Boundary-type hydrodynamic analysis of tooth movement

The mechanical representation of the periodontal ligament (PDL) that surrounds each human tooth is still an enigma for both bioengineers and orthodontists. The assumption of nearly incompressible PDL leads to Reynolds' equations in curvilinear co-ordinates along the boundary of the tooth. This paper deals with a two-dimensional rigid tooth of arbitrary shape and introduces a boundary-type symmetric stiffness matrix of order 3×3 that correlates the applied force-system on the tooth to its three displacements: two translations and one rotation. The elements of this matrix are calculated using one-dimensional Gaussian quadrature along the open boundary of the tooth in contact with the PDL. The efficiency of the method is sustained by two test cases: a typical wedge- and a parabolic-shaped root using two linear and one quadratic element, respectively. For both cases, the location of the centre of resistance, the centre of rotation and the distribution of the pressure are calculated.     

Stress distribution in dental implant with elastomeric stress barrier

Dental implant has been used and studied for the replacement of missing teeth for many years. It has been well known that the success of dental implant is heavily dependent on initial stability and long-term Osseointegration due to optimal stress distribution in the surrounding bones. For this reason, the search of the rational solutions to reduce these stresses has become an important issue in this field. Alternatives to reduce the forces transmitted to implants have been studied, including variations in implant positioning, implant design, prosthesis shape, occlusal requirements, prosthetic components and prosthetic materials. Thus, a new concept of adding a bio-elastomer to the prosthetic components of implant system was interposed between the abutment and the framework crown in order to damp the occlusive shocks and to attenuate the stress concentrated at the implant/bone interface. The new implant system design was assessed by the three dimensional finite element techniques using ABAQUS program to study the effect of elastomer material under an occlusal load on the induced equivalent von Mises interface stresses. These stresses were compared with those provoked by the standardized implant. The von Mises stress distribution indicated that stress was maximal around the top of the implant with varying intensities in the different loading cases. The stress was highest in the cortical bone at the neck of implant and lowest in the cancellous bone. Overall, the novel implant provoked lower interface stresses only in the cortical bone due to the stress shielding effect of the elastomeric stress barrier.     

基于精确齿面建模的ZA蜗杆蜗轮有限元接触分析

为了研究不同情况下蜗杆蜗轮间的接触应力和蜗杆扭转角与驱动力矩之间的关系,根据齿面方程建立具有精确齿面的ZA蜗杆蜗轮实体模型,利用ANSYS对此模型在同一载荷不同啮合位置和同一啮合位置不同载荷条件下进行有限元接触分析,研究在一个轮齿啮合周期内,各啮合齿对的接触应力分布和载荷在不同齿对上的分配情况.分析结果表明:理论接触应...     

Finite Element Analysis and Experimental Measurement of Deformation Behavior for NiTi Plate With Stress Concentration Part Under Uniaxial Tensile Loading

Abstract: The aim of this study is to verify the effectiveness of ordinary phenomenological constitutive relation of NiTi shape memory alloy under mechanical loading at a constant temperature, sufficiently. First, finite element analysis is performed by using ordinary phenomenological constitutive relation for rectangular plate with double notch under tensile loading at a constant temperature. Next, uniaxial tensile loading is carried out for 50.5Ni49.5Ti rectangular plate with double notch. At the same time, macroscopic stress–strain curve and local strain distribution are measured by using in‐house measurement system on the basis of digital image correlation. As a result, it is found that the stress–strain curve obtained from finite element analysis is much different from those obtained experimental measurement, especially during stress‐induced martensite transformation. The result can be derived from the phenomena of local strain band behavior arising in NiTi under mechanical loading. The phenomenological constitutive model used in present finite element analysis is constructed under assumptions that the material has isotropic characteristics and shows homogeneous deformation. However, this experimental result suggests that the material itself has anisotropy microscopically. Furthermore, material shows unique inhomogeneous deformation. Also, there is possibility that these anisotropic characteristic and inhomogeneous deformation behaviour may derive from its microstructure. In future, to sufficiently describe the macroscopic stress–strain curve of NiTi we should take into consideration the material microstructure.     

Thermomechanical characterization of stress localization in glass: An experimental and numerical study

Thermoelastic stress analysis and quantitative calorimetry are full‐field noncontact techniques widely used to study the thermomechanical behaviour of materials. The first one linearly relates the sum of the principal stresses to the temperature variation, and the second one can be used to measure the mechanical dissipation. However, brittle materials such as glass are a priori bad candidates for these techniques. Indeed, their low‐temperature variations under loading lead to very noisy infrared images, and their brittle mechanical behaviour does not allow to deform them significantly. In the present paper, the thermomechanical characterization of a holed glass sample under cyclic loading is performed. A preliminary new filtering methodology has been applied to the thermal movie to remove the noise. The stress field obtained from the thermoelastic stress analysis is well correlated to the finite element model showing that this technique is adapted to study the thermoelastic response of brittle materials. Finally, the corresponding calorimetric response has been determined by using a simplified formulation of the heat diffusion equation. This permits to quantify heat sources and to carry out energy balances.     

