On the stress analysis of cracked bodies by means of finite elements

The work described in this thesis deals with the development and application of a finite element program for the analysis of several cracked structures. In order to simplify the organisation of the material presented herein, the thesis has been subdivided into two Sections : In the first Section the development of a finite element program for the analysis of two-dimensional problems of plane stress or plane strain is described. The element used in this program is the six-mode isoparametric triangular element which permits the accurate modelling of curved boundary surfaces. Various cases of material aniftropy are included in the derivation of the element stiffness properties. A digital computer program is described and examples of its application are presented. In the second Section, on fracture problems, several cracked configurations are analysed by embedding into the finite element mesh a sub-region, containing the singularities and over which an analytic solution is used. The modifications necessary to augment a standard finite element program, such as that developed in Section I, are discussed and complete programs for each cracked configuration are presented. Several examples are included to demonstrate the accuracy and flexibility of the technique.

Finite element analysis of particle impact problems

Particle impacts are of fundamental importance in many areas and there has been a renewed interest in research on particle impact problems. A comprehensive investigation of the particle impact problems, using finite element (FE) methods, is presented in this thesis. The capability of FE procedures for modelling particle impacts is demonstrated by excellent agreements between FE analysis results and previous theoretical, experimental and numerical results. For normal impacts of elastic particles, it is found that the energy loss due to stress wave propagation is negligible if it can reflect more than three times during the impact, for which Hertz theory provides a good prediction of impact behaviour provided that the contact deformation is sufficiently small. For normal impact of plastic particles, the energy loss due to stress wave propagation is also generally negligible so that the energy loss is mainly due to plastic deformation. Finite-deformation plastic impact is addressed in this thesis so that plastic impacts can be categorised into elastic-plastic impact and finite-deformation plastic impact. Criteria for the onset of finite-deformation plastic impacts are proposed in terms of impact velocity and material properties. It is found that the coefficient of restitution depends mainly upon the ratio of impact velocity to yield Vni/Vy0 for elastic-plastic impacts, but it is proportional to [(Vni/Vy0)*(Y/E*)]-1/2, where Y /E* is the representative yield strain for finite-deformation plastic impacts. A theoretical model for elastic-plastic impacts is also developed and compares favourably with FEA and previous experimental results. The effect of work hardening is also investigated.

Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15

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 straightening of thin-walled seamless tubes of austenitic stainless steel

During this thesis work a coupled thermo-mechanical finite element model (FEM) was builtto simulate hot rolling in the blooming mill at Sandvik Materials Technology (SMT) inSandviken. The blooming mill is the first in a long line of processes that continuously or ingotcast ingots are subjected to before becoming finished products. The aim of this thesis work was twofold. The first was to create a parameterized finiteelement (FE) model of the blooming mill. The commercial FE software package MSCMarc/Mentat was used to create this model and the programing language Python was used toparameterize it. Second, two different pass schedules (A and B) were studied and comparedusing the model. The two pass series were evaluated with focus on their ability to healcentreline porosity, i.e. to close voids in the centre of the ingot. This evaluation was made by studying the hydrostatic stress (σm), the von Mises stress (σeq)and the plastic strain (εp) in the centre of the ingot. From these parameters the stress triaxiality(Tx) and the hydrostatic integration parameter (Gm) were calculated for each pass in bothseries using two different transportation times (30 and 150 s) from the furnace. The relationbetween Gm and an analytical parameter (Δ) was also studied. This parameter is the ratiobetween the mean height of the ingot and the contact length between the rolls and the ingot,which is useful as a rule of thumb to determine the homogeneity or penetration of strain for aspecific pass. The pass series designed with fewer passes (B), many with greater reduction, was shown toachieve better void closure theoretically. It was also shown that a temperature gradient, whichis the result of a longer holding time between the furnace and the blooming mill leads toimproved void closure.

