Review of continuum, finite element and hybrid techniques in the analysis of stress concentrations in structures

When a uniform flow of any nature is interrupted, the readjustment of the flow results in concentrations and rare-factions, so that the peak value of the flow parameter will be higher than that which an elementary computation would suggest. When stress flow in a structure is interrupted, there are stress concentrations. These are generally localized and often large, in relation to the values indicated by simple equilibrium calculations. With the advent of the industrial revolution, dynamic and repeated loading of materials had become commonplace in engine parts and fast moving vehicles of locomotion. This led to serious fatigue failures arising from stress concentrations. Also, many metal forming processes, fabrication techniques and weak-link type safety systems benefit substantially from the intelligent use or avoidance, as appropriate, of stress concentrations. As a result, in the last 80 years, the study and and evaluation of stress concentrations has been a primary objective in the study of solid mechanics. Exact mathematical analysis of stress concentrations in finite bodies presents considerable difficulty for all but a few problems of infinite fields, concentric annuli and the like, treated under the presumption of small deformation, linear elasticity. A whole series of techniques have been developed to deal with different classes of shapes and domains, causes and sources of concentration, material behaviour, phenomenological formulation, etc. These include real and complex functions, conformal mapping, transform techniques, integral equations, finite differences and relaxation, and, more recently, the finite element methods. With the advent of large high speed computers, development of finite element concepts and a good understanding of functional analysis, it is now, in principle, possible to obtain with economy satisfactory solutions to a whole range of concentration problems by intelligently combining theory and computer application. An example is the hybridization of continuum concepts with computer based finite element formulations. This new situation also makes possible a more direct approach to the problem of design which is the primary purpose of most engineering analyses. The trend would appear to be clear: the computer will shape the theory, analysis and design.

Influence of crown-to-implant ratio, retention system, restorative material, and occlusal loading on stress concentrations in single short implants

Purpose: The aim of this study was to assess the contributions of some prosthetic parameters such as crown-to-implant (C/I) ratio, retention system, restorative material, and occlusal loading on stress concentrations within a single posterior crown supported by a short implant. Materials and Methods: Computer-aided design software was used to create 32 finite element models of an atrophic posterior partially edentulous mandible with a single external-hexagon implant (5 mm wide × 7 mm long) in the first molar region. Finite element analysis software with a convergence analysis of 5% to mesh refinement was used to evaluate the effects of C/I ratio (1:1; 1.5:1; 2:1, or 2.5:1), prosthetic retention system (cemented or screwed), and restorative material (metal-ceramic or all ceramic). The crowns were loaded with simulated normal or traumatic occlusal forces. The maximum principal stress (σmax) for cortical and cancellous bone and von Mises stress (σvM) for the implant and abutment screw were computed and analyzed. The percent contribution of each variable to the stress concentration was calculated from the sum of squares analysis. Results: Traumatic occlusion and a high C/I ratio increased stress concentrations. The C/I ratio was responsible for 11.45% of the total stress in the cortical bone, whereas occlusal loading contributed 70.92% to the total stress in the implant. The retention system contributed 0.91% of the total stress in the cortical bone. The restorative material was responsible for only 0.09% of the total stress in the cancellous bone. Conclusion: Occlusal loading was the most important stress concentration factor in the finite element model of a single posterior crown supported by a short implant.

Stress analysis of carotid atheroma in transient ischemic attack patients: Evidence for extreme stress-induced plaque rupture

Plaque rupture has been considered to be the result of its structural failure. The aim of this study is to suggest a possible link between higher stresses and rupture sites observed from in vivo magnetic resonance imaging (MRI) of transient ischemic attack (TIA) patients, by using stress analysis methods. Three patients, who had recently suffered a TIA, underwent in vivo multi-spectral MR imaging. Based on plaque geometries reconstructed from the post-rupture status, six pre-rupture plaque models were generated for each patient dataset with different reconstructions of rupture sites to bridge the gap of fibrous cap from original MRI images. Stress analysis by fluid structure interaction simulation was performed on the models, followed by analysis of local stress concentration distribution and plaque rupture sites. Furthermore, the sensitivity of stress analysis to the pre-rupture plaque geometry reconstruction was examined. Local stress concentrations were found to be located at the plaque rupture sites for the three subjects studied. In the total of 18 models created, the locations of the stress concentration regions were similar in 17 models in which rupture sites were always associated with high stresses. The local stress concentration region moved from circumferential center to the shoulder region (slightly away from the rupture site) for a case with a thick fibrous cap. Plaque wall stress level in the rupture locations was found to be much higher than the value in non-rupture locations. The good correlation between local stress concentrations and plaque rupture sites, and generally higher plaque wall stress level in rupture locations in the subjects studied could provide indirect evidence for the extreme stress-induced plaque rupture hypothesis. Local stress concentration in the plaque region could be one of the factors contributing to plaque rupture.

