Double inclusion in finitely deformed inelastic solids

Conference · Sun Dec 31 04:00:00 EST 1995

OSTI ID:175336

Nemat-Nasser, S ^[1]

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1. Univ. of California, La Jolla, CA (United States)

An exact method for homogenization of an ellipsoidal inclusion in an unbounded finitely deformationed homogeneous solid is presented, generalizing Eshelby`s method for application to finite deformation problems. In terms of the nominal stress rate and the rate of change of the deformation gradient, a general phase-transformation problem is considered, and the concepts of eigenvelocity gradient and eigenstress rate are introduced. Generalized Eshelby`s tensor and its conjugate are defined and used to obtain the field quantities in an ellipsoidal inclusion, leading to exact expressions for concentration tensors and a set of identities relating these quantities. The exact values of the average nominal stress rate and the average velocity gradient, taken over an ellipsoidal region in a finitely deformed unbounded homogeneous solid, are obtained when arbitrary (variable) eigenvelocity gradients or eigenstress rates are prescribed in the ellipsoid. It is shown that many results for single- and double-inclusion problems also apply to the finite deformation rate problems, provided suitable kinematical and dynamical variables are used.

• OSTI ID: 175336
• Report Number(s): CONF-950686--
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
99 GENERAL AND MISCELLANEOUS
DEFORMATION
ELASTICITY
PHASE TRANSFORMATIONS
SOLIDS
STRESSES
TENSORS
VELOCITY