Finite element analysis of hot rolling in the blooming mill

During this thesis work a coupled thermo-mechanical finite element model (FEM) was builtto simulate hot rolling in the blooming mill at Sandvik Materials Technology (SMT) inSandviken. The blooming mill is the first in a long line of processes that continuously or ingotcast ingots are subjected to before becoming finished products. The aim of this thesis work was twofold. The first was to create a parameterized finiteelement (FE) model of the blooming mill. The commercial FE software package MSCMarc/Mentat was used to create this model and the programing language Python was used toparameterize it. Second, two different pass schedules (A and B) were studied and comparedusing the model. The two pass series were evaluated with focus on their ability to healcentreline porosity, i.e. to close voids in the centre of the ingot. This evaluation was made by studying the hydrostatic stress (σm), the von Mises stress (σeq)and the plastic strain (εp) in the centre of the ingot. From these parameters the stress triaxiality(Tx) and the hydrostatic integration parameter (Gm) were calculated for each pass in bothseries using two different transportation times (30 and 150 s) from the furnace. The relationbetween Gm and an analytical parameter (Δ) was also studied. This parameter is the ratiobetween the mean height of the ingot and the contact length between the rolls and the ingot,which is useful as a rule of thumb to determine the homogeneity or penetration of strain for aspecific pass. The pass series designed with fewer passes (B), many with greater reduction, was shown toachieve better void closure theoretically. It was also shown that a temperature gradient, whichis the result of a longer holding time between the furnace and the blooming mill leads toimproved void closure.

A three dimensional finite volume approach to the thermo-mechanical modelling of the shape casting of metals

This paper presents a three dimensional, thermos-mechanical modelling approach to the cooling and solidification phases associated with the shape casting of metals ei. Die, sand and investment casting. Novel vortex-based Finite Volume (FV) methods are described and employed with regard to the small strain, non-linear Computational Solid Mechanics (CSM) capabilities required to model shape casting. The CSM capabilities include the non-linear material phenomena of creep and thermo-elasto-visco-plasticity at high temperatures and thermo-elasto-visco-plasticity at low temperatures and also multi body deformable contact with which can occur between the metal casting of the mould. The vortex-based FV methods, which can be readily applied to unstructured meshes, are included within a comprehensive FV modelling framework, PHYSICA. The additional heat transfer, by conduction and convection, filling, porosity and solidification algorithms existing within PHYSICA for the complete modelling of all shape casting process employ cell-centred FV methods. The termo-mechanical coupling is performed in a staggered incremental fashion, which addresses the possible gap formation between the component and the mould, and is ultimately validated against a variety of shape casting benchmarks.

Numerical simulation of strain-adaptive bone remodelling in the ankle joint

Background: The use of artificial endoprostheses has become a routine procedure for knee and hip joints while ankle arthritis has traditionally been treated by means of arthrodesis. Due to its advantages, the implantation of endoprostheses is constantly increasing. While finite element analyses (FEA) of strain-adaptive bone remodelling have been carried out for the hip joint in previous studies, to our knowledge there are no investigations that have considered remodelling processes of the ankle joint. In order to evaluate and optimise new generation implants of the ankle joint, as well as to gain additional knowledge regarding the biomechanics, strain-adaptive bone remodelling has been calculated separately for the tibia and the talus after providing them with an implant. Methods: FE models of the bone-implant assembly for both the tibia and the talus have been developed. Bone characteristics such as the density distribution have been applied corresponding to CT scans. A force of 5,200 N, which corresponds to the compression force during normal walking of a person with a weight of 100 kg according to Stauffer et al., has been used in the simulation. The bone adaptation law, previously developed by our research team, has been used for the calculation of the remodelling processes. Results: A total bone mass loss of 2% in the tibia and 13% in the talus was calculated. The greater decline of density in the talus is due to its smaller size compared to the relatively large implant dimensions causing remodelling processes in the whole bone tissue. In the tibia, bone remodelling processes are only calculated in areas adjacent to the implant. Thus, a smaller bone mass loss than in the talus can be expected. There is a high agreement between the simulation results in the distal tibia and the literature regarding. Conclusions: In this study, strain-adaptive bone remodelling processes are simulated using the FE method. The results contribute to a better understanding of the biomechanical behaviour of the ankle joint and hence are useful for the optimisation of the implant geometry in the future.

