Crack band model of fracture in irregular lattices

An irregular lattice model is used to simulate mode I fracture in softening materials, such as concrete. Lattice geometry is based on a three-dimensional Voronoi discretization of the material domain. The Voronoi diagram provides scaling rules for the elemental stiffness relations, leading to an elastically uniform representation of the material for simple modes of straining. Fracture is represented using a crack band approach, in which the dimensions of the crack band are also scaled according to the Voronoi diagram. The material is viewed as homogeneous and the energy dissipation mechanisms active at finer scales are lumped into a cohesive crack relation. This energy conserving crack band approach is objective with respect to the irregular geometry of the lattice. Model accuracy and performance are demonstrated through simulated fracture testing of concrete specimens under uniaxial tension and flexural loadings. Basic qualities of the simulation approach, demonstrated here for homogeneous models of concrete, are applicable toward simulating fracture in multi-phase systems where material features are explicitly modeled.     

Topology optimization considering fracture mechanics behaviors at specified locations

As a typical form of material imperfection, cracks generally cannot be avoided and are critical for load bearing capability and integrity of engineering structures. This paper presents a topology optimization method for generating structural layouts that are insensitive/sensitive as required to initial cracks at specified locations. Based on the linear elastic fracture mechanics model (LEFM), the stress intensity of initial cracks in the structure is analyzed by using singularity finite elements positioned at the crack tip to describe the near-tip stress field. In the topology optimization formulation, the J integral, as a criterion for predicting crack opening under certain loading and boundary conditions, is introduced into the objective function to be minimized or maximized. In this context, the adjoint variable sensitivity analysis scheme is derived, which enables the optimization problem to be solved with a gradient-based algorithm. Numerical examples are given to demonstrate effectiveness of the proposed method on generating structures with desired overall stiffness and fracture strength property. This method provides an applicable framework incorporating linear fracture mechanics criteria into topology optimization for conceptual design of crack insensitive or easily detachable structures for particular applications.     

Application of an interface failure model to predict fatigue crack growth in an implanted metallic femoral stem

A novel computational modelling technique has been developed for the prediction of crack growth in load bearing orthopaedic alloys subjected to fatigue loading. Elastic-plastic fracture mechanics has been used to define a three-dimensional fracture model, which explicitly models the opening, sliding and tearing process. This model consists of 3D nonlinear spring elements implemented in conjunction with a brittle material failure function, which is defined by the fracture energy for each nonlinear spring element. Thus, the fracture energy criterion is implicit in the brittle material failure function to search for crack initiation and crack development automatically. A degradation function is employed to reduce interfacial fracture properties corresponding to the number of cycles; thus fatigue lifetime can be predicted. Unlike other failure modelling methods, this model predicts the failure load, crack path and residual stiffness directly without assuming any pre-flaw condition. As an example, fatigue of a cobalt based alloy (CoCrMo) femoral stem is simulated. Experimental fatigue data was obtained from four point bending tests. The finite element model simulated a fully embedded implant with a constant point load. Comparison between the model and mechanical test results showed good agreement in fatigue crack growth rate.     

Application of genetic algorithm in crack detection of beam-like structures using a new cracked Euler–Bernoulli beam element

In this paper, a crack identification approach is presented for detecting crack depth and location in beam-like structures. For this purpose, a new beam element with a single transverse edge crack, in arbitrary position of beam element with any depth, is developed. The crack is not physically modeled within the element, but its effect on the local flexibility of the element is considered by the modification of the element stiffness as a function of crack's depth and position. The development is based on a simplified model, where each crack is substituted by a corresponding linear rotational spring, connecting two adjacent elastic parts. The localized spring may be represented based on linear fracture mechanics theory. The components of the stiffness matrix for the cracked element are derived using the conjugate beam concept and Betti's theorem, and finally represented in closed-form expressions. The proposed beam element is efficiently employed for solving forward problem (i.e., to gain accurate natural frequencies of beam-like structures knowing the cracks’ characteristics). To validate the proposed element, results obtained by new element are compared with two-dimensional (2D) finite element results as well as available experimental measurements. Moreover, by knowing the natural frequencies, an inverse problem is established in which the cracks location and depth are identified. In the inverse approach, an optimization problem based on the new beam element and genetic algorithms (GAs) is solved to search the solution. The proposed approach is verified through various examples on cracked beams with different damage scenarios. It is shown that the present algorithm is able to identify various crack configurations in a cracked beam.     

