The Earthquake Engineering Online Archive

Constitutive models for cyclic plastic deformation of engineering materials

Kelly, James M.; Gillis, Peter P.

UCB/EERC-73/21, Earthquake Engineering Research Center, University of California, Berkeley, 1973-09-01, 22 pages (530/K38/1973)

Incremental methods are currently being developed to solve transient problems of structures subject to earthquake excitation. These incremental methods are essential when the structural system contains elements which yield during the motion. This gives, however, certain problems connected with the representation of the inelastic response of the yielding elements. It is usual to consider them to be of the bilinear type but this model does not include rate effects or time dependent effects such as cyclic hardening or cyclic softening. These effects can be attributed at the microstructural level to dislocation generation and motion and much of the experimental data of dislocation mechanics can be used to develop constitutive equations for cyclic plastic response. A general continuum theory of dislocation motion is used to investigate the response of crystalline solids to cyclic straining in uniaxial tension and compression. For macroscopically homogeneous deformation under uniaxial stress a simple one-dimensional equation suffices to relate the plastic strain rate to dislocation flux. The material is characterized by evolutionary equations for multiplication of dislocations and for immobilization of moving dislocations. Some simple example materials are considered and it is shown by numerical calculation that these exhibit respectively a Bauschinger effect, isotropic hardening and isotropic softening when subjected to a program of alternating strains at constant rate.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-73-21.pdf (929 KB)