Finite element analysis predicts experimental failure patterns in vertebral bodies loaded via intervertebral discs up to large deformation

Vertebral compression fracture is a common medical problem in osteoporotic individuals. The quantitative computed tomography (QCT)-based finite element (FE) method may be used to predict vertebral strength in vivo, but needs to be validated with experimental tests. The aim of this study was to validate a nonlinear anatomy specific QCT-based FE model by using a novel testing setup. Thirty-seven human thoracolumbar vertebral bone slices were prepared by removing cortical endplates and posterior elements. The slices were scanned with QCT and the volumetric bone mineral density (vBMD) was computed with the standard clinical approach. A novel experimental setup was designed to induce a realistic failure in the vertebral slices in vitro. Rotation of the loading plate was allowed by means of a ball joint. To minimize device compliance, the specimen deformation was measured directly on the loading plate with three sensors. A nonlinear FE model was generated from the calibrated QCT images and computed vertebral stiffness and strength were compared to those measured during the experiments. In agreement with clinical observations, most of the vertebrae underwent an anterior wedge-shape fracture. As expected, the FE method predicted both stiffness and strength better than vBMD (R2 improved from 0.27 to 0.49 and from 0.34 to 0.79, respectively). Despite the lack of fitting parameters, the linear regression of the FE prediction for strength was close to the 1:1 relation (slope and intercept close to one (0.86 kN) and to zero (0.72 kN), respectively). In conclusion, a nonlinear FE model was successfully validated through a novel experimental technique for generating wedge-shape fractures in human thoracolumbar vertebrae.

Dynamic analysis of road vehicle-bridge systems under turbulent wind by means of Finite Element Models

When an automobile passes over a bridge dynamic effects are produced in vehicle and structure. In addition, the bridge itself moves when exposed to the wind inducing dynamic effects on the vehicle that have to be considered. The main objective of this work is to understand the influence of the different parameters concerning the vehicle, the bridge, the road roughness or the wind in the comfort and safety of the vehicles when crossing bridges. Non linear finite element models are used for structures and multibody dynamic models are employed for vehicles. The interaction between the vehicle and the bridge is considered by contact methods. Road roughness is described by the power spectral density (PSD) proposed by the ISO 8608. To consider that the profiles under right and left wheels are different but not independent, the hypotheses of homogeneity and isotropy are assumed. To generate the wind velocity history along the road the Sandia method is employed. The global problem is solved by means of the finite element method. First the methodology for modelling the interaction is verified in a benchmark. Following, the case of a vehicle running along a rigid road and subjected to the action of the turbulent wind is analyzed and the road roughness is incorporated in a following step. Finally the flexibility of the bridge is added to the model by making the vehicle run over the structure. The application of this methodology will allow to understand the influence of the different parameters in the comfort and safety of road vehicles crossing wind exposed bridges. Those results will help to recommend measures to make the traffic over bridges more reliable without affecting the structural integrity of the viaduct

A dynamic programming approach to the formulation and solution of finite element equations

A method for formulating and algorithmically solving the equations of finite element problems is presented. The method starts with a parametric partition of the domain in juxtaposed strips that permits sweeping the whole region by a sequential addition (or removal) of adjacent strips. The solution of the difference equations constructed over that grid proceeds along with the addition removal of strips in a manner resembling the transfer matrix approach, except that different rules of composition that lead to numerically stable algorithms are used for the stiffness matrices of the strips. Dynamic programming and invariant imbedding ideas underlie the construction of such rules of composition. Among other features of interest, the present methodology provides to some extent the analyst's control over the type and quantity of data to be computed. In particular, the one-sweep method presented in Section 9, with no apparent counterpart in standard methods, appears to be very efficient insofar as time and storage is concerned. The paper ends with the presentation of a numerical example

A Finite Element Numerical Algorithm for Modelling and Data Fitting in Complex Systems

