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The variational formulation of viscoplastic constitutive updates

Ortiz, M. and Stainier, L. (1999) The variational formulation of viscoplastic constitutive updates. Computer Methods in Applied Mechanics and Engineering, 171 (3-4). pp. 419-444. ISSN 0045-7825. doi:10.1016/S0045-7825(98)00219-9.

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We present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as finite elastic and plastic deformations, non-Newtonian viscosity, rate-sensitivity and arbitrary flow and hardening rules. The distinguishing characteristic of the proposed constitutive updates is that, by construction, the corresponding incremental stress—strain relations derive from a pseudo-elastic strain-energy density. This, in turn, confers the incremental boundary value problem a variational structure. In particular, the incremental deformation mapping follows from a minimum principle. This minimum principle may conveniently be taken as a basis for error estimation and mesh adaption. The accuracy and robustness of the variational constitutive updates is demonstrated with the aid of convergence tests involving the finitely-deforming Mises solid and ductile single crystals. The ability of the updates to resolve the complex patterns of slip activity which arise in the latter application is particularly noteworthy.

Item Type:Article
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Ortiz, M.0000-0001-5877-4824
Stainier, L.0000-0001-6719-6616
Additional Information:© 1999 Elsevier. Received 1 April 1998, Available online 24 June 1999. The support of the DOE through Caltech's ASCI Center for the Simulation of the Dynamic Response of Materials is gratefully acknowledged.
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Department of Energy (DOE)UNSPECIFIED
Issue or Number:3-4
Record Number:CaltechAUTHORS:20171213-091546263
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Official Citation:M. Ortiz, L. Stainier, The variational formulation of viscoplastic constitutive updates, In Computer Methods in Applied Mechanics and Engineering, Volume 171, Issues 3–4, 1999, Pages 419-444, ISSN 0045-7825, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83861
Deposited By: Lydia Suarez
Deposited On:13 Dec 2017 22:56
Last Modified:15 Nov 2021 20:14

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