Unified Cyclic Viscoplastic Constitutive Equations: Development, Capabilities, and Thermodynamic Framework

This chapter focuses on the metallic materials which are developed with the objective of the inelastic analysis of structural components. They are based on the concepts of continuum mechanics, where a particular representative volume element of material can be considered as submitted to a macroscopically uniform stress, neglecting the microstress microstrain inhomogeneities at the microscale. The application domains are limited to the quasistatic deformation of metallic materials (strain rate between 10 -10 and 10 -1 ), especially under cyclic loading conditions. The constitutive equations are written in their small strain form. Also, high-temperature conditions will be considered, as well as loading under varying temperatures. Unified viscoplastic constitutive equations means the nonseparation of the plastic (rate-independent) and creep (rate-dependent) parts of the inelastic strain. Moreover, the viscoplastic equations are based on a general framework consistent both with classical plasticity (elastic domain, yield surface, loading/unloading condition) and with thermoviscoplasticity without an elastic domain. Then rate-independent conditions will be obtained consistently as a limit case of the general viscoplastic scheme.