A geometric framework for the kinematics of crystals with defects / by John D. Clayton, Douglas J. Bammann, and David L. McDowell.

Format:

Book

Government document

Author/Creator:

Clayton, John D., 1976- author.

Bammann, Douglas J., author.

McDowell, David L., author.

Contributor:

U.S. Army Research Laboratory, issuing body.

Language:

English

Subjects (All):

Crystallography.

Crystals--Elastic properties.

Crystals.

Dislocations in crystals.

Crystal lattices.

Geometry, Differential.

Multiscale modeling.

Physical Description:

1 online resource (pages 3983-4010) : illustrations

Place of Publication:

Aberdeen Proving Ground, MD : US Army Research Laboratory, 2006.

Summary:

Presented is a general theoretical framework capable of describing the finite deformation kinematics of several classes of defects prevalent in metallic crystals. Our treatment relies upon powerful tools from differential geometry, including linear connections and covariant differentiation, torsion, curvature, and anholonomic spaces. A length scale dependent, three-term multiplicative decomposition of the deformation gradient is suggested, with terms representing recoverable elasticity, residual lattice deformation due to defect fields, and plastic deformation resulting from defect fluxes. Also proposed is an additional micromorphic variable representing additional degrees-of-freedom associated with rotational lattice defects (i.e. disclinations), point defects, and, most generally, Somigliana dislocations. We illustrate how particular implementations of our general framework encompass notable theories from the literature and classify particular versions of the framework via geometric terminology.

Notes:

"February 2006."

"ARL-RP-119."

Offprint from: Philosophical magazine, 85 (2006).

Includes bibliographical references (pages 4008-4010).

Description based on online resource, PDF version; title from title page (DTIC website, viewed July 8, 2020).

OCLC:

74287526

Access Restriction:

APPROVED FOR PUBLIC RELEASE.