Reliability analysis of brittle structures under random loadings

A method for the reliability analysis of brittle structures subjected to random loads is proposed. The method is based on the weakest-link hypothesis and Weibull statistics for brittle materials. Initial flaws with a given expected size are assumed to be distributed at random with a certain density per unit volume. Basic concepts in random vibration theory and fracture mechanics are utilized in evaluating stress statistics, crack propagation and strength degradation. A structure fails when the stress intensity at any flaw reaches a critical value for rapid crack propagation. The failure of the structure is modeled as the first exceedance in random vibration theory. The effects of multi-vibration modes on the failure probability of the structure are included in the formulation. The evaluation of stress distribution and the computation of failure probability can be accomplished in a finite element analysis. Numerical examples on the evaluation of lifetime reliabilities of structures are given to demonstrate the feasibility of the proposed method.     

Topology optimization framework for structures subjected to stationary stochastic dynamic loads

The field of topology optimization has progressed substantially in recent years, with applications varying in terms of the type of structures, boundary conditions, loadings, and materials. Nevertheless, topology optimization of stochastically excited structures has received relatively little attention. Most current approaches replace the dynamic loads with either equivalent static or harmonic loads. In this study, a direct approach to problem is pursued, where the excitation is modeled as a stationary zero-mean filtered white noise. The excitation model is combined with the structural model to form an augmented representation, and the stationary covariances of the structural responses of interest are obtained by solving a Lyapunov equation. An objective function of the optimization scheme is then defined in terms of these stationary covariances. A fast large-scale solver of the Lyapunov equation is implemented for sparse matrices, and an efficient adjoint method is proposed to obtain the sensitivities of the objective function. The proposed topology optimization framework is illustrated for four examples: (i) minimization of the displacement of a mass at the free end of a cantilever beam subjected to a stochastic dynamic base excitation, (ii) minimization of tip displacement of a cantilever beam subjected to a stochastic dynamic tip load, (iii) minimization of tip displacement and acceleration of a cantilever beam subjected to a stochastic dynamic tip load, and (iv) minimization of a plate subjected to multiple stochastic dynamic loads. The results presented herein demonstrate the efficacy of the proposed approach for efficient multi-objective topology optimization of stochastically excited structures, as well as multiple input-multiple output systems.

     

Boundary element analysis of cracked homogeneous or bi-material structures under thermo-mechanical cycling

We present a sub-domain boundary element procedure to evaluate the failure capacity of cracked homogeneous and bi-material media under cyclic thermo-mechanical loads. The boundary integral equations of uncoupled, time-dependent thermo-elasticity are employed to account for the time-varying nature of the thermal load. If crack closure due to thermal distortion takes place, then the displacement and traction field may affect the heat flux between the crack faces, and the thermal and mechanical parts of the problem will need to be solved repeatedly until thermo-mechanical convergence is achieved. We present results from cases of pure mode-I fracture in homogeneous materials and for interfacial fracture in bi-materials. Our study discusses the influence of crack closure on quasi-static, sub-critical crack extension. Especially in case of interfacial cracks the type of loading, the thermal resistance between the crack faces, and the coefficient of friction are also taken into account. The results suggest that the above parameters may have a severe impact on the predicted failure capacity of cracked structures and should be considered in the evaluation of fatigue life.     