Stress analysis in bone tissue around single implants with different diameters and veneering materials: A 3-D finite element study

The aim of this study was to evaluate the stress distribution on bone tissue with a single prosthesis supported by implants of large and conventional diameter and presenting different veneering materials using the 3-D finite element method. Sixteen models were fabricated to reproduce a bone block with implants, using two diameters (3.75 × 10 mm and 5.00 × 10 mm), four different veneering materials (composite resin, acrylic resin, porcelain, and NiCr crown), and two loads (axial (200 N) and oblique (100 N)). For data analysis, the maximum principal stress and von Mises criterion were used. For the axial load, the cortical bone in all models did not exhibit significant differences, and the trabecular bone presented higher tensile stress with reduced implant diameter. For the oblique load, the cortical bone presented a significant increase in tensile stress on the same side as the loading for smaller implant diameters. The trabecular bone showed a similar but more discreet trend. There was no difference in bone tissue with different veneering materials. The veneering material did not influence the stress distribution in the supporting tissues of single implant-supported prostheses. The large-diameter implants improved the transference of occlusal loads to bone tissue and decreased stress mainly under oblique loads. Oblique loading was more detrimental to distribution stresses than axial loading.     

An automatic design optimization procedure to minimize fillet bending stresses in involute spur gears

This paper presents the development of an automatic design algorithm for gears. The criterion on which the design performance is assessed is the maximum tensile stress induced in the gear tooth fillet under service conditions. Starting from an initial set of design parameters the stresses in the gear tooth fillet are calculated. The maximum value of the stress is then expressed as a function of the design variables. By minimizing this function, the objective function, subject to both equality and inequality constraints a new set of design parameters, is produced. Iterative application of the analysis and minimization stages forms a sequence of non-linear optimization problems which converges to yield the optimal design. Finite element techniques employed to calculate accurately the stresses in the gear tooth are again used to compute the design derivatives. This process is very economical, owing to its efficient reuse of the factorized stiffness matrix. The algorithm is illustrated by its application to a spur gear tooth of involute profile. Both linear and non-linear forms of the objective function are used and a comparison made between the solutions obtained.     

Algorithms for automated meshing and unit cell analysis of periodic composites with hierarchical tri‐quadratic tetrahedral elements

Unit cell homogenization techniques together with the finite element method are very effective for computing equivalent mechanical properties of composites and heterogeneous materials systems. For systems with very complicated material arrangements, traditional, manual mesh generation can be a considerable obstacle to usage of these techniques. This problem is addressed here by developing automated meshing techniques that start from a hierarchical quad‐tree (in 2D) or oc‐tree (in 3D) mesh of pixel or voxel elements. From the pixel/voxel mesh, algorithms are presented for successive element splitting and nodal shifting to arrive at final meshes that accurately capture both material arrangements and constituent volume fractions, and the material‐scale stress and strain fields within the composite under different modalities of loading. The performance and associated convergence behaviour of the proposed techniques are demonstrated on both densely packed fibre and particulate composites, and on 3D textile‐reinforced composites. Copyright © 2003 John Wiley Sons, Ltd.     

A numerical investigation of porous titanium as orthopedic implant material

Porous titanium is being developed as an alternative orthopedic implant material to alleviate the inherent problems of bulk metallic implants by reducing the stiffness to be comparable to bone stiffness and allowing complete bone ingrowth. However, a porous microstructure is susceptible to local permanent plastic strain and residual stress under cyclic loading which reduces damage tolerance and therefore limits their application as orthopedic implants. The mechanical properties of porous titanium are governed by the microstructural configurations such as pore morphology, porosity, and bone ingrowth. To understand the influence of these features on performance, the macroscopic and microscopic responses of porous Ti are studied using three-dimensional finite element models. The models are generated based on simulated microstructures of experimental materials at porosities of 15%, 32% and 50%. The results show the effect of porosity and bone ingrowth on Young’s modulus, yield stress, and microscopic stress and strain distribution. Importantly, simulations predict that the bone ingrowth reduces the stress and strain localization under cyclic loading so significantly that it counteracts the concentration condition caused by the increased porosity of the structure.     

