Parallelization of lattice modelling for estimation of fracture process zone extent in cementitious composites

This paper is focused on the verification and validation of the developing technique for estimation of the extent (the size and shape) of the fracture process zone (FPZ) in quasi-brittle silicate-based specimens/structures during failure process (termed the ReFraPro – Reconstruction of Fracture Process – technique). Most experimental data published in the literature are incomplete for its sound validation; therefore, numerical simulations by means of physical discretization of continuum are used for supplementing the verification of the technique. A discrete spring network/lattice particle-type model formulated as a nonlinear dynamical system is utilized. Parallelized implementation within the CUDA environment helps to decrease the computational cost of the simulations to an admissible level. The conducted analysis demonstrates satisfactory agreement of the size and shape of the FPZ reconstructed by the ReFraPro technique with both the data of the performed simulations and selected experimental data from literature.     

基于扩展有限元法及虚拟裂缝模型的混凝土断裂过程区分析

提出一种利用扩展有限元法（eXtended Finite Element Method,XFEM）和虚拟裂缝模型对混凝土断裂过程区（Fracture Process Zone, FPZ)进行研究的方法.利用该方法可以求出裂缝扩展过程中混凝土FPZ的长度及位移和应力分布.利用该方法对一个三点弯曲混凝土梁进行研究,考察骨料粒径、不同软化律和不同初始裂缝长度对FPZ的影响.     

Axisymmetric shell optimization under fracture mechanics and geometric constraint

This paper describes a problem of axisymmetric shell optimization under fracture mechanics and geometric constraints. The shell is made from quasi-brittle materials, and through crack arising is admitted. It is supposed that the shell is loaded by cyclic forces. A crack propagation process related to the stress intensity factor is described by Paris fatigue law. The problem of finding the meridian shape and the thickness distribution (geometric design variables) of the shell having the smallest mass subject to constraints on the cyclic number for fatigue cracks and geometrical constraint on the shell volume is investigated. Special attention is devoted to different possibilities of problem transformation and analytical methods of their solution. Using minimax approach, optimal shapes of the shells and their thickness distributions have been found analytically.     

橡胶材料疲劳断裂特性研究进展

由于橡胶材料的动态疲劳特性对保证橡胶制品使用时的安全性和可靠性具有重要意义,综述机械载荷、环境和橡胶配方等因素对橡胶材料疲劳寿命的影响,总结用疲劳裂纹萌生寿命法和基于断裂力学的疲劳裂纹扩展法预测橡胶材料动态疲劳寿命方法的优缺点,并展望这2种方法的发展趋势.     

Lattice Element Models and Their Peculiarities

This paper presents the lattice element models, as a class of discrete models, in which the structural solid is represented as an assembly of one-dimensional elements. This idea allows one to provide robust models for propagation of discontinuities, multiple cracks interaction or cracks coalescence. Many procedures for computation of lattice element parameters for representing linear elastic continuum have been developed, with the most often used ones discussed herein. Special attention is dedicated to presenting the ability of this kind of models to consider material disorder, heterogeneities and multi-phase materials, which makes lattice models attractive for meso- or micro-scale simulations of failure phenomena in quasi-brittle materials, such as concrete or rocks. Common difficulties encountered in material failure and a way of dealing with them in the lattice models framework are explained in detail. Namely, the size of the localized fracture process zone around the propagating crack plays a key role in failure mechanism, which is observed in various models of linear elastic fracture mechanics, multi-scale theories, homogenization techniques, finite element models, molecular dynamics. An efficient way of dealing with this kind of phenomena is by introducing the embedded strong discontinuity into lattice elements, resulting with mesh-independent computations of failure response. Moreover, mechanical lattice can be coupled with mass transfer problems, such as moisture, heat or chloride ions transfer which affect the material durability. Any close interaction with a fluid can lead to additional time dependent degradation. For illustration, the lattice approach to porous media coupling is given here as well. Thus, the lattice element models can serve for efficient simulations of material failure mechanisms, even when considering multi-physics coupling. The main peculiarities of such an approach have been presented and discussed in this work.     

