Modeling and simulation of osteoporosis and fracture of trabecular bone by meshless method

Osteoporosis is a skeletal disease characterized by a decrease in bone strength as a result of a decrease of bone mass and a deterioration of bone microstructure. In this work, the imaging data of a CT scanned human femoral neck trabecular bone is directly converted into a meshless model. A model is developed to analyze osteoporosis process. A fracture criterion and the corresponding post-failure are proposed for trabecular bone. The fracture process is modeled and simulated. The simulations show that the fracture stress is not a monotonically decreasing function in the process of fracture, and the microstructure of trabecular bone has a positive effect in preventing progressive failure. The approach in this work may be used to understand the osteoporosis-related fracture and the bone density–strength relationship, and to serve as a way for prognosis of osteoporosis.     

基于拓展虚内键本构模型的多裂纹混凝土结构破坏分析

拓展虚内键(Augmented virtual internal bond, AVIB)是基于虚内键理论的一种多尺度本构模型,它同时考虑了微观虚内键的法向和切向变形,应用Xu-Needleman势函数描述虚内键,并在微观势函数基础上直接导出了宏观本构方程。由于脆性材料的抗压强度与微元体的应力状态有关,为了反映这种微元应力效应,依据混凝土三轴抗压强度准则定义了应力效应系数,并将其反映到AVIB本构模型中。对于已有裂纹,采用无厚度单元劈裂法进行建模,避免了网格重划分问题和单独设置接触单元问题。结合AVIB模型与无厚度单元劈裂法,对多裂纹混凝土结构的破坏进行了模拟分析。结果表明,预制裂纹的长度不同,导致结构的主裂纹扩展方式不同。模拟所得的结构破坏模式及荷载-主裂纹口张开位移曲线与相关文献报道结果基本一致,表明了该方法的有效性。由于该文所采用的AVIB本构方程中已蕴涵了混凝土断裂能及三轴强度准则,因而在整个断裂模拟过程中,既避免了外部的断裂准则问题,同时又不需要网格重构及附加自由度,提高了计算效率,为大体积混凝土结构的破坏分析提供了一种简单的可行方法。     

Dynamic crack nucleation and propagation in polycrystalline aluminum aggregates subjected to large inelastic deformations

The major objective of this work has been to apply a new compatibility-based fracture theory to the investigation of dynamic failure of polycrystalline metals and alloys. To model the nucleation and propagation of failure surfaces at the microstructural scale, under large deformations and dynamic loading conditions, a general fracture criterion based on the integral law of compatibility is used. This new fracture criterion, was coupled with rate-dependent dislocation-density based crystalline plasticity formulations to elucidate the microstructural mechanisms related to the evolution of intergranular and transgranular failure and to understand how grain sizes and strain-rate sensitivity affect aggregate strength, ductility, and dynamic damage tolerance. It is shown that cracks commonly nucleate at triple junctions and at grain boundaries as intergranular cracks, and that slip bands through grains result in transgranular cracks.     

Modelling brittle impact failure of disc particles using material point method

Understanding the impact failure of particles made of brittle materials such as glasses, ceramics and rocks is an important issue for many engineering applications. During the impact, a solid particle is turned into a discrete assembly of many fragments through the development of multiple cracks. The finite element method is fundamentally ill-equipped to model this transition. Recently a so-called material point method (MPM) has been used to study a wide range of problems of material and structural failures. In this paper we propose a new material point model for the brittle failure which incorporates a statistical failure criterion. The capability of the method for modelling multiple cracks is demonstrated using disc particles. Three impact failure patterns observed experimentally are captured by the model: Hertzian ring cracks, meridian cracks, and multi-fragment cracks. Detailed stress analysis is carried out to interpret the experimental observations. In particular it is shown that the experimentally observed dependence of a threshold velocity for the initiation of meridian cracks on the particle size can be explained by the proposed model. The material point based scheme requires a relatively modest programming effort and avoids node splitting which makes it very attractive over the traditional finite element method.     

Multi-length scale micromorphic process zone model

The prediction of fracture toughness for hierarchical materials remains a challenging research issue because it involves different physical phenomena at multiple length scales. In this work, we propose a multiscale process zone model based on linear elastic fracture mechanics and a multiscale micromorphic theory. By computing the stress intensity factor in a K-dominant region while maintaining the mechanism of failure in the process zone, this model allows the evaluation of the fracture toughness of hierarchical materials as a function of their microstructural properties. After introducing a multi-length scale finite element formulation, an application is presented for high strength alloys, whose microstructure typically contains two populations of particles at different length scales. For this material, the design parameters comprise of the strength of the matrix–particle interface, the particle volume fraction and the strain-hardening of the matrix. Using the proposed framework, trends in the fracture toughness are computed as a function of design parameters, showing potential applications in computational materials design.     