Stress analysis of carotid atheroma in a transient ischaemic attack patient using the MRI-based fluid-structure interaction method

Rupture of atherosclerotic plaque is a major cause of mortality. Plaque stress analysis, based on patient-specific multisequence in vivo MRI, can provide critical information for the understanding of plaque rupture and could eventually lead to plaque rupture prediction. However, the direct link between stress and plaque rupture is not fully understood. In the present study, the plaque from a patient who recently experienced a transient ischaemic attack (TIA) was studied using a fluid-structure interaction method to quantify stress distribution in the plaque region based on in vivo MR images. The results showed that wall shear stress is generally low in the artery with a slight increase at the plaque throat owing to minor luminal narrowing. The oscillatory shear index is much higher in the proximal part of the plaque. Both local wall stress concentrations and the relative stress variation distribution during a cardiac cycle indicate that the actual plaque rupture site is collocated with the highest rupture risk region in the studied patient.

Carotid arterial plaque stress analysis using fluid-structure interactive simulation based on in-vivo magnetic resonance images of four patients

The rupture of atherosclerotic plaques is known to be associated with the stresses that act on or within the arterial wall. The extreme wall tensile stress (WTS) is usually recognized as a primary trigger for the rupture of vulnerable plaque. The present study used the in-vivo high-resolution multi-spectral magnetic resonance imaging (MRI) for carotid arterial plaque morphology reconstruction. Image segmentation of different plaque components was based on the multi-spectral MRI and co-registered with different sequences for the patient. Stress analysis was performed on totally four subjects with different plaque burden by fluid-structure interaction (FSI) simulations. Wall shear stress distributions are highly related to the degree of stenosis, while the level of its magnitude is much lower than the WTS in the fibrous cap. WTS is higher in the luminal wall and lower at the outer wall, with the lowest stress at the lipid region. Local stress concentrations are well confined in the thinner fibrous cap region, and usually locating in the plaque shoulder; the introduction of relative stress variation during a cycle in the fibrous cap can be a potential indicator for plaque fatigue process in the thin fibrous cap. According to stress analysis of the four subjects, a risk assessment in terms of mechanical factors could be made, which may be helpful in clinical practice. However, more subjects with patient specific analysis are desirable for plaque-stability study.

Stress transfer and damage evolution simulations of fiber-reinforced polymer-matrix composites

The stress transfer from broken fibers to unbroken fibers in fiber-reinforced thermosetting polymer-matrix composites and thermoplastic polymer-matrix composites was studied using a detailed finite element model. In order to check the validity of this approach, an epoxy-matrix monolayer composite was used as thermosetting polymer-matrix composite and a polypropylene (PP)-matrix monolayer composite was used as thermoplastic polymer-matrix composite, respectively. It is found that the stress concentrations near the broken fiber element cause damage to the neighboring epoxy matrix prior to the breakage of other fibers, whereas in the case of PP-matrix composites the fibers nearest to the broken fiber break prior to the PP matrix damage, because the PP matrix around the broken fiber element yields. In order to simulate composite damage evolution, a Monte Carlo technique based on a finite element method has been developed in the paper. The finite element code coupled with statistical model of fiber strength specifically written for this problem was used to determine the stress redistribution. Five hundred samples of numerical simulation were carried out to obtain statistical deformation and failure process of composites with fixed fiber volume fraction.

