The application of ideas associated with materials with memory to modelingthe inelastic behavior of solid bodies

In this paper, we present a new way to describe the rate-independent inelas tic behavior of metals undergoing finite deformations. Experiments indicate that the stress often has a stronger dependence on the inelastic history i n the more recent past as compared to that in the distant past. For this re ason, an "annihilation" function is used to weight the inelastic history so that less importance is given to the strains in the more distant past. Thi s "annihilation" function does not depend explicitly on time, but instead o n the pathlength associated with the history of stress-free or natural conf igurations in the strain space relative to the current natural configuratio n. lit this formulation the current configuration is adopted as the referen ce configuration for the kinematic quantities. The constitutive equation fo r stress is expressed in terms of the strain associated with the current na tural configuration relative to the current actual configuration. Equations have been developed to prescribe the change in the natural configuration a s the material yields. A general yield function has been defined in terms o f the relative natural strain to restrict the manner in which the natural c onfiguration changes. Since the yield conditions are in terms of the relati ve natural strain, we can account for situations in which a material yields during the process of unloading. For the sake of simplicity, the elastic p roperties of the material are considered to be constant throughout the defo rmation with the material remaining isotropic with respect to the natural c onfiguration. With the proposed theory, we have examined the "Bauschinger e ffect" which is exhibited by metals that are deformed beyond the yield limi t before being deformed beyond the yield limit in the reverse direction. (C ) 2001 Elsevier Science Ltd. All rights reserved.