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PREDICTIVE SCIENCE AND TECHNOLOGY IN MECHANICS AND MATERIALS

Finite Deformations and Internal Forces in Elastic-Plastic Crystals: Interpretations From Nonlinear Elasticity and Anharmonic Lattice Statics

[+] Author and Article Information
J. D. Clayton

Impact Physics, US Army Research Laboratory, Aberdeen Proving Ground, MD 21005jclayton@arl.army.mil

D. J. Bammann

Center for Advanced Vehicular Systems, Mississippi State University, Starkville, MS 39762bammann@cavs.msstate.edu

J. Eng. Mater. Technol 131(4), 041201 (Aug 27, 2009) (15 pages) doi:10.1115/1.3183773 History: Received January 14, 2009; Revised March 30, 2009; Published August 27, 2009

Large deformation kinematics and internal forces arising from defects in crystalline solids are addressed by a nonlinear kinematic description and multiscale averaging concepts. An element of crystalline material with spatially uniform properties and containing defects such as dislocation lines and loops is considered. The average deformation gradient for this element is decomposed multiplicatively into terms accounting for effects of dislocation flux, recoverable elastic stretch and rotation, and residual elastic deformation associated with self-equilibrating internal forces induced by defects. Two methods are considered for quantifying average residual elastic deformation: continuum elasticity and discrete lattice statics. Average residual elastic strains and corresponding average residual elastic volume changes are negligible in the context of linear elasticity or harmonic force potentials but are not necessarily inconsequential in the more general case of nonlinear elasticity or anharmonic interactions.

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Copyright © 2009 by American Society of Mechanical Engineers
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