Photoelastic Stress Analysis in Screwed and Cemented Implant-Supported Dentures With External Hexagon Implants

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Photoelastic Analysis of the Influence of Platform Switching on Stress Distribution in Implants

The aim of this study was to evaluate the stress distribution of platform switching implants using a photoelastic method. Three models were constructed of the photoelastic resin PL-2, with a single implant and a screw-retained implant-supported prosthesis. These models were Model A, platform 5.0 mm/abutment 4.1 mm; Model B, platform 4.1 mm/abutment 4.1 mm; and Model C, platform 5.00 mm/abutment 5.00 mm. Axial and oblique (45 degrees) loads of 100 N were applied using a Universal Testing Machine (EMIC DL 3000). Images were photographed with a digital camera and visualized with software (AdobePhotoshop) to facilitate the qualitative analysis. The highest stress concentrations were observed at the apical third of the 3 models. With the oblique load, the highest stress concentrations were located at the implant apex, opposite the load application. Stress concentrations decreased in the cervical region of Model A (platform switching), and Models A (platform switching) and C (conventional/wide-diameter) displayed similar stress magnitudes. Finally, Model B (conventional/regular diameter) displayed the highest stress concentrations of the models tested.

Stress Analysis in Simulation Models With or Without Implant Threads Representation

Purpose: This study aimed to evaluate the influence of implants with or without threads representation on the outcome of a two-dimensional finite element (FE) analysis. Materials and Methods: Two-dimensional FE models that reproduced a frontal section of edentulous mandibular posterior bone were constructed using a standard crown/implant/screw system representation. To evaluate the effect of implant threads, two models were created: a model in which the implant threads were accurately simulated (precise model) and a model in which implants with a smooth surface (press-fit implant) were used (simplified model). An evaluation was performed on ANSYS software, in which a load of 133 N was applied at a 30-degree angulation and 2 mm off-axis from the long axis of the implant on the models, The Von Mises stresses were measured. Results: The precise model (1.45 MPa) showed higher maximum stress values than the simplified model (1.2 MPa). Whereas in the cortical bone, the stress values differed by about 36% (292.95 MPa for the precise model and 401.14 MPa for the simplified model), in trabecular bone (19.35 MPa and 20.35 MPa, respectively), the stress distribution and stress values were similar. Stress concentrations occurred around the implant neck and the implant apex. Conclusions: Considering implant and cortical bone analysis, remarkable differences in stress values were found between the models. Although the models showed different absolute stress values, the stress distribution was similar. INT J ORAL MAXILLOFAC IMPLANTS 2009;24:1040-1044

Finite Element Stress Analysis of Edentulous Mandibles with Different Bone Types Supporting Multiple-Implant Superstructures

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Stress analysis of an upper central incisor restored with different posts

The effect of different anatomic shapes and materials of posts in the stress distribution on an endodontically treated incisor was evaluated in this work. This study compared three post shapes (tapered, cylindrical and two-stage cylindrical) made of three different materials (stainless steel, titanium and carbon fibre on Bisphenol A-Glycidyl Methacrylate (Bis-GMA) matrix). Two-dimensional stress analysis was performed using the Finite Element Method. A static load of 100N was applied at 45degrees inclination with respect to the incisor's edge. The stress concentrations did not significantly affect the region adjacent to the alveolar bone crest at the palatine portion of the tooth, regardless of the post shape or material. However, stress concentrations on the post/dentin interface on the palatine side of the tooth root presented significant variations for different post shapes and materials. Post shapes had relatively small impact on the stress concentrations while post materials introduced higher variations on them. Stainless steel posts presented the highest level of stress concentration, followed by titanium and carbon/Bis-GMA posts.

Influence of high insertion torque on implant placement - an anisotropic bone stress analysis

The aim of this study was to evaluate the influence of the high values of insertion torques on the stress and strain distribution in cortical and cancellous bones. Based on tomography imaging, a representative mathematical model of a partial maxilla was built using Mimics 11.11 and Solid Works 2010 softwares. Six models were built and each of them received an implant with one of the following insertion torques: 30, 40, 50, 60, 70 or 80 Ncm on the external hexagon. The cortical and cancellous bones were considered anisotropic. The bone/implant interface was considered perfectly bonded. The numerical analysis was carried out using Ansys Workbench 10.0. The convergence of analysis (6%) drove the mesh refinement. Maximum principal stress (σ max) and maximum principal strain (ε max) were obtained for cortical and cancellous bones around to implant. Pearson's correlation test was used to determine the correlation between insertion torque and stress concentration in the periimplant bone tissue, considering the significance level at 5%. The increase in the insertion torque generated an increase in the σ max and ε max values for cortical and cancellous bone. The σmax was smaller for the cancellous bone, with greater stress variation among the insertion torques. The ε max was higher in the cancellous bone in comparison to the cortical bone. According to the methodology used and the limits of this study, it can be concluded that higher insertion torques increased tensile and compressive stress concentrations in the periimplant bone tissue.