A multiscale micromechanical approach to model the deteriorating impact of alkali-silica reaction on concrete

The alkali-silica reaction (ASR) in concrete is one of the most harmful deterioration processes, which leads to expansion and cracking of the material. To understand the evolution of ASR in concrete and its deteriorating impact on the material, a multiscale material model, from aggregate to concrete level, is proposed. The concrete, which at macro scale is considered a homogeneous material, is micromechanically modelled by a matrix-cracks system, in which each phase is uniform and behaves elastically. The damage criterion, associated to the cracks, is formulated on the basis of linear fracture mechanics theory. The model, which is analytically solved, is based on a limited numbers of input parameters, to be determined via micro and macro experimental investigations. The model is able to predict the non-linear behaviour of concrete subject to uniaxial loading in good agreement with code formulations, which are usually input for numerical analyses of structures. For the case of ASR-affected material, the model overestimates the degradation rate of mechanical properties as a function of the expansion. On the contrary, the relationship between stiffness and strength deterioration is correctly approximated. Various model modifications are explored suggesting that the assumption of elastic behaviour of each phase should be reconsidered.     

Correlating cryogenic fracture strength using a modified two-parameter method

Damage tolerant approaches have been employed increasingly in the design of critical engineering components. In these approaches, one has to assess the residual strength of a component with an assumed pre-existing crack. In other cases, cracks may be detected during service. Then, there is a need to evaluate the residual strength of the cracked components in order to decide whether they can be continued safely or repair and replacement are imperative. A modified two-parameter fracture criterion is applied to correlate fracture data from tensile cracked plates made of aluminium alloys, titanium alloys and stainless steel at cryogenic temperatures. Fracture parameters to generate the failure assessment diagram are determined for the materials considered in the present study. An attempt is made to correlate the fracture data on pressure vessels tested at cryogenic temperatures. The fracture parameters obtained from the fracture data of tensile cracked plates and pressure vessels were found to be closely matching with each other. Failure pressure estimates were found to be in good agreement with test results. This study indicates that the failure assessment diagram of a material generated from tensile fracture plate configurations can be applied for failure pressure estimations of flawed pressure vessels.     

正交铺设陶瓷基复合材料单轴拉伸行为

采用细观力学方法对正交铺设陶瓷基复合材料单轴拉伸应力-应变行为进行了研究。采用剪滞模型分析了复合材料出现损伤时的细观应力场。采用断裂力学方法、 临界基体应变能准则、 应变能释放率准则及Curtin统计模型4种单一失效模型确定了90°铺层横向裂纹间距、 0°铺层基体裂纹间距、 纤维/基体界面脱粘长度和纤维失效体积分数。将剪滞模型与4种单一损伤模型结合, 对各损伤阶段应力-应变曲线进行了模拟, 建立了复合材料强韧性预测模型。与室温下正交铺设陶瓷基复合材料单轴拉伸应力-应变曲线进行了对比, 各个损伤阶段的应力-应变、 失效强度及应变与试验数据吻合较好。分析了90°铺层横向断裂能、 0°铺层纤维/基体界面剪应力、 界面脱粘能、 纤维Weibull模量对复合材料损伤及拉伸应力-应变曲线的影响。      

考虑孔隙及微裂纹影响的混凝土宏观力学特性研究

混凝土是一种典型的多孔介质材料,孔隙分布错综复杂,孔径尺寸跨越微观尺度和宏观尺度,对混凝土弹性模量及强度等力学参数产生巨大影响.认为混凝土是由骨料、孔隙及砂浆基质组成的三相复合材料,采用Monte Carlo 法将孔隙、微裂纹及微缺陷与骨料颗粒随机投放在砂浆基质中.根据三相球模型及中空圆柱形杆件模型得到含孔材料的有效力学性质,并推导得到含孔材料的等效本构模型.建立含孔隙混凝土试件的细观单元等效化力学模型,对二级配含孔隙混凝土试件在单轴拉伸及压缩条件下的反应进行了非线性分析.结果表明:孔隙、微裂纹的存在对混凝土宏观弹性模量、强度及残余强度等力学性质都有很大影响,在对混凝土宏观力学特性分析及研究混凝土损伤断裂时不应忽略其影响.     

