The Constitutive Law of Deformation Kinetics

Constitutive Modeling for Sheet Metal Forming

“…The constitutive laws generally consist of a state equation (sometimes referred to as the kinetic equation, see Krausz in [2]) and evolution equations. The state equation describes the relationship between the strain rate ε , strain ε , stress σ , temperature T and state variables i S , which represents the microstructural state of the material.…”

“…Because slip plays a major role in plasticity, it seems important to look at this mechanism in term of both its geometrical effect on anisotropy and its effect on strain hardening. The Kocks and Mecking approach (Estrin in [2]) has laid the foundations for many subsequent studies by connecting the dislocation density ρ to the flow stress τ using the following state equation…”

“…Of course, other viscous terms can be used in constitutive equations. Another approach to viscoplasticity is to assume that there is no yield surface and that any level of stress produces some amount of inelastic deformation, possibly extremely small when the stress is small (Krempl in [2]). …”

Methods in entropic thermomechanics

“…[17] where such models are applied to small strain thermoviscoplasticity and (rate-independent) thermoplasticity. A similar group of rate-dependent models is thoroughly reviewed in [78]; Walker [79], Lindholm et al [80] and Krempl [81] are additional reviews to be considered. Hall [21] casts the finite deformation thermoviscoplasticity development of Chaboche [48] within the Section 3.3.3 framework, and incorporates the plastic spin suggested by Dafalias [68].…”

Experimental and Mechanical Characterizations of a Lead Free Solder Alloy for Electronic Devices

“…In this case, some kinds of unified thermoelastoviscoplastic models which consider that the plasticity and creep effects may be represented by only one time-dependent deformation are suitable for the modeling under complex loading conditions. The concept of state variables is also introduced in these models [7] in order to reproduce some other physical phenomena such as isotropic or kinematic hardening, dynamic and thermal static recovery, ratcheting, aging,… In despite of their complex formulation based on stiff, highly coupled first order differential equations, unified models are frequently used and are more integrated in the finite element codes. Anand's unified viscoplastic model is usually employed for the deformation modeling of the solder alloys [8][9][10].…”