Fracture resistance via topology optimization

The fracture resistance of structures is optimized using the level-set method. Fracture resistance is assumed to be related to the elastic energy released by a crack propagating in a normal direction from parts of the boundary that are in tension, and is calculated using the virtual crack extension technique. The shape derivative of the fracture-resistance objective function is derived. Two illustrative two-dimensional case studies are presented: a hole in a plate subjected to biaxial strain; and a bridge fixed at both ends subjected to a single load in which the compliance and fracture resistance are jointly optimized. The structures obtained have rounded corners and more material at places where they are in tension. Based on the results, we propose that fracture resistance may be modeled more easily but less directly by including a term proportional to surface area in the objective function, in conjunction with nonlinear elasticity where the Young’s modulus in tension is lower than in compression.     

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.     

A three-dimensional self-adaptive cohesive zone model for interfacial delamination

Discrete crack models with cohesive binding forces in the fracture process zone have been widely used to address failure in quasi-brittle materials and interfaces. However, the numerical concerns and limitations stemming from the application of interface cohesive zone models in a quasi-static finite element framework increase considerably as the relative size of the process zone decreases. An excessively fine mesh is required in the process zone to accurately resolve the distribution of tractions in a relatively small moving zone. With a moderate mesh size, inefficient path-following techniques have to be employed to trace the local discretization-induced snap-backs. In order to increase the applicability of cohesive zone models by reducing their numerical deficiencies, a self-adaptive finite element framework is proposed, based on a hierarchical enrichment of the standard elements. With this approach, the planar mixed-mode crack growth in a general three-dimensional continuum, discretized by a coarse mesh, can be modeled while the set of equations of the non-linear system is solved by a standard Newton–Raphson iterative procedure. This hierarchical scheme was found to be most effective in reducing the oscillatory behavior of the global response.     

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.     

A hybrid finite element-scaled boundary finite element method for crack propagation modelling

This study develops a novel hybrid method that combines the finite element method (FEM) and the scaled boundary finite element method (SBFEM) for crack propagation modelling in brittle and quasi-brittle materials. A very simple yet flexible local remeshing procedure, solely based on the FE mesh, is used to accommodate crack propagation. The crack-tip FE mesh is then replaced by a SBFEM rosette. This enables direct extraction of accurate stress intensity factors (SIFs) from the semi-analytical displacement or stress solutions of the SBFEM, which are then used to evaluate the crack propagation criterion. The fracture process zones are modelled using nonlinear cohesive interface elements that are automatically inserted into the FE mesh as the cracks propagate. Both the FEM’s flexibility in remeshing multiple cracks and the SBFEM’s high accuracy in calculating SIFs are exploited. The efficiency of the hybrid method in calculating SIFs is first demonstrated in two problems with stationary cracks. Nonlinear cohesive crack propagation in three notched concrete beams is then modelled. The results compare well with experimental and numerical results available in the literature.     

Shape optimization of quasi-brittle axisymmetric shells by genetic algorithm

This paper describes the application of genetic algorithm to the shape optimization of axisymmetric shells. The primary problem of axisymmetric shell optimization under fracture mechanics constraint is formulated as the weight (volume of shell material) minimization under stress intensity constraints. It is assumed that the shells are made from quasi-brittle materials and through-thickness crack presence is admitted. Taking into account the fact of incomplete information concerning crack arising (size, location and orientation) this paper presents some numerical results based on a guaranteed approach.     

An entropic optimization approach for a parameter identification problem in quasibrittle fracture

The cohesive crack model is a widely used idealization to represent simply and reliably the quasibrittle fracture behavior of concrete-like materials. However, knowledge of the parameters characterizing this model is of prime importance and cannot all be obtained directly from experiments. Typically, recourse is made to some inverse numerical approach. Our particular formulation can be elegantly cast as an instance of a challenging optimization problem known as a mathematical program with equilibrium (or, more precisely in our case, complementarity) constraints (MPEC). The present paper investigates application of an entropic optimization approach to solve the MPEC, and compares its performance with our previously proposed Fischer–Burmeister smoothing scheme. We use actual experimental data for the comparison.     