Numerical modelling methodologies are important by their application to engineering and scientific problems, because there are processes where analytical mathematical expressions cannot be obtained to model them. When the only available information is a set of experimental values for the variables that determine the state of the system, the modelling problem is equivalent to determining the hyper-surface that best fits the data. This paper presents a methodology based on the Galerkin formulation of the finite elements method to obtain representations of relationships that are defined a priori, between a set of variables: y = z(x1, x2,...., xd). These representations are generated from the values of the variables in the experimental data. The approximation, piecewise, is an element of a Sobolev space and has derivatives defined in a general sense into this space. The using of this approach results in the need of inverting a linear system with a structure that allows a fast solver algorithm. The algorithm can be used in a variety of fields, being a multidisciplinary tool. The validity of the methodology is studied considering two real applications: a problem in hydrodynamics and a problem of engineering related to fluids, heat and transport in an energy generation plant. Also a test of the predictive capacity of the methodology is performed using a cross-validation method.

Parameters affecting the performance of wetting and drying in a two-dimensional finite element long wave hydrodynamic model

The marsh porosity method, a type of thin slot wetting and drying algorithm in a two-dimensional finite element long wave hydrodynamic model, is discussed and analyzed to assess model performance. Tests, including comparisons to simple examples and theoretical calculations, examine the effects of varying the marsh porosity parameters. The findings demonstrate that the wetting and drying concept of marsh porosity, often used in finite element hydrodynamic modeling, can behave in a more complex manner than initially expected.

Updating finite element models using measured vibration data

The modelling of mechanical structures using finite element analysis has become an indispensable stage in the design of new components and products. Once the theoretical design has been optimised a prototype may be constructed and tested. What can the engineer do if the measured and theoretically predicted vibration characteristics of the structure are significantly different? This thesis considers the problems of changing the parameters of the finite element model to improve the correlation between a physical structure and its mathematical model. Two new methods are introduced to perform the systematic parameter updating. The first uses the measured modal model to derive the parameter values with the minimum variance. The user must provide estimates for the variance of the theoretical parameter values and the measured data. Previous authors using similar methods have assumed that the estimated parameters and measured modal properties are statistically independent. This will generally be the case during the first iteration but will not be the case subsequently. The second method updates the parameters directly from the frequency response functions. The order of the finite element model of the structure is reduced as a function of the unknown parameters. A method related to a weighted equation error algorithm is used to update the parameters. After each iteration the weighting changes so that on convergence the output error is minimised. The suggested methods are extensively tested using simulated data. An H frame is then used to demonstrate the algorithms on a physical structure.

Modelling the human accommodation system using finite element analysis

The human accommodation system has been extensively examined for over a century, with a particular focus on trying to understand the mechanisms that lead to the loss of accommodative ability with age (Presbyopia). The accommodative process, along with the potential causes of presbyopia, are disputed; hindering efforts to develop methods of restoring accommodation in the presbyopic eye. One method that can be used to provide insight into this complex area is Finite Element Analysis (FEA). The effectiveness of FEA in modelling the accommodative process has been illustrated by a number of accommodative FEA models developed to date. However, there have been limitations to these previous models; principally due to the variation in data on the geometry of the accommodative components, combined with sparse measurements of their material properties. Despite advances in available data, continued oversimplification has occurred in the modelling of the crystalline lens structure and the zonular fibres that surround the lens. A new accommodation model was proposed by the author that aims to eliminate these limitations. A novel representation of the zonular structure was developed, combined with updated lens and capsule modelling methods. The model has been designed to be adaptable so that a range of different age accommodation systems can be modelled, allowing the age related changes that occur to be simulated. The new modelling methods were validated by comparing the changes induced within the model to available in vivo data, leading to the definition of three different age models. These were used in an extended sensitivity study on age related changes, where individual parameters were altered to investigate their effect on the accommodative process. The material properties were found to have the largest impact on the decline in accommodative ability, in particular compared to changes in ciliary body movement or zonular structure. Novel data on the importance of the capsule stiffness and thickness was also established. The new model detailed within this thesis provides further insight into the accommodation mechanism, as well as a foundation for future, more detailed investigations into accommodation, presbyopia and accommodative restoration techniques.

