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In the framework of electro-elasticity theory and the finite element method (FEM), a model is set up for the computation of quantities in surface acoustic wave (SAW) devices accounting for nonlinear effects. These include second-order and third-order intermodulations, second and third harmonic generation and the influence of electro-acoustic nonlinearity on the frequency characteristics of SAW resonators. The model is based on perturbation theory, and requires input material constants, e.g., the elastic moduli up to fourth order for all materials involved. The model is two-dimensional, corresponding to an infinite aperture, but all three Cartesian components of the displacement and electrical fields are accounted for. The first version of the model pertains to an infinite periodic arrangement of electrodes. It is subsequently generalized to systems with a finite number of electrodes. For the latter version, a recursive algorithm is presented which is related to the cascading scheme of Plessky and Koskela and strongly reduces computation time and memory requirements. The model is applied to TC-SAW systems with copper electrodes buried in an oxide film on a LiNbO3 substrate. Results of computations are presented for the electrical current due to third-order intermodulations and the displacement field associated with the second harmonic and second-order intermodulations, generated by monochromatic input tones. The scope of this review is limited to methodological aspects with the goal to enable calculations of nonlinear quantities in SAW devices on inexpensive and easily accessible computing platforms.
Experimental and numerical investigations into the forming of tailored strips and tailored tubes
(2008)
Through the application of tailored strips and tailored tubes, the wall thickness of components can be manufactured in a load-optimised manner. Thus, it is also possible to optimise component weight. Prior to the application of tailored products, wall thicknesses and the respective degree of deformation as well as the welding seam position can be determined in a FEM (finite element method) simulation. These results are then verified in test series on transfer presses and tube bending machines, with the necessary tool adaptations being determined in the process. This results in weight and cost reductions for deep-drawn components and tube sections. Moreover, this means that especially with regard to tubes, multiple sections can be combined in one component. A feasibility study shows that the level of possible weight and cost savings depends on the respective component geometry and load situation. Additional costs for the production of tailored products and - if necessary - tool modifications also need to be considered. Thus, the amount of savings possible for a part can only be determined on an individual basis.
In this paper a practical way for fatigue life prediction of rubber products under multiaxial loads is shown. This is done by means of fracture mechanical concepts and the energy release rate as the failure criterion. Due to a FEA post-processor the potential energy release rate might be calculated at every material point supposed there was a crack. And therefore the risk of failure and with the help of a strain number curve the time to fatigue is able to be calculated by FEA. This concept is applied for an estimation of the life time of a test specimen with tensile loading from fatigue data of a shear loaded specimen of different design. This rather more theoretical concept of the energy release rate is complemented by experimental crack growth data by a Tear Fatigue Analyzer with its great advantage of reduction of testing time and costs compared to those of fatigue tests. For some materials a thorough characterization of crack growth and fatigue behavior is presented and is applied to estimate the time to fatigue by FEA for a real component under multiaxial loads.
Structures for interconnecting active microwave semiconductor-devices, e.g. FET's and MIC's, with the electrical surrounding or with each other have to be designed more and more carefully when increasing the desired upper frequency limit. Therefore, several connecting structures for device embedding have been examined. Mainly, their applicability for the frequency range from 10 GHz to 100 GHz was considered. Additionally, different equivalent circuits were developed to approximately describe their behaviour for CAD-applications.
The embedding of microwave devices is treated by applying the finite-difference method to three-dimensional shielded structures. A program package was developed to evaluate electromagnetic fields inside arbitrary transmission-line connecting structures and to compute the scattering matrix. The air bridge, the transition through a wall, and the bond wire are examined as interconnecting structures. Detailed results are given and discussed regarding the fundamental behavior of embedding.
In this entry, the 3D CAD reconstructions and 3D multi-material polymer replica printings of knight Götz von Berlichingen´s first „Iron Hand,“ which were developed in the last few years at Offenburg University, are presented. Even by today's standards, the first “Iron Hand”–as could be shown in the replicas–demonstrates sophisticated mechanics and well thought-out functionality and still offers inspiration and food for discussion when it comes to the question of an artificial prosthetic replacement for a hand.