Continuum damage modeling of dynamic crack velocity,branching, and energy dissipation in brittle materials

This study is aimed at evaluating continuum scale predictions of dynamic crack propagation and branching in brittle materials using local damage modeling. Classical experimental results on crack branching in PMMA and the corresponding nonlocal modeling results by Wolff et al. (Int J Numer Meth Eng 101(12):933, 2015) are used as a benchmark. An isotropic damage model based on a frame-invariant effective strain is adapted. Mesh objectivity is achieved by calibrating the damage model for a suitable element size and subsequently retaining that mesh size in all subsequent analyses. Crack propagation and branching are predicted by simulating accurately the test conditions. It is found that a local, rate-independent damage model considerably overpredicts the dynamic crack velocity and the extent of crack branching. Subsequently, the effect of various strain rate-dependent phenomena, viz. material viscoelasticity, rate-dependent strength, fracture energy, and failure strain is evaluated. Incorporating the material strain rate effects is found to improve the predictions and match the test data. In this regard, radially scaling the damage law is found to work the best. Despite an overprediction of micro-branching, the macro-crack branching is found to occur in agreement with the Yoffe instability criterion. Overall, various experimentally observed aspects of dynamic cracks are reproduced, including acceleration of cracks to a steady state velocity, increased micro-branching and macro-branching with increased strain rates, and crack velocity dependence of energy dissipation and fracture surface area.

     

Application of Fracture Mechanics Concepts to Hierarchical Biomechanics of Bone and Bone-like Materials

Fracture mechanics concepts are applied to gain some understanding of the hierarchical nanocomposite structures of hard biological tissues such as bone, tooth and shells. At the most elementary level of structural hierarchy, bone and bone-like materials exhibit a generic structure on the nanometer length scale consisting of hard mineral platelets arranged in a parallel staggered pattern in a soft protein matrix. The discussions in this paper are organized around the following questions: (1) The length scale question: why is nanoscale important to biological materials? (2) The stiffness question: how does nature create a stiff composite containing a high volume fraction of a soft material? (3) The toughness question: how does nature build a tough composite containing a high volume fraction of a brittle material? (4) The strength question: how does nature balance the widely different strengths of protein and mineral? (5) The optimization question: Can the generic nanostructure of bone and bone-like materials be understood from a structural optimization point of view? If so, what is being optimized? What is the objective function? (6) The buckling question: how does nature prevent the slender mineral platelets in bone from buckling under compression? (7) The hierarchy question: why does nature always design hierarchical structures? What is the role of structural hierarchy? A complete analysis of these questions taking into account the full biological complexities is far beyond the scope of this paper. The intention here is only to illustrate some of the basic mechanical design principles of bone-like materials using simple analytical and numerical models. With this objective in mind, the length scale question is addressed based on the principle of flaw tolerance which, in analogy with related concepts in fracture mechanics, indicates that the nanometer size makes the normally brittle mineral crystals insensitive to cracks-like flaws. Below a critical size on the nanometer length scale, the mineral crystals fail no longer by propagation of pre-existing cracks, but by uniform rupture near their limiting strength. The robust design of bone-like materials against brittle fracture provides an interesting analogy between Darwinian competition for survivability and engineering design for notch insensitivity. The follow-up analysis with respect to the questions on stiffness, strength, toughness, stability and optimization of the biological nanostructure provides further insights into the basic design principles of bone and bone-like materials. The staggered nanostructure is shown to be an optimized structure with the hard mineral crystals providing structural rigidity and the soft protein matrix dissipating fracture energy. Finally, the question on structural hierarchy is discussed via a model hierarchical material consisting of multiple levels of self-similar composite structures mimicking the nanostructure of bone. We show that the resulting “fractal bone”, a model hierarchical material with different properties at different length scales, can be designed to tolerate crack-like flaws of multiple length scales.     