Three-dimensional finite element analysis of the effects of anisotropy on bone mechanical properties measured by nanoindentation

A three-dimensional finite element analysis (FEA) model with elastic-plastic anisotropy was built to investigate the effects of anisotropy on nanoindentation measurements for cortical bone. The FEA model has demonstrated a capability to capture the cortical bone material response under the indentation process. By comparison with the contact area obtained from monitoring the contact profile in FEA simulations, the Oliver-Pharr method was found to underpredict or overpredict the contact area due to the effects of anisotropy. The amount of error (less than 10% for cortical bone) depended on the indentation orientation. The indentation modulus results obtained from FEA simulations at different surface orientations showed a trend similar to experimental results and were also similar to moduli calculated from a mathematical model. The Oliver-Pharr method has been shown to be useful for providing first-order approximations in the analysis of anisotropic mechanical properties of cortical bone, although the indentation modulus is influenced by anisotropy.

Weak form equation–based finite-element modeling of viscoelastic asphalt mixtures

The objective of this study is to demonstrate using weak form partial differential equation (PDE) method for a finite-element (FE) modeling of a new constitutive relation without the need of user subroutine programming. The viscoelastic asphalt mixtures were modeled by the weak form PDE-based FE method as the examples in the paper. A solid-like generalized Maxwell model was used to represent the deforming mechanism of a viscoelastic material, the constitutive relations of which were derived and implemented in the weak form PDE module of Comsol Multiphysics, a commercial FE program. The weak form PDE modeling of viscoelasticity was verified by comparing Comsol and Abaqus simulations, which employed the same loading configurations and material property inputs in virtual laboratory test simulations. Both produced identical results in terms of axial and radial strain responses. The weak form PDE modeling of viscoelasticity was further validated by comparing the weak form PDE predictions with real laboratory test results of six types of asphalt mixtures with two air void contents and three aging periods. The viscoelastic material properties such as the coefficients of a Prony series model for the relaxation modulus were obtained by converting from the master curves of dynamic modulus and phase angle. Strain responses of compressive creep tests at three temperatures and cyclic load tests were predicted using the weak form PDE modeling and found to be comparable with the measurements of the real laboratory tests. It was demonstrated that the weak form PDE-based FE modeling can serve as an efficient method to implement new constitutive models and can free engineers from user subroutine programming.

Finite Element Simulations of stretch-blow moulding with experimental validation over a broad process window

Injection stretch blow moulding is a well-established method of forming thin-walled containers and has been extensively researched for numerous years. This paper is concerned with validating the finite element analysis of the free-stretch-blow process in an effort to progress the development of injection stretch blow moulding of poly(ethylene terephthalate). Extensive data was obtained experimentally over a wide process window accounting for material temperature and air flow rate, while capturing cavity pressure, stretch-rod reaction force and preform surface strain. This data was then used to assess the accuracy of the correlating FE simulation constructed using ABAQUS/Explicit solver and an appropriate viscoelastic material subroutine. Results reveal that the simulation is able to give good quantitative correlation for conditions where the deformation was predominantly equal biaxial whilst qualitative correlation was achievable when the mode of deformation was predominantly sequential biaxial. Overall the simulation was able to pick up the general trends of how the pressure, reaction force, strain rate and strain vary with the variation in preform temperature and air flow rate. The knowledge gained from these analyses provides insight into the mechanisms of bottle formation, subsequently improving the blow moulding simulation and allowing for reduction in future development costs.

Finite Element Modeling of Spiral Frequency Steerable Acoustic Transducers (FSATs) for guided waves based Structural Health Monitoring of plate-like structures

Structural Health Monitoring (SHM) is an emerging area of research associated to improvement of maintainability and the safety of aerospace, civil and mechanical infrastructures by means of monitoring and damage detection. Guided wave structural testing method is an approach for health monitoring of plate-like structures using smart material piezoelectric transducers. Among many kinds of transducers, the ones that have beam steering feature can perform more accurate surface interrogation. A frequency steerable acoustic transducer (FSATs) is capable of beam steering by varying the input frequency and consequently can detect and localize damage in structures. Guided wave inspection is typically performed through phased arrays which feature a large number of piezoelectric transducers, complexity and limitations. To overcome the weight penalty, the complex circuity and maintenance concern associated with wiring a large number of transducers, new FSATs are proposed that present inherent directional capabilities when generating and sensing elastic waves. The first generation of Spiral FSAT has two main limitations. First, waves are excited or sensed in one direction and in the opposite one (180 ̊ ambiguity) and second, just a relatively rude approximation of the desired directivity has been attained. Second generation of Spiral FSAT is proposed to overcome the first generation limitations. The importance of simulation tools becomes higher when a new idea is proposed and starts to be developed. The shaped transducer concept, especially the second generation of spiral FSAT is a novel idea in guided waves based of Structural Health Monitoring systems, hence finding a simulation tool is a necessity to develop various design aspects of this innovative transducer. In this work, the numerical simulation of the 1st and 2nd generations of Spiral FSAT has been conducted to prove the directional capability of excited guided waves through a plate-like structure.

