they can be found in Part II of this work.     

Finite element analysis of filling stage in die‐casting process using marker surface method and adaptive grid refinement technique

The marker surface method and the adaptive grid refinement technique have been applied to the three‐dimensional (3‐D) finite element analysis of the filling stage in the die‐casting process. Especially, the marker surface plugging technique and the marker surface regeneration technique incorporated in the marker surface method have been proposed for the efficient analysis of 3‐D practical problems. Through the marker surface plugging technique, new parts of marker surface are effective lycreated in order to eliminate the gaps between the parts of marker surface or between the edge of marker surface and cavity wall. By using the marker surface regeneration technique, the marker surface including a great number of marker elements is recreated on the basis of its original shape in order to decrease the number of marker elements and computational time. A3‐D example used as the benchmark test and a typical industrial problem of the die‐casting process have been analysed. The numerical results have been in good agreement with the experimental results and the efficiency of the adaptive grid refinement technique has been verified. It has been shown that the proposed techniques incorporated in the marker surface method and the adaptive grid refinement technique can be effectively applied to general industrial problems. Copyright © 2004 John Wiley & Sons, Ltd.     

An implementation of the Spalart–Allmaras DES model in an implicit unstructured hybrid finite volume/element solver for incompressible turbulent flow

In this paper, we describe an implicit hybrid finite volume (FV)/element (FE) incompressible Navier–Stokes solver for turbulent flows based on the Spalart–Allmaras detached eddy simulation (SA‐DES). The hybrid FV/FE solver is based on the segregated pressure correction or projection method. The intermediate velocity field is first obtained by solving the original momentum equations with the matrix‐free implicit cell‐centered FV method. The pressure Poisson equation is solved by the node‐based Galerkin FE method for an auxiliary variable. The auxiliary variable is closely related to the real pressure and is used to update the velocity field and the pressure field. We store the velocity components at cell centers and the auxiliary variable at vertices, making the current solver a staggered‐mesh scheme. The SA‐DES turbulence equation is solved after the velocity and the pressure fields have been updated at the end of each time step. The same matrix‐free FV method as the one used for momentum equations is used to solve the turbulence equation. The turbulence equation provides the eddy viscosity, which is added to the molecular viscosity when solving the momentum equation. In our implementation, we focus on the accuracy, efficiency and robustness of the SA‐DES model in a hybrid flow solver. This paper will address important implementation issues for high‐Reynolds number flows where highly stretched elements are typically used. In addition, some aspects of implementing the SA‐DES model will be described to ensure the robustness of the turbulence model. Several numerical examples including a turbulent flow past a flat plate and a high‐Reynolds number flow around a high angle‐of‐attack NACA0015 airfoil will be presented to demonstrate the accuracy and efficiency of our current implementation. Copyright © 2008 John Wiley & Sons, Ltd.     

Euler–Lagrange/DEM simulation of wood gasification in a bubbling fluidized bed reactor

We present an Euler–Lagrange method for the simulation of wood gasification in a bubbling fluidized bed. The gas phase is modeled as a continuum using the 2D Navier–Stokes equations and the solid phase is modeled by a Discrete Element Method (DEM) using a soft-sphere approach for the particle collision dynamic. Turbulence is included via a Large-Eddy approach using the Smagorinsky sub-grid model. The model takes into account detailed gas phase chemistry, zero-dimensional modeling of the pyrolysis and gasification of each individual particle, particle shrinkage, and heat and mass transfer between the gas phase and the particulate phase. We investigate the influence of wood feeding rate and compare exhaust gas compositions and temperature results obtained with the model against experimental data of a laboratory scale bubbling fluidized bed reactor.     

A two-dimensional effective model describing fluid–structure interaction in blood flow: analysis, simulation and experimental validation

We derive a closed system of effective equations describing a time-dependent flow of a viscous incompressible Newtonian fluid through a long and narrow elastic tube. The 3D axially symmetric incompressible Navier–Stokes equations are used to model the flow. Two models are used to describe the tube wall: the linear membrane shell model and the linearly elastic membrane and the curved, linearly elastic Koiter shell model. We study the behavior of the coupled fluid–structure interaction problem in the limit when the ratio between the radius and the length of the tube, , tends to zero. We obtain the reduced equations that are of Biot type with memory. An interesting feature of the reduced equations is that the memory term explicitly captures the viscoelastic nature of the coupled problem. Our model provides significant improvement over the standard 1D approximations of the fluid–structure interaction problem, all of which assume an ad hoc closure assumption for the velocity profile. We performed experimental validation of the reduced model using a mock circulatory flow loop assembled at the Cardiovascular Research Laboratory at the Texas Heart Institute. Experimental results show excellent agreement with the numerically calculated solution. Major applications include blood flow through large human arteries. To cite this article: S. Čanić et al., C. R. Mecanique 333 (2005).