A phenomenological model of finite strain viscoplasticity with distortional hardening

Abstract

In this paper we suggest a thermodynamically consistent approach to the simulation of a rate dependent material response at finite strains. The nonlinear mechanical phenomena which are covered by the proposed material model include distortional, kinematic, and isotropic hardening. Firstly, we present a new two‐dimensional rheological model of distortional hardening, which predicts the yield curve in the stress space to be a limaçon of Pascal. Such effects like the distortion of the yield surface in the stress space and its orientation depending on the loading path are captured by the rheological model in a vivid way. Next, the rheological model serves as a guideline for the construction of the constitutive equations. In particular, the kinematic assumptions, the ansatz for the free energy, and the form of the yield function are motivated by the rheological model. Further, two types of flow rules are considered in this study: a normality rule and a radial rule, both thermodynamically consistent. Moreover, we formulate explicitly the constraints on the material parameters, which guarantee the convexity of the yield surface. Furthermore, implicit time‐stepping methods are considered which exactly preserve the incompressibility of the inelastic flow. Finally, the basic features of the predicted material response are illustrated by a series of numerical simulations. In particular, the simulation results are compared to the real experimental data.

Simulation of distortional hardening by generalizing a uniaxial model of finite strain viscoplasticity

“…In order to illustrate the yield surfaces within the stress-space the engineering stresses r and s are required, which can be calculated from the Cauchy-stresses r yy and r xy and the parameters a 1 and a 2 (see Shutov et al, 2011). r ¼ a 1 a 2 r yy ; s ¼ a 2 1 a 2 r xy In contrast to the experiments of Dannemeyer we use a modified definition for the yield point which is advantageous with regard to the smoothness of the simulated yield surfaces. But in fact, the shape of the yield surfaces does not hardly change due to the modified criterion.…”

“…The model captures hardening stagnation and the crosshardening effect. Finally, we mention a phenomenological model of finite strain viscoplasticity proposed by Shutov et al (2011), which can be motivated by a two-dimensional rheological model. The rheological model can be considered as a generalization of the one-dimensional Schwedoff body, which is achieved by the introduction of a new idealized rheological element.…”

Generalization of a uniaxial elasto‐plastic material model based on the Prandtl‐Reuss theory

“…Especially the distortional hardening is addressed by Feigenbaum & Dafalias, [7] Plesek et al [19] and Shutov et al [21] Feigenbaum & Dafalias characterize it as an increase of the curvature of the yield surface in the loading direction and a flattening in the opposite direction. This effect among others is examined in this study regarding the presented material model in Section 7.…”

A rheological model for arbitrary symmetric distortion of the yield surface

“…Some variants of this simplified approach were considered in [1][2][3]. In [4], a two-dimensional rheological model of distortional hardening was suggested, which implies the yield surface to be the the limaçon of Pascal. This approach was used to construct thermodynamically consistent constitutive equations of finite strain plasticity/viscoplasticity.…”