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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e-mail: jclayton@arl.army.mil
e-mail: bammann@cavs.msstate.edu
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October 2009
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
J. D. Clayton,
J. D. Clayton
Mem. ASME
Impact Physics,
e-mail: jclayton@arl.army.mil
US Army Research Laboratory
, Aberdeen Proving Ground, MD 21005
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D. J. Bammann
D. J. Bammann
Fellow ASME
Center for Advanced Vehicular Systems,
e-mail: bammann@cavs.msstate.edu
Mississippi State University
, Starkville, MS 39762
Search for other works by this author on:
J. D. Clayton
Mem. ASME
Impact Physics,
US Army Research Laboratory
, Aberdeen Proving Ground, MD 21005e-mail: jclayton@arl.army.mil
D. J. Bammann
Fellow ASME
Center for Advanced Vehicular Systems,
Mississippi State University
, Starkville, MS 39762e-mail: bammann@cavs.msstate.edu
J. Eng. Mater. Technol. Oct 2009, 131(4): 041201 (15 pages)
Published Online: August 27, 2009
Article history
Received:
January 14, 2009
Revised:
March 30, 2009
Published:
August 27, 2009
Citation
Clayton, J. D., and Bammann, D. J. (August 27, 2009). "Finite Deformations and Internal Forces in Elastic-Plastic Crystals: Interpretations From Nonlinear Elasticity and Anharmonic Lattice Statics." ASME. J. Eng. Mater. Technol. October 2009; 131(4): 041201. https://doi.org/10.1115/1.3183773
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