Exact Formulation of Subloading Surface Model: Unified Constitutive Law for Irreversible Mechanical Phenomena in Solids

The subloading surface model is endowed with the intrinsic far-reaching ability to describe the wide classes of irreversible mechanical behavior, e.g. the monotonic and the cyclic loading behavior of elastoplastic and viscoplastic materials, the friction behavior and the crystal plastic behavior as has been examined in the former paper (Hashiguchi in Arch Comput Methods Eng 20:361–417, 2013). However, the past formulations of the subloading surface model have contained several inexact equations, which have been modified repeatedly since the concept of the subloading surface was proposed in 1977 (Hashiguchi and Ueno 1977). The exact formulation is presented first in this article for the hypoelastic-based plasticity, which enjoys the distinguished superiority in the both aspects of the description of material behavior in high accuracy and of the numerical calculation in high efficiency. It is further provided for all the four basic frameworks, i.e. the infinitesimal hypoelastic-based plasticity, the infinitesimal hyperelastic-based plasticity, the hypoelastic-based plasticity and the multiplicative hyperelastic-based plasticity for finite strain. Further, the subloading-crystal plasticity model is formulated modifying the former one (Hashiguchi 2013) by incorporating the decomposition of the crystalline shear strain rate into the elastic and the plastic parts. This would be the guidebook to the subloading surface model and also the memorial monograph for the historical development of the subloading surface model.