Analysis of fracture behaviour of the cement mantle of reconstructed acetabulum

In this study, the finite element method was used to analyse the crack behaviour in the cement of a reconstructed acetabulum by computing the stress intensity factors at the crack tip. Three loading cases were examined (Fig. 6). These cases present the different human body postures. Both positions and orientations of crack effect on the SIF variation were analysed. When valuating the crack position effect, one notices no risk of crack propagation under the load type 1; however, under the load type 2 and the load type 3 this risk is more important. Load type 3 is the most dangerous loading condition. When computing crack orientation, one noted that the risk of crack propagation is higher when the crack inclination is 20° and 100°.     

On the solution of the centre cracked plate with a quadratic thermal gradient

The problem of a centre-cracked plate of finite crack length to plate width ratio when subjected to a quadratic thermal gradient is studied. Stress intensity factors are derived from elastic analysis using an analytical approach and the finite element method. The analytical approach is exact only for an infinitely wide plate so that the finite element results enable the evaluation of finite width correction factors. Various techniques for evaluating the stress intensity factor under thermal loading are reviewed, and the preferred ones are applied to the present problem. The resulting finite width correction factors are compared to those derived for the tensile Mode I loading case.     

A finite-element model study of occlusal schemes in full-arch implant restoration

A three-dimensional finite-element model of a human mandible is presented, and the stresses and deformations computed for loading states induced by two different gnathologic reconstructions using six and four implants are discussed. Occlusal canine guidance and posterior and anterior group functions on cantilevered and distally supported prostheses have been simulated. The stress distributions generated by the different loading conditions on either the osseointegrated prosthesis or the bone tissue surrounding the implants are described. The analysis of the stress distribution on the working side reveals that the posterior group function undergoes a reduction in stress intensity on the cortical bone surrounding the implants (especially for the distal implant) compared with the anterior group function and canine guidance in both gnathologic reconstructions. © 1998 Chapman & Hall     

Applications of normal stress dominated cohesive zone models for mixed-mode crack simulation based on extended finite element methods

In conventional cohesive zone models the traction-separation law starts from zero load, so that the model cannot be applied to predict mixed-mode cracking. In the present work the cohesive zone model with a threshold is introduced and applied for simulating different mixed-mode cracks in combining with the extended finite element method. Computational results of cracked specimens show that the crack initiation and propagation under mixed-mode loading conditions can be characterized by the cohesive zone model for normal stress failure. The contribution of the shear stress is negligible. The maximum principal stress predicts crack direction accurately. Computations based on XFEM agree with known experiments very well. The shear stress becomes, however, important for uncracked specimens to catch the correct crack initiation angle. To study mixed-mode cracks one has to introduce a threshold into the cohesive law and to implement the new cohesive zone based on the fracture criterion. In monotonic loading cases it can be easily realized in the extended finite element formulation. For cyclic loading cases convergence of the inelastic computations can be critical.     

Experimental–Numerical Investigation on the Biomimetic Recovery of Natural Tooth Structural Response after Porcelain Veneer Restoration

Abstract: This study analyzes the effect of porcelain veneer restoration on the structural response of a maxillary incisor. Tooth deformation is evaluated, prior to and after restoration, by the synergic use of Phase‐Shifting Electronic Speckle Pattern Interferometry (PS‐ESPI) and 3D finite element (FE) analyses. The intact maxillary incisor and the porcelain veneer restored tooth are subject to flexural load. Displacement fields are measured with Phase‐Shifting Electronic Speckle Pattern Interferometry. Experimental tests are simulated with 3D FE analyses tuning materials parameters via an optimisation‐based inverse procedure. ESPI measurements indicate that the restoration design under study produced deformations very similar to those of the intact tooth under load. FE results show sharp changes in displacement and stress 1 mm above the cement–enamel junction on the facial side of the restored tooth. Severe stress concentration (about 50% increase with respect to natural tooth) appears at the interface between veneer restoration and intact enamel and dentine tissues. This confirms the hypothesis that veneer restorations can amplify the effect of occlusal loading on the loss of dental hard tissue in the tooth cervical region.     

Characterisation of a metallic foam–cement composite under selected loading conditions

An open-cell metallic foam was employed as an analogue material for human trabecular bone to interface with polymethyl methacrylate (PMMA) bone cement to produce composite foam–cement interface specimens. The stress-displacement curves of the specimens were obtained experimentally under tension, shear, mixed tension and shear (mixed-mode), and step-wise compression loadings. In addition, under step-wise compression, an image-guided failure assessment (IGFA) was used to monitor the evolution of micro-damage of the interface. Microcomputed tomography (µCT) images were used to build a subject-specific model, which was then used to perform finite element (FE) analysis under tension, shear and compression. For tension–shear loading conditions, the strengths of the interface specimens were found to increase with the increase of the loading angle reaching the maximum under shear loading condition, and the results compare reasonably well with those from bone–cement interface. Under compression, however, the mechanical strength measured from the foam–cement interface is much lower than that from bone–cement interface. Furthermore, load transfer between the foam and the cement appears to be poor under both tension and compression, hence the use of the foam should be discouraged as a bone analogue material for cement fixation studies in joint replacements.     

