Hysteretic Fracturing Endochronic Theory for Concrete

by Zdeněk P. Bažant, (F.ASCE), Prof. of Civ. Engrg.; Northwestern Univ., Evanston, Ill.,
Ching-Long Shieh, Struct. Engrg. Specialist; Sargent and Lundy, Engrs., Chicago, Ill.; formerly, Post-Doctoral Assoc., Northwestern Univ., Evanston, Ill.,

Serial Information: Journal of the Engineering Mechanics Division, 1980, Vol. 106, Issue 5, Pg. 929-950

Document Type: Journal Paper


An improved endochronic nonlinear triaxial constitutive relation for concrete is developed: (1)In addition to plastic strain increments proportional to stress tensor, fracturing strain increments proportional to strain tensor are used to model strain-softening; (2)the plastic and fracturing inelastic strain increments are characterized by different intrinsic times; (3)degradation of the elastic shear modulus is determined by the intrinsic time for the fracturing strain increments, and degradation of the bulk modulus is related to that of the shear modulus using Budianski-O'Connell's expressions for the elastic moduli of randomly microcracked material; (4)jump-kinematic hardening, in which the center of the loading surface jumps into the current stress and strain point whenever loading reverses to unloading or vice versa, is introduced. The theory also exhibits hydrostatic pressure sensitivity, inelastic dilatancy, initial shear compaction in triaxial loading, and inelastic strain due to hydrostatic pressure.

Subject Headings: Triaxial loads | Strain | Shear modulus | Stress strain relations | Inelasticity | Load factors | Cracking | Concrete

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