Numerical investigations on the strain-adaptive bone remodelling in the periprosthetic femur: Influence of the boundary conditions

Background: There are several numerical investigations on bone remodelling after total hip arthroplasty (THA) on the basis of the finite element analysis (FEA). For such computations certain boundary conditions have to be defined. The authors chose a maximum of three static load situations, usually taken from the gait cycle because this is the most frequent dynamic activity of a patient after THA. Materials and methods: The numerical study presented here investigates whether it is useful to consider only one static load situation of the gait cycle in the FE calculation of the bone remodelling. For this purpose, 5 different loading cases were examined in order to determine their influence on the change in the physiological load distribution within the femur and on the resulting strain-adaptive bone remodelling. First, four different static loading cases at 25%, 45%, 65% and 85% of the gait cycle, respectively, and then the whole gait cycle in a loading regime were examined in order to regard all the different loadings of the cycle in the simulation. Results: The computed evolution of the apparent bone density (ABD) and the calculated mass losses in the periprosthetic femur show that the simulation results are highly dependent on the chosen boundary conditions. Conclusion: These numerical investigations prove that a static load situation is insufficient for representing the whole gait cycle. This causes severe deviations in the FE calculation of the bone remodelling. However, accompanying clinical examinations are necessary to calibrate the bone adaptation law and thus to validate the FE calculations.

Characterisation and investigation of local variations in mechanical behaviour in cast aluminium using gradient solidification, Digital Image Correlation and finite element simulation

Due to design and process-related factors, there are local variations in the microstructure and mechanical behaviour of cast components. This work establishes a Digital Image Correlation (DIC) based method for characterisation and investigation of the effects of such local variations on the behaviour of a high pressure, die cast (HPDC) aluminium alloy. Plastic behaviour is studied using gradient solidified samples and characterisation models for the parameters of the Hollomon equation are developed, based on microstructural refinement. Samples with controlled microstructural variations are produced and the observed DIC strain field is compared with Finite Element Method (FEM) simulation results. The results show that the DIC based method can be applied to characterise local mechanical behaviour with high accuracy. The microstructural variations are observed to cause a redistribution of strain during tensile loading. This redistribution of strain can be predicted in the FEM simulation by incorporating local mechanical behaviour using the developed characterization model. A homogeneous FEM simulation is unable to predict the observed behaviour. The results motivate the application of a previously proposed simulation strategy, which is able to predict and incorporate local variations in mechanical behaviour into FEM simulations already in the design process for cast components.

Finite element modeling of tube deformation during cold pilgering

A three-dimensional finite element model of cold pilgering of stainless steel tubes is developed in this paper. The objective is to use the model to increase the understanding of forces and deformations in the process. The focus is on the influence of vertical displacements of the roll stand and axial displacements of the mandrel and tube. Therefore, the rigid tools and the tube are supported with elastic springs. Additionally, the influences of friction coefficients in the tube/mandrel and tube/roll interfaces are examined. A sensitivity study is performed to investigate the influences of these parameters on the strain path and the roll separation force. The results show the importance of accounting for the displacements of the tube and rigid tools on the roll separation force and the accumulative plastic strain.

Experimental study of strain fields during shearing of medium and high-strength steel sheet

There is a shortage of experimentally determined strains during sheet metal shearing. These kinds of data are a requisite to validate shearing models and to simulate the shearing process. In this work, strain fields were continuously measured during shearing of a medium and a high strength steel sheet, using digital image correlation. Preliminary studies based on finite element simulations, suggested that the effective surface strains are a good approximation of the bulk strains below the surface. The experiments were performed in a symmetric set-up with large stiffness and stable tool clearances, using various combinations of tool clearance and clamping configuration. Due to large deformations, strains were measured from images captured in a series of steps from shearing start to final fracture. Both the Cauchy and Hencky strain measures were considered, but the difference between these were found negligible with the number of increments used (about 20 to 50). Force-displacement curves were also determined for the various experimental conditions. The measured strain fields displayed a thin band of large strain between the tool edges. Shearing with two clamps resulted in a symmetric strain band whereas there was an extended area with large strains around the tool at the unclamped side when shearing with one clamp. Furthermore, one or two cracks were visible on most of the samples close to the tool edges well before final fracture. The fracture strain was larger for the medium strength material compared with the high-strength material and increased with increasing clearance.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.