Abstract
Hyperelastic-based plastic constitutive equation based on the multiplicative decomposition of the deformation gradient tensor is reviewed comprehensively and its exact formulation is given for the description of the finite deformation and rotation in this article. Further, it is extended to describe the general loading behavior including the monotonic, the cyclic and the non-proportional loading behaviors by incorporating the rigorous plastic flow rules and the subloading surface model. In addition, it is extended also to the rate-dependency based on the overstress model, and the exact hyperelastic-based plastic constitutive equation of friction is formulated by incorporating the subloading-friction model. They are the exact constitutive equations describing the monotonic and the cyclic loading behavior up to the finite deformation/rotation and the friction behavior under the finite sliding/rotation with the rate-dependency, which have remained to be unsolved for a long time, although they have been required in the history of elastoplasticity theory.
Highlights
The elastic deformation and the plastic deformation are physically different to each other such that the former is induced by the deformation of material particles themselves but the latter is induced by the mutual slips between the material particles
The elastoplasticity is based on the premise that the deformation is decomposed into the elastic and the plastic deformations, so that the irreversible change of substructure is described by the isotropic and the anisotropic hardenings which evolve only by the plastic deformation, while the elastic deformation is irrelevant to the irreversible change of substructure
The exact elastoplastic constitutive equation must be formulated by incorporating the definite decomposition of the deformation gradient tensor into the elastic and the plastic parts which is realized by the multiplicative decomposition of the deformation gradient & Koichi Hashiguchi hashikoi87@gmail.com
Summary
The elastic deformation and the plastic deformation are physically different to each other such that the former is induced by the deformation of material particles themselves but the latter is induced by the mutual slips between the material particles. Among various unconventional models the multi surface model [51, 66], the two surface model [12, 53, 91] and the superposed-kinematic hardening model [10, 67] are well-known They inherit a small yield surface enclosing purely-elastic domain from the conventional plasticity model and are based on the premise that the plastic strain rate develops with the translation of the small yield surface so that they are called the cyclic kinematic hardening model. The exact hyperelastic-based plastic constitutive equation will be formulated within the framework of the multiplicative decomposition of the deformation gradient tensor, incorporating the rigorous plastic flow rules and the subloading surface model. The symbol h i designates the Macaulay’s bracket defined by hsi 1⁄4 ðs þ jsj=2Þ, i.e. s\0 : hsi 1⁄4 0 and s ! 0 : hsi 1⁄4 s (s: arbitrary scalar variable)
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