A 3D constitutive equation for large elastoplastic deformation is derived by taking into account the energy stored in the residual microstress fields in plastically deformed material and its effect on subsequent plastic deformation: this model may be used to describe the non-linear behaviour of material at the onset of loading and unloading. Non-linear mixed isotropic and kinematic hardening, and the effects of temperature and strain rate on material properties, are also considered. Expressions with and without a yield surface are provided. A numerical algorithm which corresponds to the constitutive equation without a yield surface is proposed and the material-user-subroutine UMAT is programmed and embedded in the commercial software ABAQUS. The analyses of necking, upsetting and extrusion were used to validate the proposed constitutive model and the corresponding numerical approach in metal forming analysis.

Based on a nonclassical hardening law and the Hill s self-consistent scheme, a new approach is proposed for the analysis of polycrystal nonproportional cyclic plasticity. A novel parameter related to the plastic dissipation on each slip system is proposed and embedded in the Bassani s definition of cross-hardening. The tangential elastoplastic tensor relating the increments of stress and strain in a single crystal is derived and the corresponding numerical algorithm for polycrystal plasticity is developed. The elastoplastic response of 316 stainless steel subjected to typical biaxial nonproportional strain cycling is analyzed, and the main features are well replicated. The validity of the proposed approach is demonstrated by the satisfactory agreement between the computed results and experimental observation.

Making use of the microstructure-based constitutive equation for a single dual-phase pearlitic colony and the KBW's self-consistent scheme, a description of dual-phase pearlitic steel is performed. It is based on the assumption that a representative element of the material is an aggregate of numerous spherical pearlitic colonies with randomly distributed orientations, and each colony is composed of many parallel fine lamellas of ferrite and cementite. The corresponding numerical algorithm is developed. The cyclic plasticity of single-phase hard-drawn copper and dual-phase pearlitic steel BS11 subjected to asymmetrically cyclic loading is analyzed and compared with the experimental results. The nonproportional cyclic plasticity of the two materials is also analyzed, in which stress develops along a semi-circle in biaxial tension/compression and shear stress plane, as is experienced by the surface elements in a rolling and sliding contact. The local responses of ferrite and cementite for prescribed orientations are investigated simultaneously. The developed approach can describe the main characteristics in the cyclic plasticity of the dual-phase materials. The corresponding numerical algorithm shows successful stability concerning convergence and accuracy at a large number of cycles.

A simplified continuum damage mechanics model is proposed to describe the inelastic behavior of concrete reinforced with randomly distributed short fibers. The constitutive and damage behavior of such a concrete usually involves anisotropic damage, unilateral effect, coupled volumetric and deviatoric inelastic deformation and complicated failure mechanisms due to its heterogeneous morphology. In order to avoid the analytical and computational complexity, a scalar damage variable is adopted, while the anisotropy and unilateral effect of damage corresponding to different states of stress and stress histories are described through introducing the Lode parameter lr. The proposed model can take into account the effect of fiber content on damage development and the effect of volumetric stress on deviatoric inelastic response. The validity of the proposed model is demonstrated by comparing the theoretical and experimental results for plain and fiber-reinforced concrete specimens subjected to triaxial stress histories. The in uence of fiber content on the response of concrete subjected to cyclic loading histories and on the fatigue life is also analyzed.

Based on the concept of local thermal inconsistency, a constitutive model was developed for the description of the behaviors of metallic materials subjected to thermomechanical loading with fast heating, with reference to heating-assisted forming applications. The model considers effect of plastic deformation, of temperature as well as heating-rate and of recrystallization, on the mechanical property, hardening and damage of the materials. It can account for the reduction of the rupture strength of metallic materials subjected to high heating-rates or heating-rate histories, and the reduction of failure temperature of pre-stressed metallic materials heated at high heating-rates. The constitutive behavior of brass H62 subjected to uniaxial thermomechanical loading with fast heating is described and compared with experimental results. The satisfactory agreement between the computed and the experimental results shows the validity of the proposed model.