基于水动力学、分数阶微分及Steger算法的线状目标提取

目的 线状目标的检测具有非常广泛的应用领域,如车道线、道路及裂缝的检测等,而裂缝是其中最难检测的线状目标。为避免直接提取线状目标时图像分割难的问题,以裂缝和车道线为例,提出了一种新的跟踪线状目标中线的算法。方法 对图像进行高斯平滑,用一种新的分数阶微分模板增强图像中的模糊及微细线状目标;基于Steger算法提出一种提取线状目标中心线特征点的算法,避免了提取整体目标的困难;根据水动力学思想将裂隙看成溪流,通过最大熵阈值处理后,先进行特征点的连接,再基于线段之间的距离及夹角进行线段之间的连接（溪流之间的融合）。结果 对300幅裂缝图像及4种类别的其他线状目标图像进行试验,并与距离变换、最大熵阈值法+细线化Otsu阈值分割+细线化、谷底边界检测等类似算法进行比较分析,本文算法检测出的线状目标的连续性好、漏检（大间隙少）和误检（毛刺及多余线段少）率均较低。结论 本文算法能够在复杂的线状目标图像中准确快速地提取目标的中心线,一定程度上改善了复杂线状目标图像分割难的问题。     

Fracture behaviour of single crystal silicon microstructures

The fracture behaviour of single crystal silicon (SCSi) microstructures is analysed based on microme-chanical torsional and tensile experiments. The uniaxial testpieces are characterised by the presence of sharp not-ches at the gauge length extremities. The critical loading conditions are reproduced in a finite element model in order to identify the analogies of the failure conditions in tension and torsion. The stress field in the vicinity of the notch tip (were cracks originate) is analyzed, and fracture mechanics parameters are determined. In the finite element model a crack, reproducing the failure process observed in the experiments, is included. The crack area is incrementally increased and the energy release rate for the critical loading conditions in tension and torsion is calculated. Based on these results a failure criterion is formulated along with a procedure for the mechanical integrity analysis of SCSi microstructures of arbitrary shape and loading conditions.     

Nonlinear analysis of reinforced concrete hyperboloid cooling towers—I. Material model, finite element model and validation

This is the first part of a two-part series of papers in which the constitutive material modelling of reinforced concrete, in shell structures, which resist applied loads predominantly through membrane action, is presented. The material model includes the effects of tensile cracking, tension stiffening, compression softening, interface shear transfer, and change in material stiffness due to crack rotation. A four-noded isoparametric curved shell element has been used in the nonlinear finite element analysis. The results obtained by using the model for analysis of a shear wall panel subjected to in-plane loading have been compared with those from experimental investigation.     

A finite element analysis of the finite width interface mixed mode bi-material fracture problem

One aspect of the terminal crack, mixed mode bi-material fracture mechanics problem is investigated using finite elements. The influence of a finite width bond line interface is considered for one representative material pair combination (E₂/E₁ = 0.10). The stress intensity factors for an inclined crack terminating at a variable thickness interface are established as a function of crack inclination. Since the order of the stress singularity is not the typical r^−1/2 associated with LEFM problems, variable power singular finite elements are used to model the terminating crack tip. Crack tip stress distributions and probable angles of crack extension are presented as a function of crack inclination and bond line thickness. Crack tip stress distributions assuming an interfacial debonding criterion are presented as a function of crack inclination and bond line thickness.     

Nonlinear finite element analysis of reinforced concrete plates and shells under monotonic loading

Plane stress constitutive models are proposed for the nonlinear finite element analysis of reinforced concrete structures under monotonic loading. An elastic strain hardening plastic stress-strain relationship with a nonassociated flow rule is used to model concrete in the compression dominating region and an elastic brittle fracture behavior is assumed for concrete in the tension dominating area. After cracking takes place, the smeared cracked approach together with the rotating crack concept is employed. The steel is modeled by an idealized bilinear curve identical in tension and compressions. Via a layered approach, these material models are further extended to model the flexural behavior of reinforced concrete plates and shells. These material models have been tested against experimental data and good agreement has been obtained.     

