Abstract
Planar flow of an incompressible rigid plastic material obeying a special case of the double slip and rotation model is studied in the vicinity of an envelope of characteristics. An orthogonal coordinate system whose base vectors are normal and tangent to the envelope is adopted. It is shown that solutions are in general singular. In particular, the magnitude of the shear strain rate in coordinate system chosen approaches infinity near the envelope of characteristics. An asymptotic representation for the stresses and velocities in the vicinity of such envelopes is derived. This representation can be used in numerical codes to overcome a difficulty caused by the singular behavior of exact solutions.
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Acknowledgements
The research described in this paper has been supported by the grant RFBR-17-01-00624. The second author was partly supported by Moscow Technological University [24].
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Alexandrov, S., Pirumov, A. (2019). Solution Behavior Near an Envelope of Characteristics in Planar Flow of a Material Obeying the Double Slip and Rotation Model. In: Öchsner, A., Altenbach, H. (eds) Engineering Design Applications. Advanced Structured Materials, vol 92. Springer, Cham. https://doi.org/10.1007/978-3-319-79005-3_24
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DOI: https://doi.org/10.1007/978-3-319-79005-3_24
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