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Constitutive theories based on the multiplicative decomposition of deformation gradient: Thermoelasticity, elastoplasticity, and biomechanics

[+] Author and Article Information
Vlado A Lubarda

Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411vlubarda@ucsd.edu

Appl. Mech. Rev 57(2), 95-108 (Apr 26, 2004) (14 pages) doi:10.1115/1.1591000 History: Online April 26, 2004
Copyright © 2004 by ASME
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Figures

Grahic Jump Location
The intermediate configuration Bθ at a nonuniform temperature θ is obtained from the deformed configuration B by isothermal destressing to zero stress. The deformation gradient from initial to deformed configuration F is decomposed into elastic part Fe and thermal part Fθ, such that F=Fe⋅Fθ.
Grahic Jump Location
The intermediate configuration Bp is obtained from the deformed configuration B by destressing to zero stress. The elastoplastic deformation gradient is decomposed into its elastic and plastic part, such that F=Fe⋅Fp.
Grahic Jump Location
Kinematic model of elastoplastic deformation of a single crystal. The material flows through the crystalline lattice by crystallographic slip, which gives rise to deformation gradient Fp. Subsequently, the material with embedded lattice deforms elastically from the intermediate to current configuration. The corresponding deformation gradient is F*.
Grahic Jump Location
Schematic representation of the multiplicative decomposition of deformation gradient into its elastic and growth parts. The mass of an infinitesimal volume element in the initial configuration Bo is dmo. The corresponding mass in the configurations Bg and B is dm.

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