Variation of yield loci in finite element analysis by considering texture evolution for AA5042 aluminum sheets

 Yield function has various material parameters that describe how materials respond plastically in given conditions. However, a significant number of mechanical tests are required to identify the many material parameters for yield function. In this study, an effective method using crystal plasticity through a virtual experiment is introduced to develop the anisotropic yield function for AA5042. The crystal plasticity approach was used to predict the anisotropic response of the material in order to consider a number of stress or strain modes that would not otherwise be evident through mechanical testing. A rate-independent crystal plasticity model based on a smooth single crystal yield surface, which removes the innate ambiguity problem within the rate-independent model and Taylor model for polycrystalline deformation behavior were employed to predict the material’s response in the balanced biaxial stress, pure shear, and plane strain states to identify the parameters for the anisotropic yield function of AA5042.

Slope stability analysis for filled slopes using finite element limit analysis method

This paper uses the finite element upper and lower bound limit analysis to assess the stability of slopes mostly found in embankment cases where frictional materials are filled on purely cohesive undrained clay. For comparison purposes, the commonly used stability assessment method, limit equilibrium method (LEM) is also employed. The final results for both methods are then presented in the form of comprehensive chart solutions for the convenience of practicing engineers during preliminary slope designs. The failure mechanism will also be discussed in this paper. Ultimately, it should be noted that finite element limit analysis method holds the upper hand as its prior assumptions are not required. Thus, the obtained failure mechanism from the slope stability analysis will be more realistic. Hence, it will provide a better understanding for the slope failure surface. Therefore, engineers should design more carefully when the LEM is applied to the slopes with frictional materials filled on purely cohesive undrained clay. © 2014 American Society of Civil Engineers.

Finite element modeling and analysis of thrombosis in middle cerebral artery

Thrombotic stroke, which is caused by blood clot in the cerebral artery, is a major source of increased mortality and morbidity. Considering as efficient and fastest methods, mathematical approaches have gained significant importance for analyzing and understanding the biological events like thrombosis. This paper presents a computational model to analyze the effects of thrombosis using the theory of coupled fluid dynamics-structure interaction. The finite element method is used for the modeling of thrombosis (blood clot) of different stages in the middle cerebral artery with physiological compliance. The developed model is used to investigate the consequences that occur due to the various sizes of clots in the artery in the form of blood flow velocity, blood pressure, and artery wall stress. Such numerical assessment will facilitate better understanding of the biophysical process in case of thrombosis and thus would support medical practitioners to take faster curing steps.

Finite element analysis of residual stresses in metallic coatings through a compound casting

Al and Mg alloys are widely used in industry as main lightweight alloys. They have excellent properties, such as low density, high ductility, and high specific strength, and so on. Generally speaking, Mg alloys are better than Al alloys. However the corrosion of Mg alloys is much more difficult to control compared Al alloys. Therefore to combine these two lightweight alloys, a composite-like structure is an ideal solution since Al alloys can be used as protective coatings for Mg alloys. Compound casting is a realistic technique to get this coating system. In the current study, we numerically study the compound casting using finite element method (FEM) to make these two alloys, a composite-like structure, satisfy requirements to resist corrosion required from industry, in which the aluminum layer is acting as a protective coating for the magnesium substrate. Several finite element models have been developed by using the birth and death element technique and we focus on compound casting-induced residual stresses in the compounded structure. The numerical results obtained from the proposed finite element models show the distribution profiles of thermal residual stresses. We found the major factors influencing the residual stresses are the temperature to pre-heating the Al substrate and the thickness of Mg deposits. © (2014) Trans Tech Publications, Switzerland.

Slope stability charts for two-layered purely cohesive soils based on finite-element limit analysis methods

Stability charts for soil slopes, first produced in the first half of the twentieth century, continue to be used extensively as design tools, and draw the attention of many investigators. This paper uses finite-element upper and lower bound limit analysis to assess the short-term stability of slopes in which the slopematerial and subgrade foundation material have two distinctly different undrained strengths. The stability charts are proposed, and the exact theoretical solutions are bracketed to within 4.2% or better. In addition, results from the limit-equilibrium method (LEM) have been used for comparison. Differences of up to 20% were found between the numerical limit analysis and LEM solutions. It also shown that the LEM sometimes leads to errors, although it is widely used in practice for slope stability assessments.

Slope stability analysis for fill slopes using finite element limit analysis

This paper investigates the stability of fill slopes often found in embankment cases where frictional fill materials are placed on purely cohesive undrained clay with increasing strength. By using finite element upper and lower bound limit analysis for this investigation, the limit load can be truly bounded. It is known that two-dimensional analysis yields a more conservative result due to plain strain condition when compared to three-dimensional analysis. Therefore, this paper will focus on three-dimensional (3D) slope stability analysis and for comparison purposes two-dimensional analysis results will be employed. In fact, the final results are presented in the form of comprehensive chart solutions for the convenience of practicing engineers during preliminary slope design. The failure mechanism will also be discussed in order to further illustrate the situation during failure. It should be highlighted that the failure mechanisms are obtained through the numerical method itself and no prior assumptions are required, therefore, are more realistic and able to provide a better understanding for the slope failure surfaces.

