Basic constitutive equation in multiplicative hyperelastic-based plasticity

Abstract

The exact formulation of the multiplicative hyperelastic-based plastic constitutive equation is given for the conventional elastoplastic constitutive equation with the yield surface enclosing the purely-elastic domain undergoing the isotropic and the kinematic hardenings in this article. The generalized flow rules for the plastic strain rate and the rate of kinematic hardening variable and their related plastic spins are incorporated in this formulation.

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

“…The multiplicative hyperelastic-based plastic constitutive equation [34] for the conventional model on the premise that the inside of the yield surface is a purely elastic domain, which is applicable only to the description of monotonic loading behavior, will be given based on the equations formulated in the preceding sections.…”

The combined plastic and discrete fracture deformation framework for finite‐discrete element methods

“…16 It could be argued that Tresca 28 was one of the pioneers in providing a formal mathematical framework for the description of plastic deformation; the advent of computers has helped fuel a renewed interest on the theory of plasticity and the numerical methods used to describe it. 29 The different approaches to describe the elastoplastic deformation of a material were summarized by Hashiguchi 30 (Figure 1).…”

“…An alternative to these is to use a multiplicative hyperelastic-based plasticity approach, which is able to accurately describe finite elastoplastic deformations and rotations. 30 The introduction of the multiplicative decomposition of the deformation gradient tensor is attributed to the seminal work by Eckart 36 and Kröner. 37 This prompted the development of several hyperelastic-based plasticity approaches by Simo, 38 Nemat-Nasser, 39,40 Menzel and Steinmann, 41 and Hashiguchi, 30 among others.…”

“…Very often, these are employed using the so‐called corotational formulation. An alternative to these is to use a multiplicative hyperelastic‐based plasticity approach, which is able to accurately describe finite elastoplastic deformations and rotations . The introduction of the multiplicative decomposition of the deformation gradient tensor is attributed to the seminal work by Eckart and Kröner .…”