Updating of Finite Element Models using static and dynamic optical strains with application to damage assessment

In the recent years, vibration-based structural damage identification has been subject of significant research in structural engineering. The basic idea of vibration-based methods is that damage induces mechanical properties changes that cause anomalies in the dynamic response of the structure, which measures allow to localize damage and its extension. Vibration measured data, such as frequencies and mode shapes, can be used in the Finite Element Model Updating in order to adjust structural parameters sensible at damage (e.g. Young’s Modulus). The novel aspect of this thesis is the introduction into the objective function of accurate measures of strains mode shapes, evaluated through FBG sensors. After a review of the relevant literature, the case of study, i.e. an irregular prestressed concrete beam destined for roofing of industrial structures, will be presented. The mathematical model was built through FE models, studying static and dynamic behaviour of the element. Another analytical model was developed, based on the ‘Ritz method’, in order to investigate the possible interaction between the RC beam and the steel supporting table used for testing. Experimental data, recorded through the contemporary use of different measurement techniques (optical fibers, accelerometers, LVDTs) were compared whit theoretical data, allowing to detect the best model, for which have been outlined the settings for the updating procedure.

Computational solid mechanics using a vertex-based finite volume method

A number of research groups are now developing and using finite volume (FV) methods for computational solid mechanics (CSM). These methods are proving to be equivalent and in some cases superior to their finite element (FE) counterparts. In this paper we will describe a vertex-based FV method with arbitrarily structured meshes, for modelling the elasto-plastic deformation of solid materials undergoing small strains in complex geometries. Comparisons with rational FE methods will be given.

Load balancing for aspect ratio in adaptive finite element simulations

In parallel adaptive finite element simulations the work load on the individual processors may change frequently. To (re)distribute the load evenly over the processors a load balancing heuristic is needed. Common strategies try to minimise subdomain dependencies by optimising the cutsize of the partitioning. However for certain solvers cutsize only plays a minor role, and their convergence is highly dependent on the subdomain shapes. Degenerated subdomain shapes cause them to need significantly more iterations to converge. In this work a new parallel load balancing strategy is introduced which directly addresses the problem of generating and conserving reasonably good subdomain shapes in a dynamically changing Finite Element Simulation. Geometric data is used to formulate several cost functions to rate elements in terms of their suitability to be migrated. The well known diffusive method which calculates the necessary load flow is enhanced by weighting the subdomain edges with the help of these cost functions. The proposed methods have been tested and results are presented.

A finite element framework for the interplay between delamination and buckling of rubber-like bi-material systems and stretchable electronics

In this study, a finite element (FE) framework for the analysis of the interplay between buckling and delamination of thin layers bonded to soft substrates is proposed. The current framework incorporates the following modeling features: (i) geometrically nonlinear solid shell elements, (ii) geometrically nonlinear cohesive interface elements, and (iii) hyperelastic material constitutive response for the bodies that compose the system. A fully implicit Newton–Raphson solution strategy is adopted to deal with the complex simultaneous presence of geometrical and material nonlinearities through the derivation of the consistent FE formulation. Applications to a rubber-like bi-material system under finite bending and to patterned stiff islands resting on soft substrate for stretchable solar cells subjected to tensile loading are proposed. The results obtained are in good agreement with benchmark results available in the literature, confirming the accuracy and the capabilities of the proposed numerical method for the analysis of complex three-dimensional fracture mechanics problems under finite deformations.