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

Complete implicit stress integration algorithm with extended subloading surface model for elastoplastic deformation analysis

“…The constitutive equation in the extended subloading surface model is addressed briefly in this section, where the infinitesimal strain theory is adopted. The infinitesimal strain ϵ is additively decomposed into the elastic strain ϵ e and the plastic strain ϵ p as follows: …”

Multiplicative Hyperelastic-Based Plasticity for Finite Elastoplastic Deformation/Sliding: A Comprehensive Review

“…Then, 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. It will be extended to the ratedependency based on the overstress model by revising the former formulations of the overstress model so as to be applicable to the general rate ranging from the quasi-static to the impact loading behaviors [31,33]. Further, the exact hyperelastic-based plastic constitutive equation of friction is formulated rigorously, in which not only the rotation but also the deformation of the contact surface can be incorporated, although the hypoelastic-based plastic constitutive equation has been formulated in the past [31,33,40,41].…”

“…It will be extended to the ratedependency based on the overstress model by revising the former formulations of the overstress model so as to be applicable to the general rate ranging from the quasi-static to the impact loading behaviors [31,33]. Further, the exact hyperelastic-based plastic constitutive equation of friction is formulated rigorously, in which not only the rotation but also the deformation of the contact surface can be incorporated, although the hypoelastic-based plastic constitutive equation has been formulated in the past [31,33,40,41]. They are the exact constitutive equations describing not only the monotonic and the cyclic loading behavior under the finite deformation/rotation and the cyclic friction behavior under the finite sliding/rotation.…”

“…[68,[74][75][76][77][79][80][81]) in the last century, in which the logarithmic strain has been used mainly leading to the coaxiality of stress and strain rate so that it has been limited to the isotropy. It has been developed actively from this century on by Menzel and Steinmann [63], Wallin et al [87], Dettmer and Reese [14], Menzel et al [64], Wallin and Ristinmaa [86], Gurtin and Anand [18], Sansour et al [73], Vladimirov et al [84,85], Henann and Anand [47], Hashiguchi and Yamakawa [46], Brepols et al [6], Hashiguchi [27,31], etc. in which constitutive relations are formulated in the intermediate configuration imagined fictitiously by the hyperelastic unloading to the stress-free state.…”

Modelling of cyclic creep in the finite strain range using a nested split of the deformation gradient

“…Following [34], the classical decomposition of the deformation gradient into inelastic (creep) and elastic parts is now supplemented by a nested multiplicative split of the inelastic part into some dissipative and conservative parts. This decomposition allows one to incorporate evolving backstresses in a thermodynamically consistent way in different applications (see [23] for shape memory alloys, [7,11,28,49,51,61,67] for conventional plasticity and viscoplasticity, [22] for unconventional plasticity). Accurate and efficient numerical implementation of various models based on the nested multiplicative split was discussed, among others, in [20,46,51,57,67].…”