A thermomechanical model for adhesion reduction of MEMS cantilevers

Presents a thermomechanical model that describes adhesion reduction in MEMS structures using laser heating. A fracture mechanics model is developed where the interface between the stiction-failed microcantilever and the substrate is treated as a crack, and the energy release rate is calculated using elastic theory. In order to include the effect of a temperature difference between the microcantilever and the substrate, an associated thermal strain energy is included in the fracture model. If the free length is longer than the critical buckling length, the beam buckles decreasing the strain energy of the system. For surface-micromachined polycrystalline silicon cantilevers with an initial crack length of 400 /spl mu/m, the model predicts that a temperature difference of 100 K repairs microcantilevers as long as 1300 /spl mu/m. The peeling of adhered beams from the substrate after laser irradiation is experimentally shown with measured crack lengths within 15% of predicted values indicating that the proposed model establishes the mechanism of adhesion reduction by laser irradiation.     

基于XFEM的折弯片断裂仿真

采用Abaqus的XFEM功能对折弯片的断裂问题进行仿真,断裂区为转角处的过渡区域.转角处圆弧的半径影响裂纹的开裂时间.裂纹的扩展路径具有任意性,细化网格下裂纹扩展方向不稳定,会超出断裂区.1阶单元和1阶减缩积分单元的分析结果比较接近.通用静态分析比动态隐式分析效率更高一些.在端部压力的作用下,折弯片约在1 ms内开裂,8 ms完全断开.Cohesive element算法的裂纹路径较LEFM方法更平滑一些.     

A finite element analysis of the mixed mode bi-material fracture mechanics problem

Two aspects of the mixed mode bi-material fracture mechanics problem are investigated using finite elements. The stress intensity factors for an inclined crack at various distances from a bi-material interface are established as a function of inclination for two material pair combinations. The probable angle of crack extension is established for this problem using the maximum hoop stress criterion. The inclined terminal crack problem is studied using variable power singular elements at the interface. Crack tip stress distributions and probable angle of crack extension are presented as functions of crack inclination and material pair combinations. Crack tip stress distributions assuming an interfacial debonding criterion are also presented as functions of crack inclination and material pair combinations.     

Laminate optimization of blended composite structures using a modified Shepard’s method and stacking sequence tables

This article presents an optimization tool for the stacking sequence design of blended composite structures. Enforcing blending ensures the manufacturability of the optimized laminate. A novel optimization strategy is proposed combining a genetic algorithm (GA) for stacking sequence tables with a multi-point structural approximation using a modified Shepard’s interpolation in stiffness-space. A successive approximation approach is used where the set of design points used to create the structural approximations is successively enriched using the elite of the previous step. Additional improvement in the generality and efficiency of the algorithm is obtained by using load approximations thus enabling the implementation of a wide range of stress-based design criteria. A multi-panel, blended composite problem is used as an application to demonstrate the performance of the developed tool. The optimization is performed with mass as the objective to be minimized, subjected to strength and buckling constraints. The results presented show that completely blended and feasible stacking sequence designs can be obtained, having their structural performance close to the theoretical continuous optimum itself. Additionally, the multi-point Shepard’s approximation shows a considerable saving in computational costs, while the limitations of inexpensive stiffness-matching optimizations are observed.     

正交异性钢桥肋-桥面板焊缝裂纹的三维断裂力学分析

正交异性钢桥的肋-桥面板焊缝处的疲劳裂纹是典型的三维裂纹问题,但是现在普遍采用平面应变二维裂纹模型对其进行断裂力学分析.基于Schwartz-Neuman交替法建立正交异性钢桥肋-桥面板焊缝裂纹的局部三维断裂力学分析模型;评估焊缝处表面裂纹的形状和深度对应力强度因子的影响;采用Paris公式估算等应力幅下焊缝的疲劳寿命.计算结果表明:用平面应变二维裂纹模型进行正交异性钢桥的肋-面板焊缝的断裂力学分析会严重低估其疲劳寿命;采用三维断裂力学模型进行肋-桥面板焊缝裂纹的疲劳寿命分析十分必要.