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The Two-Dimensional Structure of Dynamic Boundary Layers and Shear Bands in Thermoviscoplastic Solids

Gioia, G. and Ortiz, M. (1996) The Two-Dimensional Structure of Dynamic Boundary Layers and Shear Bands in Thermoviscoplastic Solids. Journal of the Mechanics and Physics of Solids, 44 (2). pp. 251-292. ISSN 0022-5096. doi:10.1016/0022-5096(95)00071-2.

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A general boundary layer theory for thermoviscoplastic solids which accounts for inertia, rate sensitivity, hardening, thermal coupling, heat convection and conduction, and thermal softening is developed. In many applications of interest, the boundary layer equations can be considerably simplified by recourse to similarity methods, which facilitates the determination of steady-state and transient fully non-linear two-dimensional solutions. A simple analysis of the asymptotic behavior of the steady-state solutions leads to a classification of stable and unstable regimes. Under adiabatic conditions, the resulting material stability criterion coincides with that previously derived by Molinari and Clifton [(1987) Analytical characterization of shear localization in thermoviscoplastic solids. J. Appl, Mech. 54, 806–812] by a quasi-static, one-dimensional analysis. The transition from initially stable to unstable behavior can also be conveniently described by similarity methods. This provides a powerful semi-analytical tool for the interpretation of impact tests exhibiting dynamic shear bands, and for the characterization of the two-dimensional structure of such bands. It follows from the theory that, if the velocity of the impactor is held steady, the leading tip of the shear band propagates at a constant speed. This shear band tip speed follows readily from the theory as a function of the impact velocity and material parameters. The two-dimensional velocity, stress, temperature and plastic work fields attendant to the propagating shear band are also determined.

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Ortiz, M.0000-0001-5877-4824
Additional Information:© 1996 Elsevier. (Received 5 April 1995) This work has been funded by the National Science Foundation through Brown University’s Materials Research Group on “Micro-Mechanics of Failure Resistant Materials.” We are grateful to Professors A. J. Rosakis and G. Ravichandran of Caltech and Professor M. Zhou of Georgia Tech for helpful discussions and suggestions and for granting us access to as yet unpublished experimental data.
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Official Citation:G. Gioia, M. Ortiz, The two-dimensional structure of dynamic boundary layers and shear bands in thermoviscoplastic solids, In Journal of the Mechanics and Physics of Solids, Volume 44, Issue 2, 1996, Pages 251-292, ISSN 0022-5096, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83893
Deposited By: Lydia Suarez
Deposited On:15 Dec 2017 23:25
Last Modified:15 Nov 2021 20:15

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