等离子喷涂HA/TiO2复合涂层

采用大气等离子喷涂方法,成功地制备了ＨＡ／ＴｉＯ２复合涂层,对复合涂层的结合强度、微观结构、水浸渍下的表面形貌进行了较为深入的研究,结果表明,由于ＴｉＯ２的加入,ＨＡ／ＴｉＯ２涂层的结合强度明显高于纯ＨＡ涂层,而且导致涂层破坏机理由粘合破坏向内聚破坏转化,这是由于ＨＡ／ＴｉＯ２的复合缓和了涂层与基体间的膨胀系数失配现象,改善了涂层与基体之间的结合,ＳＥＭ观察显示,ＨＡ／ＴｉＯ２涂层表面有一些细小的     

Modeling of structural failure of Zircaloy claddings induced by multiple hydride cracks

Zirconium alloys have been serving as primary structural materials for nuclear fuel claddings. Structural failure analysis under extreme conditions is critical to the assessment of the performance and safety of nuclear fuel claddings. This work focuses on simulating structural failure of Zircaloy tubes with multiple hydride defects through modeling explicit crack propagation in ductile media. First, we developed an integrated cladding failure model by taking into account both crack initiation induced by hydride/matrix interface separation and ligament tearing-off between activated hydride cracks. Second, to accommodate the initiation, propagation, and coalescence of multiple cracks in finite plastic media we incorporated this structural failure model into a coupled continuous/discontinuous Galerkin (DG) based finite element code, a traditionally preferred implicit numerical framework. Third, to improve the adaptive placement of DG interface elements for crack propagation and to identify potential coalescence of cracks due to the interaction between adjacent hydride cracks, we defined a special failure index for the assessment of potential failure zones using both true plastic strain developed and predicted failure strain based on the Johnson–Cook material failure criterion. Finally, by calibrating the proposed material failure model using a cluster of Zircaloy material experimental tests, we successfully simulated a complete failure process of a fuel cladding tube with multiple hydride cracks.     

A design-centered approach in developing Al-Si-based light-weight alloys with enhanced fatigue life and strength

Material heterogeneities and discontinuities such as porosity, second phase particles, and other defects at meso/micro/nano scales, determine fatigue life, strength, and fracture behavior of aluminum castings. In order to achieve better performance of these alloys, a design-centered computer-aided renovative approach is proposed. Here, the term “design-centered” is used to distinguish the new approach from the traditional trial-and-error design approach by formulating a clear objective, offering a scientific foundation, and developing a computer-aided effective tool for the alloy development. A criterion for tailoring “child” microstructure, obtained by “parent” microstructure through statistical correlation, is proposed for the fatigue design at the initial stage. A dislocations pileup model has been developed. This dislocation model, combined with an optimization analysis, provides an analytical-based solution on a small scale for silicon particles and dendrite cells to enhance both fatigue performance and strength for pore-controlled castings. It can also be used to further tailor microstructures. In addition, a conceptual damage sensitivity map for fatigue life design is proposed. In this map there are critical pore sizes, above which fatigue life is controlled by pores; otherwise it is controlled by other mechanisms such as silicon particles and dendrite cells. In the latter case, the proposed criteria and the dislocation model are the foundations of a guideline in the design-centered approach to maximize both the fatigue life and strength of Al-Si-based light-weight alloy.     

Fracture Strength of Photovoltaic Silicon Wafers Evaluated Using a Controlled Flaw Method

Propagation of pre‐existing micro cracks and their associated residual contact stresses, generated from the wafer sawing process, is the leading cause for photovoltaic (PV) silicon wafer/cell breakage during handling and processing. In the current work, the impact of a single micro crack on the fracture strength of PV silicon wafer is investigated based on a controlled flaw method. Radial/median cracks with controllable scales are introduced through microindentation at the center of a PV silicon sample to simulate micro cracks resulting from wafer sawing, handling, or thermal processing. Results indicate that the fracture strength of PV silicon wafer decreases linearly with the increasing of the microindentation load (radial crack scale). In addition, it is found that the impurity carbon plays an important role in the contact cracking‐fracture process. The fracture strength increased ≈21% when the substitutional carbon concentration is increased from 1.2 × 10¹⁸ to 6.4 × 10¹⁸ cm^?3.     

Mixed Mode Fracture of Cracks and Wedge Shaped Notches in Expanded PVC Foam

Fracture initiated from a sharp crack or wedge shaped notch in a homogeneous material, subjected to different loading is considered. Singularities in the stress fields at edges and vertices are discussed. A point-stress criterion is used to predict fracture for sharp cracks as well as 90° wedge notches in expanded PVC foam. The point-stress criterion is formulated in a manner allowing failure predictions in general 3D stress situations. The influence of nonsingular T-stress at cracks is discussed and substantiated by experimental results.     

