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Simple Shear of Hypo‐Elastic Materials with Internal Variables
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.19770570102
Subject(s) - von mises yield criterion , internal stress , simple shear , shear (geology) , work hardening , mathematics , work (physics) , scalar (mathematics) , internal friction , simple (philosophy) , shear stress , variable (mathematics) , mechanics , mathematical analysis , materials science , physics , geometry , thermodynamics , composite material , finite element method , philosophy , microstructure , epistemology
The simple shear deformations of two special hypo‐elastic materials with internal variables are analyzed. Two bodies are treated; one is the P‐R body, which has a scalar internal variable and is subjected to the modified Huber‐Mises yield criterion, and the other is the T body, which has a tensor internal variable and is subjected to the modified Tresca yield criterion. The general formulae are obtained, where the stress, time and the angle of shear are given by functions of internal variables. Numerical calculations for several values of material constants are done, and the results are illustrated, which disclose that the two bodies show work‐hardening phenomenon.