Wave propagation and focussing in plates. Ballmann, J. & Staat, M. In Chiem, C Y, Kunze, H D, & Meyer, L W, editors, Impact Loading and Dynamic Behaviour of Materials, IMPACT '87 - International Conference on Impact Loading and Dynamic Behaviour of Materials. May 18-22, 1987, Bremen, Germany, volume 2, pages 949–956, 1988. Deutsche Gesellschaft für Metallkunde Informationsgesellschaft, Oberursel. ZSCC: NoCitationData[s0]abstract bibtex A method of bicharacteristics for the computation of stress waves in linear elastic plates with straight boundaries was first devised by CLIFTON on the basis of a proposal for gas dynamics. Also starting from gas dynamics we applied this method to plates with curved boundaries and plate structures including shear and bending. Of major interest was the computation of stress concentrations as a result of the focussing of waves that were reflected from concave boundaries, as well as from internal boundaries. We compared our numerical results with experiments that were carried out in the Shock Waves Laboratory of Aachen Technical University. Good correlations were observed which we wish to further improve upon by means of a higher order plate theory. Currently we have developed methods of characteristics for non-elastic and nonlinear materials. In regard to non-elastic materials, we have previously considered linear elastic-viscoplastic laws such as the PERZYNA model, as well as the BODNER-PARTOM model. They lead to semi-linear hyperbolic laws, i.e. the highest derivatives appear only linearly. In the case of nonlinear materials with large deformations and physical nonlinearity, we have considered isotropic elastic media. If homogeneously prestressed they show anisotropic wave propagation, resembling the observations made in linear transversely isotropic elastic media. Also in plasticity very similar effects of anisotropic wave propagation are expected, if e.g. PRANDTL-REUSS-like laws are used. Generally the strain induced anisotropy changes from point to point according to the local deformation. Attempts have been made to use this anisotropic effect in the non destructive evaluation of residual stresses with ultrasonics. A numerical method of bicharacteristics for the computation of strong stress waves in nonlinear elastic plates has been proposed by the authors for points in the interior of the domain of calculation. It was demonstrated that the numerical scheme based on this method maintains very well the form of the wave front in cases with strong anisotropy. Nonlinear behaviour of plastic materials could currently only be taken into account using deformation theory. As with many materials, especially for some rubber-like plastics and brittle materials like concrete and metal castings the nonlinear part is often dominant. With this in mind, valid statements can be made with the available program in many cases.
@inproceedings{ballmann_wave_1988,
title = {Wave propagation and focussing in plates},
volume = {2},
copyright = {All rights reserved},
isbn = {3-88355-126-0},
abstract = {A method of bicharacteristics for the computation of stress waves in linear elastic plates with straight boundaries was first devised by CLIFTON on the basis of a proposal for gas dynamics. Also starting from gas dynamics we applied this method to plates with curved boundaries and plate structures including shear and bending. Of major interest was the computation of stress concentrations as a result of the focussing of waves that were reflected from concave boundaries, as well as from internal boundaries. We compared our numerical results with experiments that were carried out in the Shock Waves Laboratory of Aachen Technical University. Good correlations were observed which we wish to further improve upon by means of a higher order plate theory. Currently we have developed methods of characteristics for non-elastic and nonlinear materials. In regard to non-elastic materials, we have previously considered linear elastic-viscoplastic laws such as the PERZYNA model, as well as the BODNER-PARTOM model. They lead to semi-linear hyperbolic laws, i.e. the highest derivatives appear only linearly. In the case of nonlinear materials with large deformations and physical nonlinearity, we have considered isotropic elastic media. If homogeneously prestressed they show anisotropic wave propagation, resembling the observations made in linear transversely isotropic elastic media. Also in plasticity very similar effects of anisotropic wave propagation are expected, if e.g. PRANDTL-REUSS-like laws are used. Generally the strain induced anisotropy changes from point to point according to the local deformation. Attempts have been made to use this anisotropic effect in the non destructive evaluation of residual stresses with ultrasonics. A numerical method of bicharacteristics for the computation of strong stress waves in nonlinear elastic plates has been proposed by the authors for points in the interior of the domain of calculation. It was demonstrated that the numerical scheme based on this method maintains very well the form of the wave front in cases with strong anisotropy. Nonlinear behaviour of plastic materials could currently only be taken into account using deformation theory. As with many materials, especially for some rubber-like plastics and brittle materials like concrete and metal castings the nonlinear part is often dominant. With this in mind, valid statements can be made with the available program in many cases.},
booktitle = {Impact {Loading} and {Dynamic} {Behaviour} of {Materials}, {IMPACT} '87 - {International} {Conference} on {Impact} {Loading} and {Dynamic} {Behaviour} of {Materials}. {May} 18-22, 1987, {Bremen}, {Germany}},
publisher = {Deutsche Gesellschaft für Metallkunde Informationsgesellschaft, Oberursel},
author = {Ballmann, Josef and Staat, Manfred},
editor = {Chiem, C Y and Kunze, H D and Meyer, L W},
year = {1988},
note = {ZSCC: NoCitationData[s0]},
keywords = {Rayleigh waves, acceleration waves, von Schmidt waves},
pages = {949--956},
}
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Good correlations were observed which we wish to further improve upon by means of a higher order plate theory. Currently we have developed methods of characteristics for non-elastic and nonlinear materials. In regard to non-elastic materials, we have previously considered linear elastic-viscoplastic laws such as the PERZYNA model, as well as the BODNER-PARTOM model. They lead to semi-linear hyperbolic laws, i.e. the highest derivatives appear only linearly. In the case of nonlinear materials with large deformations and physical nonlinearity, we have considered isotropic elastic media. If homogeneously prestressed they show anisotropic wave propagation, resembling the observations made in linear transversely isotropic elastic media. Also in plasticity very similar effects of anisotropic wave propagation are expected, if e.g. PRANDTL-REUSS-like laws are used. Generally the strain induced anisotropy changes from point to point according to the local deformation. Attempts have been made to use this anisotropic effect in the non destructive evaluation of residual stresses with ultrasonics. A numerical method of bicharacteristics for the computation of strong stress waves in nonlinear elastic plates has been proposed by the authors for points in the interior of the domain of calculation. It was demonstrated that the numerical scheme based on this method maintains very well the form of the wave front in cases with strong anisotropy. Nonlinear behaviour of plastic materials could currently only be taken into account using deformation theory. As with many materials, especially for some rubber-like plastics and brittle materials like concrete and metal castings the nonlinear part is often dominant. With this in mind, valid statements can be made with the available program in many cases.","booktitle":"Impact Loading and Dynamic Behaviour of Materials, IMPACT '87 - International Conference on Impact Loading and Dynamic Behaviour of Materials. 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Also starting from gas dynamics we applied this method to plates with curved boundaries and plate structures including shear and bending. Of major interest was the computation of stress concentrations as a result of the focussing of waves that were reflected from concave boundaries, as well as from internal boundaries. We compared our numerical results with experiments that were carried out in the Shock Waves Laboratory of Aachen Technical University. Good correlations were observed which we wish to further improve upon by means of a higher order plate theory. Currently we have developed methods of characteristics for non-elastic and nonlinear materials. In regard to non-elastic materials, we have previously considered linear elastic-viscoplastic laws such as the PERZYNA model, as well as the BODNER-PARTOM model. They lead to semi-linear hyperbolic laws, i.e. the highest derivatives appear only linearly. 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