Tensile properties and microstructure characterization of Hi-NicalonTM SiC fibers after loading at high temperature

Loading tests were performed on the Hi-Nicalon^TM fiber yarns by applying different dead loads at elevated temperatures in Ar atmosphere. After each loading test, the room temperature tensile properties of single filaments as a function of load, exposure time and temperature, were evaluated on these fibers. Strength degradation of single filament occurred after loading test, and strength retention decreased with increasing the exposure temperature and load. The microstructure observation revealed that oxidation and loading accelerated new flaw nucleation and growth resulting in stress corrosion cracks. The stress corrosion cracks acted as critical flaws and could be mainly responsible for the strength degradation. The mirror size corresponding to the critical flaw size was measured and fracture mechanics was applied to analyze failure mechanism of single filament.     

An improved failure criterion for biological and engineered staggered composites

High-performance biological materials such as nacre, spider silk or bone have evolved a staggered microstructure consisting of stiff and strong elongated inclusions aligned with the direction of loading. This structure leads to useful combinations of stiffness, strength and toughness, and it is therefore increasingly mimicked in bio-inspired composites. The performance of staggered composites can be tuned; for example, their mechanical properties increase when the overlap between the inclusions is increased. However, larger overlaps may lead to excessive tensile stress and fracture of the inclusions themselves, a highly detrimental failure mode. Fracture of the inclusions has so far only been predicted using highly simplified models, which hinder our ability to properly design and optimize engineered staggered composites. In this work, we develop a new failure criterion that takes into account the complex stress field within the inclusions as well as initial defects. The model leads to an ‘optimum criterion’ for cases where the shear tractions on the inclusions is uniform, and a ‘conservative’ criterion for which the tractions are modelled as point forces at the ends of the overlap regions. The criterion can therefore be applied for a wide array of material behaviour at the interface, even if the details of the shear load transfer is not known. The new criterion is validated with experiments on staggered structures made of millimetre-thick alumina tablets, and by comparison with data on nacre. Formulated in a non-dimensional form, our new criterion can be applied on a wide variety of engineered staggered composites at any length scale. It also reveals new design guidelines, for example high aspect ratio inclusions with weak interfaces are preferable over inclusions with low aspect ratio and stronger interfaces. Together with existing models, this new criterion will lead to optimal designs that harness the full potential of bio-inspired staggered composites.     

Mechanistic fracture criteria for the failure of human cortical bone

A mechanistic understanding of fracture in human bone is critical to predicting fracture risk associated with age and disease. Despite extensive work, a mechanistic framework for describing how the microstructure affects the failure of bone is lacking. Although micromechanical models incorporating local failure criteria have been developed for metallic and ceramic materials, few such models exist for biological materials. In fact, there is no proof to support the widely held belief that fracture in bone is locally strain-controlled, as for example has been shown for ductile fracture in metallic materials. In the present study, we provide such evidence through a novel series of experiments involving a double-notch-bend geometry, designed to shed light on the nature of the critical failure events in bone. We examine how the propagating crack interacts with the bone microstructure to provide some mechanistic understanding of fracture and to define how properties vary with orientation. It was found that fracture in human cortical bone is consistent with strain-controlled failure, and the influence of microstructure can be described in terms of several toughening mechanisms. We provide estimates of the relative importance of these mechanisms, such as uncracked-ligament bridging.     

单向纤维增强陶瓷基复合材料单轴拉伸行为

采用细观力学方法对单向纤维增强陶瓷基复合材料的单轴拉伸应力-应变行为进行了研究。采用Budiansky-Hutchinson-Evans（BHE）剪滞模型分析了复合材料出现损伤时的细观应力场,结合临界基体应变能准则、应变能释放率准则以及Curtin统计模型三种单一失效模型分别描述陶瓷基复合材料基体开裂、界面脱粘以及纤维失效三种损伤机制,确定了基体裂纹间隔、界面脱粘长度和纤维失效体积分数。将剪滞模型与3种单一失效模型相结合,对各个损伤阶段的应力-应变曲线进行模拟,建立了准确的复合材料强韧性预测模型,并讨论了界面参数和纤维韦布尔模量对复合材料损伤以及应力-应变曲线的影响。与室温下陶瓷基复合材料单轴拉伸试验数据进行了对比,各个损伤阶段的应力-应变、失效强度及应变与试验数据吻合较好。