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IssuesArchive of Issues2003-4pp.148-160

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V. N. Kukudzhanov and A. L. Levitin, "On the Dynamical Boundary Effect in an Elastoviscoplastic Half-space Subjected to Transverse-longitudinal Impact," Mech. Solids. 38 (4), 148-160 (2003)
Year 2003 Volume 38 Number 4 Pages 148-160
Title On the Dynamical Boundary Effect in an Elastoviscoplastic Half-space Subjected to Transverse-longitudinal Impact
Author(s) V. N. Kukudzhanov (Moscow)
A. L. Levitin (Moscow)
Abstract We consider a half-space subjected to a skew impact loading with the tangential component of the applied stress being sufficiently large and exceeding the material yield stress. In this case, the classical elastoplastic model is inconsistent and admits no solutions. This gives rise to the question of the model to be used for solving this problem. The elastoviscoplastic model is the simplest generalization of the elastoplastic model for which a solution of the problem exists. This model may be regarded as a regularization of the classical elastoplastic model which is invariant to the change of time scale. As shown in [1, 2], for small relaxation times (compared with the characteristic time of the problem), the solutions obtained on the basis of the elastoviscoplastic model converge to solutions of elastoplastic equations in the region of slow variation of the solutions. In the region of their fast variation and on the jumps of the elastoviscoplastic solution inside the body, there appear boundary effects (boundary layers). Near the boundary of the body, boundary effects appear if there is no agreement between the static condition of plasticity and the boundary conditions [3]. A simple problem of this type is that of tangential impact along the boundary of a half-space. If the impact velocity exceeds some critical value (at which the elastoplastic solution ceases to exist), then a boundary layer appears near the surface in which plastic strains are localized up to complete material fracture [4].
References
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13.  M. Zhou, A. Needleman, and R. J. Clifton, "Finite element simulations of shear localization in plate impact," J. Mech. and Phys. Solids, Vol. 42, No. 3, pp. 423-458, 1994.
14.  R. P. Fedorenko, An Introduction to Computational Physics [in Russian], Izd-vo MFTI, Moscow, 1994.
15.  V. N. Kukudzhanov, Difference Methods in Problems of Mechanics of Deformable Bodies [in Russian], Izd-vo MFTI, Moscow, 1992.
16.  A. G. Kulikovskii, N. V. Pogorelov, and A. Yu. Semenov, Mathematical Problems in the Numerical Analysis of Hyperbolic Systems [in Russian], Fizmatlit, Moscow, 2001.
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Received 14 May 2003
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