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

• Published in: International journal of plasticity Vol. 17; no. 8; pp. 1087 - 1117
• Main Authors: Makosey, S.J., Rajagopal, K.R.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2001
• Subjects: Annihilation function; Bauschinger effect; Constitutive equations; Inelastic history; Natural configurations; Rate-independent plasticity; Relative strain; Bauschinger effect; Relative strain; Natural configurations; Inelastic history; Annihilation function; Rate-independent plasticity; Constitutive equations
• ISSN: 0749-6419; 1879-2154
• DOI: 10.1016/S0749-6419(00)00081-4

In this paper, we present a new way to describe the rate-independent inelastic behavior of metals undergoing finite deformations. Experiments indicate that the stress often has a stronger dependence on the inelastic history in the more recent past as compared to that in the distant past. For this reason, an “annihilation” function is used to weight the inelastic history so that less importance is given to the strains in the more distant past. This “annihilation” function does not depend explicitly on time, but instead on the pathlength associated with the history of stress-free or natural configurations in the strain space relative to the current natural configuration. In this formulation the current configuration is adopted as the reference configuration for the kinematic quantities. The constitutive equation for stress is expressed in terms of the strain associated with the current natural configuration relative to the current actual configuration. Equations have been developed to prescribe the change in the natural configuration as the material yields. A general yield function has been defined in terms of the relative natural strain to restrict the manner in which the natural configuration changes. Since the yield conditions are in terms of the relative natural strain, we can account for situations in which a material yields during the process of unloading. For the sake of simplicity, the elastic properties of the material are considered to be constant throughout the deformation with the material remaining isotropic with respect to the natural configuration. With the proposed theory, we have examined the “Bauschinger effect” which is exhibited by metals that are deformed beyond the yield limit before being deformed beyond the yield limit in the reverse direction.