Hot working tools are subjected to complex thermal and mechanical loads during service. Locally, the stresses can exceed the material’s yield strength in highly loaded areas. During production, this causes cyclic plastic deformation and thus thermomechanical fatigue, which can significantly shorten the lifetime of hot working tools. To sustain this high loads, the hot working tools are typically made of tempered martensitic hot work tool steels. While the annealing temperatures of the tool steels usually lie in the range of 400 to 600 °C, the steels may experience even higher temperatures during hot working, resulting in softening of the material due to changes in microstructure. Therefore, the temperature-dependent cyclic mechanical properties of the frequently used hot work tool steel 1.2367 (X38CrMoV5-3) after tempering are investigated in this work. To this end, hardness measurements are performed. Furthermore, the Institute of Forming Technology and Machines (IFUM) provides test results from cyclic tests at temperatures ranging from 20 °C (room temperature) to 650 °C. To describe the observed time- and temperature-dependent softening during tempering, a kinetic model for the evolution of the mean size of secondary carbides based on Ostwald ripening is developed. In addition, both mechanism-based and phenomenological relationships for the cyclic mechanical properties of the Ramberg- Osgood model depending on carbide size and temperature are proposed. The stress-strain hysteresis loops measured at different temperatures and after different heat treatments can be well described with the proposed kinetic and mechanical model. Furthermore, the model is suitable for integration in advanced mechanism-based lifetime models. However, since the Ramberg-Osgood model is not suitable for finite element implementation, a temperature-dependent incremental cyclic plasticity model is presented as well. Thus, softening due to particle coarsening can be applied in the finite element method (FEM). Therefore, a kinetic model is coupled with a cyclic plasticity model including kinematic hardening. The plasticity model is implemented via subroutines in the finite element program ABAQUS for implicit integration (subroutine called UMAT) and explicit integration (subroutine called VUMAT). The implemented model is used for the simulation of an exemplary hot working process to assess the effects of softening due to particle coarsening. It shows that the thermal softening at high temperatures, which occur over a long time at a mechanically highly loaded area, has a great influence. If this influence is not considered in tool design, an unexpected tool failure might occur bringing the production to a standstill.
In this paper, the multiaxial formulation of a mechanism-based model for fatigue life prediction is presented whichcan be applied to low-cycle fatigue (LCF) and thermomechanical fatigue (TMF) problems in which high-cycle fa-tigue loadings are superimposed. The model assumes that crack growth is the lifetime limiting mechanism and thatthe crack advance in a loading cycleda/dNcorrelates with the cyclic crack-tip opening displacement ΔCTOD.The multiaxial formulation makes use of fracture mechanics solutions and thus, does not need additional modelparameters quantifying the effect of the multiaxiality. Furthermore, the model includes contributions of HCF on ΔCTODand assesses the effect of the direction of the HCF loadings with respect to LCF or TMF loadings inthe life prediction. The model is implemented into the finite-element program ABAQUS. It is applied to predictthe fatigue life of a thermomechanically loaded notched specimen that should represent the situation between theinlet and outlet bore holes of cylinder heads. A good correlation of the predicted and the measured fatigue lives isobtained.
The aim of this study was to develop a biomechanically validated finite element model to predict the biomechanical behaviour of the human lumbar spine in compression.
For validation of the finite element model, an in vitro study was performed: Twelve human lumbar cadaveric spinal segments (six segments L2/3 and six segments L4/5) were loaded in axial compression using 600 N in the intact state and following surgical treatment using two different internal stabilisation devices. Range of motion was measured and used to calculate stiffness.
A finite element model of a human spinal segment L3/4 was loaded with the same force in intact and surgically altered state, corresponding to the situation of biomechanical in vitro study.
The results of the cadaver biomechanical and finite element analysis were compared. As they were close together, the finite element model was used to predict: (1) load-sharing within human lumbar spine in compression, (2) load-sharing within osteoporotic human lumbar spine in compression and (3) the stabilising potential of the different spinal implants with respect to bone mineral density.
A finite element model as described here may be used to predict the biomechanical behaviour of the spine. Moreover, the influence of different spinal stabilisation systems may be predicted.
In this paper, an unconditionally stable algorithm for the numerical integration and finite-element implementation of a class of pressure dependent plasticity models with nonlinear isotropic and kinematic hardening is presented. Existing algorithms are improved in the sense that the number of equations to be solved iteratively is significantly reduced. This is achieved by exploitation of the structure of Armstrong-Frederik-type kinematic hardening laws. The consistent material tangent is derived analytically and compared to the numerically computed tangent in order to validate the implementation. The performance of the new algorithm is compared to an existing one that does not consider the possibility of reducing the number of unknowns to be iterated. The algorithm is used to implement a time and temperature dependent cast iron plasticity model, which is based on the pressure dependent Gurson model, in the finite-element program ABAQUS. The implementation is applied to compute stresses and strains in a large-scale finite-element model of a three cylinder engine block. This computation proofs the applicability of the algorithm in industrial practice that is of interest in applied sciences.