Logarithmic rate implementation in constitutive relations of finite elastoplasticity with kinematic hardening

Abstract

The objective of this article is the evaluation of the validity range of two objective rates, the nowadays most frequently used Jaumann rate and the recently introduced logarithmic rate, in material behaviour prediction due to large deformations. For that purpose the model subjected to large monotonic uniaxial elastoplastic deformation has been examined as well as the initially prestressed models which are afterwards exposed to the cyclic process of combined elastic lengthening and shearing. It is shown that whenever the participation of shear deformation to the total deformation stays in the small deformation range both rates are almost equal in constitutive relations implementation since the outputs for both rates are nearly congruent. Otherwise, if the influence of rotations is significant the Jaumann rate gives theoretically and experimentally unexpected results whereas the logarithmic rate results are stable and consistent with the notion of elasticity, i.e. without any residual stresses at the end of the elastic deformation cycles.

Realistic hardening-to-softening transition effects of metals over the finite strain range up to failure

“…In this case, anisotropic hardening and softening need be taken into account toward properly simulating finite rotation effects involved in shearing and twisting problems (cf., e.g. Bruhns et al , 2001; Bakhshiani et al , 2003; Colak, 2004; Trajković-Milenković and Bruhns, 2018; Wang et al , 2018 and Zhan et al , 2019a).…”

An accurate and explicit approach to modeling realistic hardening‐to‐softening transition effects of metals

“…Unlike the usually treated uniaxial stretching response, the simple shearing response display finite rotation effects and is accordingly of significance to disclosing an essential aspect of finite strain response features. In fact, much attention has been directed to this aspect (cf., e.g., [11–20]), as indicated in the introduction section. However, a complete study with realistic hardening and softening effects up to failure has long been unavailable.…”

“…That would especially be the case in the sense of accurately simulating realistic hardening and softening effects. In particular, early results (see, e.g., [11–13]) for simple shearing responses with finite rotation effects were found to be unreasonable and subsequent results (see, e.g., [14–20]) in this respect were shown to be qualitatively reasonable for certain limited cases of hardening.…”

On instability of constitutive models for isotropic elastic-perfectly plastic material behaviour at finite deformations

“…2,3 Definition of a suitable constitutive model for finite elastoplasticity with the objective rates implementation was the topic of numerous theoretical studies at turn of the century [4][5][6][7][8][9][10][11][12][13] as well as in the recent detailed numerical studies. [14][15][16][17][18][19] It is proved on theoretical models that the application of the objective rates incorporated in the material models of contemporary commercial packages for structural analysis gives physically unrealistic results in the case of large, monotonic as well as cyclic deformations, in which the shear deformation is predominant. It is also shown that only constitutive relations based on the recently discovered logarithmic rate [8][9][10][11][12][14][15][16][17][18][19] predict the theoretically expected behaviour of materials.…”

“…[14][15][16][17][18][19] It is proved on theoretical models that the application of the objective rates incorporated in the material models of contemporary commercial packages for structural analysis gives physically unrealistic results in the case of large, monotonic as well as cyclic deformations, in which the shear deformation is predominant. It is also shown that only constitutive relations based on the recently discovered logarithmic rate [8][9][10][11][12][14][15][16][17][18][19] predict the theoretically expected behaviour of materials.…”