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Acoustic emission sources from fast dislocation motion
Hora, Petr ; Machová, Anna ; Červ, Jan ; Uhnáková, Alena
Acoustic emission from the fast dislocations emitted from an edge crack in 3D bcc iron crystal is studied via atomistic simulations by molecular dynamics technique. Acoustic emission patterns arising from the fast dislocation motion in molecular dynamics are visualized via the local kinetic energies of individual atoms and further modeled as a moving source of the stress waves in the anisotropic continuum.
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Transient response of layered orthotropic strip to transverse load
Adámek, V. ; Valeš, František ; Červ, Jan
This work concerns the transient response of an infinite two-layered strip subjected to a transverse load of impact character. The material of each layer is assumed to be specially orthotropic, i.e. the material and geometric axes coincide. Moreover, the material is modelled as linear viscoelastic using the model of standard linear viscoelastic solid such that the damping behaviour of the strip for long wavelengths and long times can be addressed. The non-stationary wave phenomena in the strip are studied using analytical approach. The system of equations of motion for the case of 2D plane-stress problem is solved using the classical method of integral transform. Once the formulas for the Laplace transforms of fundamental mechanical quantities are derived, the numerical inverse Laplace transform is used to obtain the response in time domain for a strip with free-fixed boundaries. The results for a strip composed of two orthotropic layers of specific material properties are presented in this work. Finally, this solution is confronted with the results of numerical simulations reached by a professional FE code.
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Application of numerical inverse Laplace transform to elastodynamic problems
Adámek, V. ; Valeš, František ; Červ, Jan
Laplace transform represents one of the most used transforms in time domain. There exist two possible approaches to its inversion, analytical and numerical. The first method is based on the exact evaluation of the inverse integral. This is usually done by the help of Cauchy´s residue theorem. The substance of the second method lies in the numerical evaluation of the inverse integral. This numerical approach is faster than an analytical solution and it can be also applied to more complicated problems where e.g. the existence of branch points makes the inverse process, based on the analytic techniques, much more complicated.
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Component-wise partitioned finite element method in linear wave propagation problems: benchmark tests
Kolman, Radek ; Cho, S.S. ; Červ, Jan ; Park, K.C.
A novel explicit time scheme for nite element computations of wave propagation problems in solids is presented. The presented algorithm, with the component-wise partition of equations of motion to the longitudinal and shear parts, is designed to more precisely integrate wave propagation in accordance with their dierent propagation wave speeds. The suggested three-time step integrator is fully explicit with the diagonal mass matrix, of second-order accuracy, conditionally stable and it exhibits minimal sensitivity behavior on time step size satisfying the stability limit. We present two numerical tests of wave propagation phenomena to show accuracy and performance of the proposed method.
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Comparison of two possible approaches to inverse laplace transform applied to wave problems
Adámek, V. ; Valeš, František ; Červ, Jan
This paper concerns the investigation of non-stationary wave phenomena in a thin elastic disc under radial impact by means of analytical methods. When the method of integral transforms is used for solving the system of PDEs describing a wave problem solved, one has to overcome the problem of inverse transform. This work focuses on two possible approaches to the inverse Laplace transform. Using the existing analytical solution of the problem, the classic method making use of the residue theorem and the method based on the numerical inverse Laplace transform are compared. Advantages and disadvantages of both approaches, mainly from computational point of view, are discussed and demonstrated.
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