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Loading and Unloading of Hypo‐Elastic Materials with Internal Variable
Author(s) -
Tokuoka T.
Publication year - 1977
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19770570406
Subject(s) - von mises yield criterion , antiplane shear , work hardening , materials science , singularity , hardening (computing) , strain hardening exponent , mechanics , variable (mathematics) , work (physics) , structural engineering , mathematics , composite material , stress intensity factor , fracture mechanics , mathematical analysis , physics , engineering , thermodynamics , microstructure , layer (electronics) , finite element method
Abstract The work‐hardening and the hysteresis of two special hypo‐elastic materials with an internal variable are analyzed. The materials have the modified Huber‐Mises yield criterion and the modified Tresca yield criterion as their singularity relations. The loading and the unloading responses in simple shear and in uniaxial stress extension are illustrated. The phenomenon of the rounding of the corner of the stress‐strain reloading curve is shown, and the loading‐unloading cycles show remarkable work‐hardening character. A fracture law for a material is proposed on the basis of the concept that the non‐decreasing internal variable has an ultimate intrinsic value.