Experimental and finite element analysis of machinability of AL-6XN super austenitic stainless steel

This paper presents a finite element cutting modelbased on physical microstructure to investigate the thermomechanicalbehaviour of AL-6XN Super AusteniticStainless Steel in the primary shear zone. Frozen chip rootsamples were created under dry turning operation to observethe plasticity behaviour occurring in the shear zones to comparewith the model for analysis. Chip samples were generatedunder cutting velocities at 65 and 94 m/min, feed rate at0.2 mm/rev and depth of cut at 1 mm. Temperature on thecutting zone was recorded by infrared thermal camera.Secondary and backscatter electron detectors were used toinvestigate the deformed microstructure and to calculate theplastic strain. Experimental results showed the formation ofmicrocracks (build-up edge triggers) at the chip root stagnationzone of both samples. The austenite phase patterns wereevident against the cutting tool tip in the stagnation zone of thechip root fabricated at 65 m/min. The movement of thesepatterns caused the formation of the slip lines within thegrains. The backscatter diffraction maps showed the formationof special grain boundaries within the slip lines, workhardeninglayer and in the chip region. Strain measurementsin the microstructures of the chip roots fabricated at 94 and65 m/min showed high values of 6.5 and 5.7 (mm/mm) respectively.The finite element model was used to measure thestress, strain, temperature and chip morphology. Numericalresults were compared to the outcomes of the experimentalwork to validate the finite element model. The model validatingprocess showed good agreement between theexperimental and numerical results, and the error values werecalculated. For a 94- and 65-m/min cutting speeds, 7.5 and5.2% were the errors in the strain, 3 and 2.5% were the error inthe temperature and 4.7 and 6.8% were the error in the shearplane angles.

Contact pressure and wear in sheet metal forming - an FEM analysis

Wear is the principal cause of tool failure in most sheet metal forming processes. It is well known that the contact pressure between the blank and the tool has a large influence on the wear of the tool, and hence the tool life. This investigation utilises the finite element method to analyse the contact pressure distribution over the die radius for a particular deep drawing process. Furthermore, the evolution of the predicted contact pressure distribution throughout the entire stroke of the punch is also examined. It was found that the majority of the process shows a steady state pressure distribution, with two characteristic peaks over the die radius, at the beginning and end of the sheet contact area. Interestingly, the initial transient contact pressure response showed extremely high localised peak pressures; more than twice that of the steady state peaks. Results are compared to wear reported in the literature, during similar experimental deep drawing processes. Finally, the significance and effect of the results on wear and wear-testing techniques are discussed.

Analysis of spherical indentation of superelastic shape memory alloys

Dimensional analysis and the finite element method are applied in this paper to study spherical indentation of superelastic shape memory alloys. The scaling relationships derived from dimensional analysis bridge the indentation response and the mechanical properties of a superelastic shape memory alloy. Several key variables of a superelastic indentation curve are revealed and examined. We prove that the bifurcation force in a superelastic indentation curve only relies on the forward transformation stress and the elastic properties of the initial austenite; and the return force in a superelastic indentation curve only relies on the reverse transformation stress and the elastic properties of the initial austenite. Furthermore, the dimensionless functions to determine the bifurcation force and the return force are proved to be identical. These results not only enhance our understanding of spherical indentation of superelastic shape memory alloys, but also provide the theoretical basis for developing a practicable method to calibrate the mechanical properties of a superelastic material from the spherical indentation test.

Computer aided ultrasonic thickness strain analysis of automotive sheet metal stampings using FEA information

This paper discusses a computer-aided methodology for thickness strain analysis (TSA) of sheet metal stampings using geometry and strain information that is extracted from finite element analysis (FEA) results. The system utilises both FEA results and an ultrasonic gauge capability expert system to assist press shop personnel, providing them with capabilities such as optimum measurement point location and an estimate of gauge error. Key advantages of this enhanced TSA methodology are related to overall efficiency and accuracy gains.

Design and analysis of hull configurations for a low-cost, autonomous underwater robot as an enabling technology for system of system applications

The objective of this research is to model and analyze candidate hull configurations for a low-cost, modular, autonomous underwater robot. As the computational power and speed of microprocessors continue to progress, we are seeing a growth in the research, development, and the utilization of underwater robots. The number of applications is broadening in the R&D and science communities, especially in the area of multiple, collaborative robots. These underwater collaborative robots represent an instantiation of a System of Systems (SoS). While each new researcher explores a unique application, control method, etc. a new underwater robot vehicle is designed, developed, and deployed. This sometimes leads to one-off designs that are costly. One limit to the wide-scale utilization of underwater robotics is the cost of development. Another limit is the ability to modify the configuration for new applications and evolving requirements. Consequently, we are exploring autonomous underwater vehicle (AUV) hull designs towards the goal of modularity, vehicle dexterity, and minimizing the cost. In our analysis, we have employed 3D solid modeling tools and finite element methods. In this paper we present our initial results and discuss ongoing work.