Numerical and experimental analysis of residual stresses for fatigue crack growth

In this paper computational and experimental results are presented concerning residual stress effects on fatigue crack growth in a Compact Tension Shear (CTS) specimen under cyclic mode I loading. For a crack of constant length it is found that hardly any compressive residual stresses or crack closure effects are generated along the crack surfaces behind the crack tip through the considered cyclic mode I loading with a load ratio of R=0.1. Only if fatigue crack growth is modelled during the simulation of the cyclic loading process these well-known effects are found. On the other hand it is shown that they have hardly any influence on the residual stresses ahead of the crack tip and thus on further fatigue crack growth. For all cases considered the computational finite element results agree well with the experimental findings obtained through X-ray diffraction techniques.     

行星滚柱丝杠副运转过程动态特性分析

以行星滚柱丝杠副为研究对象,建立行星滚柱丝杠副有限元模型。基于显式动力学有限元算法,采用全积分单元进行沙漏控制,通过调整单元密度和采用混合时间积分算法提高计算速度,对行星滚柱丝杠副进行动态特性分析。分析结果表明：随着滚柱转速增大,丝杠相对滚柱的轴向位移、速度大小及波动幅度均变大;不同转速下,螺纹牙上同一接触单元von Mises应力基本一致;同一转速下,丝杠副的4个螺纹牙上的接触单元均存在载荷分布不均现象,且第1个螺纹牙上的von Mises应力波动最大;丝杠侧接触单元von Mises应力大于螺母侧接触单元von Mises应力。     

基于接触应力优化的摆线轮修形设计

对摆线轮进行合理的修形能够极大改善RV（rotary vector,旋转矢量）减速器的传动性能和承载能力。为了进一步优化“反弓”齿廓的接触应力,在综合分析组合修形对反弓齿廓啮合力和接触应力的影响的基础上,提出了一种两段修形方法。该方法是将摆线轮齿廓分成2段,并根据需要对不同工作段的齿廓采用不同的修形量,以更灵活地设计摆线轮的齿廓。以RV-40E减速器为例,先利用MATLAB软件建立摆线轮受力分析模型,并按照两段修形方法确定新齿廓的修形量和方程;再利用ANSYS软件建立摆线轮与针齿接触的有限元模型,并对比新齿廓与反弓齿廓的接触应力。理论计算结果显示,新齿廓的最大接触应力降低了8.34%;有限元仿真结果显示,新齿廓的最大接触应力降低了4.39%,并分析了可能的误差来源。研究表明,两段修形方法可以改善摆线轮齿廓的接触应力和延长摆线轮的使用寿命,这为摆线轮的修形设计提供了一定的参考。     

弯曲载荷下机织复合材料T型接头渐进失效分析

根据树脂传递模塑(RTM)成型的缎纹机织复合材料T型接头的结构特征和纤维布局特点, 基于ANSYS有限元数值分析平台, 建立符合其真实结构的几何模型和有限元分析模型。基于渐进失效强度预测方法的基本思想, 使用有限元计算软件ANSYS的参数化设计语言(APDL)开发相应的程序, 实现改进形式的Hashin失效准则。采用合适的最终失效评价方法, 建立二维机织结构复合材料T型接头受弯曲载荷时的渐进失效预测方法, 能够有效地模拟从初始加载到最终失效过程中机织复合材料T型接头结构的力学响应及损伤的萌生与发展, 并预测结构的静强度。      

Dynamic micromechanical modeling of textile composite strength under impact and multi-axial loading

Micromechanical finite element modeling has been employed to define the failure behavior of S2 glass/BMI textile composite materials under impact loading. Dynamic explicit analysis of a representative volume element (RVE) has been performed to explore dynamic behavior and failure modes including strain rate effects, damage localization, and impedance mismatch effects. For accurate reflection of strain rate effects, differences between an applied nominal strain rate across a representative volume element (RVE) and the true realized local strain rates in regions of failure are investigated. To this end, contour plots of strain rate, as well as classical stress contours, are developed during progressive failure. Using a previously developed cohesive element failure model, interfacial failure between tow and matrix phases is considered, as well as classical failure modes such as fiber breakage and matrix microcracking. In-plane compressive and tensile loading have been investigated, including multi-axial loading cases. Highly refined meshes have been employed to ensure convergence and accuracy in such load cases which exhibit large stress gradients across the textile RVE. The effect of strain rate and phase interfacial strength have been included to develop macro-level material failure envelopes for a 2D plain weave and 3D orthogonal microgeometry.