基于Abaqus柔度标定法的Q235材料断裂韧性仿真

为简便、准确地获得Q235材料的应力强度因子值和J积分值,用Abaqus对Q235材料进行有限元仿真,得到三点弯曲试样及其裂纹尖端区域的应力分布情况;针对裂纹尖端的奇异性,引入折叠单元进行裂纹尖端单元的奇异性建模.不同尺寸试件应力强度因子仿真值与试验值基本一致,表明该方法可以准确预测材料断裂参数.     

FraMePID-3PB software for material parameter identification using fracture tests and inverse analysis

Knowledge regarding the values of fracture-mechanical parameters is critical for the virtual failure modeling of elements and structures made of concrete. A key parameter in nonlinear fracture mechanics modeling is the specific fracture energy of concrete, and its variability. Three-point bending tests on notched-beam specimens are fundamental experiments for the determination of fracture-mechanical parameters. In the present paper, two basic approaches are applied to determine fracture-mechanical parameter values from these tests: (i) the effective crack model/work-of-fracture method, and (ii) inverse analysis using artificial neural networks and stochastic simulations. First, the paper describes suitable methods for the determination of fracture-mechanical parameters. Second, the FraMePID-3PB software tool, which has been developed in order to automate the whole time consuming process of inverse analysis, is described. Finally, the verification of methodology and software is presented using two illustrative examples.     

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.     

基于倍频双晶复合传感器的构件疲劳微裂纹非线性超声检测

通过对固体中非线性超声传播模型的研究,分析了裂纹静态压力与超声波作用力对裂纹超声非线性响应的影响,在此基础上,建立了反映裂纹区应力-应变非线性关系的弹性接触机制超声非线性响应模型;以及反映裂纹闭合状态转换的碰撞接触机制超声非线性响应模型。基于上述理论,通过实验研究发现裂纹尖端区的二次谐波激发效率与裂纹的开口区和闭合区及裂纹最终扩展的极限长度有关。因此,可使用二次谐波激发效率作为定量表征金属试件疲劳微裂纹缺陷的特征参数,实验中使用了自主研制倍频双晶复合换能器,这种倍频双晶复合换能器在工程实际应用中作在线检测更为方便、实用。     

A new calibration method for ductile fracture models as chip separation criteria in machining

Several leading commercial FEM codes offer a number of fracture options without giving any guidance to the users in determining the fracture parameters for different materials. A modification is implemented to Johnson and Cook’s calibration method to provide simultaneous consideration of both active failure mechanisms in actual domain of the field variables. Application of FE simulation of machining to accumulate damage is the key point to solve problems of available calibration method. As a result, a new set of fracture constants is presented for AISI 1045 steel. It is demonstrated that due to different failure mechanism a unique fracture model cannot be the representative of crack generation in all machining zone. Then the classical Lagrangian simulation is modified based on this concept.     

A cohesive approach to thin-shell fracture and fragmentation

We develop a finite-element method for the simulation of dynamic fracture and fragmentation of thin-shells. The shell is spatially discretized with subdivision shell elements and the fracture along the element edges is modeled with a cohesive law. In order to follow the propagation and branching of cracks, subdivision shell elements are pre-fractured ab initio and the crack opening is constrained prior to crack nucleation. This approach allows for shell fracture in an in-plane tearing mode, a shearing mode, or a bending of hinge mode. The good performance of the method is demonstrated through the simulation of petalling failure experiments in aluminum plates.     

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.     

Study of elastic behaviour of plates containing cracks by finite element analysis

This work applies finite element analysis very simply to cracked plates. An infinite plate and a finite plate, both with a central crack, are considered to study their elastic behaviour and some fracture mechanics concepts, such as the geometry factor and the fracture toughness. These magnitudes are calculated by means of finite element methods and the results are in very good agreement with the established theory, which proves that the finite element approach is very appropriate. The fracture toughness fraction is defined and calculated for a finite plate to predict its failure.