Stability theory and numerical analysis of non-autonomous dynamical systems

The development and use of cocycles for analysis of non-autonomous behaviour is a technique that has been known for several years. Initially developed as an extension to semi-group theory for studying rion-autonornous behaviour, it was extensively used in analysing random dynamical systems [2, 9, 10, 12]. Many of the results regarding asymptotic behaviour developed for random dynamical systems, including the concept of cocycle attractors were successfully transferred and reinterpreted for deterministic non-autonomous systems primarily by P. Kloeden and B. Schmalfuss [20, 21, 28, 29]. The theory concerning cocycle attractors was later developed in various contexts specific to particular classes of dynamical systems [6, 7, 13], although a comprehensive understanding of cocycle attractors (redefined as pullback attractors within this thesis) and their role in the stability of non-autonomous dynamical systems was still at this stage incomplete. It was this purpose that motivated Chapters 1-3 to define and formalise the concept of stability within non-autonomous dynamical systems. The approach taken incorporates the elements of classical asymptotic theory, and refines the notion of pullback attraction with further development towards a study of pull-back stability arid pullback asymptotic stability. In a comprehensive manner, it clearly establishes both pullback and forward (classical) stability theory as fundamentally unique and essential components of non-autonomous stability. Many of the introductory theorems and examples highlight the key properties arid differences between pullback and forward stability. The theory also cohesively retains all the properties of classical asymptotic stability theory in an autonomous environment. These chapters are intended as a fundamental framework from which further research in the various fields of non-autonomous dynamical systems may be extended. A preliminary version of a Lyapunov-like theory that characterises pullback attraction is created as a tool for examining non-autonomous behaviour in Chapter 5. The nature of its usefulness however is at this stage restricted to the converse theorem of asymptotic stability. Chapter 7 introduces the theory of Loci Dynamics. A transformation is made to an alternative dynamical system where forward asymptotic (classical asymptotic) behaviour characterises pullback attraction to a particular point in the original dynamical system. This has the advantage in that certain conventional techniques for a forward analysis may be applied. The remainder of the thesis, Chapters 4, 6 and Section 7.3, investigates the effects of perturbations and discretisations on non-autonomous dynamical systems known to possess structures that exhibit some form of stability or attraction. Chapter 4 investigates autonomous systems with semi-group attractors, that have been non-autonomously perturbed, whilst Chapter 6 observes the effects of discretisation on non-autonomous dynamical systems that exhibit properties of forward asymptotic stability. Chapter 7 explores the same problem of discretisation, but for pullback asymptotically stable systems. The theory of Loci Dynamics is used to analyse the nature of the discretisation, but establishment of results directly analogous to those discovered in Chapter 6 is shown to be unachievable. Instead a case by case analysis is provided for specific classes of dynamical systems, for which the results generate a numerical approximation of the pullback attraction in the original continuous dynamical system. The nature of the results regarding discretisation provide a non-autonomous extension to the work initiated by A. Stuart and J. Humphries [34, 35] for the numerical approximation of semi-group attractors within autonomous systems. . Of particular importance is the effect on the system's asymptotic behaviour over non-finite intervals of discretisation.

Application of real and functional analysis to solve boundary value problems

This thesis is about using appropriate tools in functional analysis arid classical analysis to tackle the problem of existence and uniqueness of nonlinear partial differential equations. There being no unified strategy to deal with these equations, one approaches each equation with an appropriate method, depending on the characteristics of the equation. The correct setting of the problem in appropriate function spaces is the first important part on the road to the solution. Here, we choose the setting of Sobolev spaces. The second essential part is to choose the correct tool for each equation. In the first part of this thesis (Chapters 3 and 4) we consider a variety of nonlinear hyperbolic partial differential equations with mixed boundary and initial conditions. The methods of compactness and monotonicity are used to prove existence and uniqueness of the solution (Chapter 3). Finding a priori estimates is the main task in this analysis. For some types of nonlinearity, these estimates cannot be easily obtained, arid so these two methods cannot be applied directly. In this case, we first linearise the equation, using linear recurrence (Chapter 4). In the second part of the thesis (Chapter 5), by using an appropriate tool in functional analysis (the Sobolev Imbedding Theorem), we are able to improve previous results on a posteriori error estimates for the finite element method of lines applied to nonlinear parabolic equations. These estimates are crucial in the design of adaptive algorithms for the method, and previous analysis relies on, what we show to be, unnecessary assumptions which limit the application of the algorithms. Our analysis does not require these assumptions. In the last part of the thesis (Chapter 6), staying with the theme of choosing the most suitable tools, we show that using classical analysis in a proper way is in some cases sufficient to obtain considerable results. We study in this chapter nonexistence of positive solutions to Laplace's equation with nonlinear Neumann boundary condition. This problem arises when one wants to study the blow-up at finite time of the solution of the corresponding parabolic problem, which models the heating of a substance by radiation. We generalise known results which were obtained by using more abstract methods.