Finite strain viscoplasticity with nonlinear kinematic hardening: Phenomenological modeling and time integration

Abstract

This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of inelastic part is used to describe a nonlinear kinematic hardening of Armstrong-Frederick type.Two implicit time-stepping methods are adopted for numerical integration of evolution equations, such that the plastic incompressibility constraint is exactly satisfied. The first method is based on the tensor exponential. The second method is a modified Euler-Backward method. Special numerical tests show that both approaches yield similar results even for finite inelastic increments.The basic features of the material response, predicted by the material model, are illustrated with a series of numerical simulations.

Finite Element Simulation of the Presta Joining Process for Assembled Camshafts: Application to Aluminum Shafts

“…The phenomenological material model of finite strain viscoplasticity with nonlinear kinematic hardening introduced by Shutov and Kreißig [1] has been extended to a formulation providing multiple backstresses in Shutov et al [7] (Figure 2). This material model is able to properly reproduce the material behavior at large deformations [4,7,8].…”

“…Thus, numerically-efficient implementations of material models with high prediction accuracy and applicability in multi-stage forming processes are required. In this contribution, a phenomenological material model of finite strain viscoplasticity with nonlinear kinematic hardening introduced by Shutov and Kreißig [1] is applied to an industrial multi-stage manufacturing process: the Presta joining process (PJP).…”

On the simulation of nonlinear hardening in metallic materials using the concept of representative directions

“…The concept of representative directions is similar (but not identical) to the micro-sphere approach (see [3] and references therein). In order to construct a new constitutive law, the material model [5] was reduced to the case of uniaxial isochoric tension-/compression. After that, the uniaxial constitutive relations were generalized using the concept of representative directions presented in [2].…”

“…A phenomenological model of finite strain metal viscoplasticity was proposed in [5], which takes nonlinear isotropic and kinematic hardening into account. In the case of nonproportional loading conditions with abrupt change of the loading path, the distortion of the shape of the yield surface must be taken into account.…”

Numerical treatment of a finite strain viscoplasticity model based on a double multiplicative split

“…Therefore, we consider the construction of a phenomenological model in a unified framework together with the design of corresponding numerical algorithms. In this work we discuss the numerical treatment of a viscoplastic material model [4], in particular, the numerical integration of evolution equations, which describe dissipative processes in the material.…”