Abstract
The paper proposes a hyperelasticity-based concept of finite strain plasticity with combined hardening using evolving structure tensors to represent the evolution of elastic and plastic anisotropy in the material. By defining the Helmholtz free energy density and the yield surface as functions of the evolving structure tensors, we are able to describe both evolving elastic and plastic anisotropy, respectively. The model considers also nonlinear kinematic and isotropic hardening and is derived from a thermodynamic framework based on the multiplicative split of the deformation gradient. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong-Frederick kinematic hardening. Exploiting the dissipation inequality leads to the important result that the model includes only symmetric tensor-valued internal variables. Evolution of elastic and plastic anisotropy is numerically investigated by means of simulations of cylindrical deep drawing of metal sheets and thermoforming of thermoplastic polymer blends.
Highlights
Finite element analysis is increasingly being used in modern sheet forming processes, provided that it relies on modules that capture the realistic behaviour sufficiently well
Sheet metal parts are subjected to stretching, bending and reverse bending during forming, and an accurate prediction of e.g. the blank springback requires the use of an appropriate material model, which is capable of modelling the kinematic and isotropic hardening behaviour of metals
It should be noted that due to the fact that both the Helmholtz free energy ψ and the yield potential Φ depend on the non-constant structure tensors M1 and M2, which live in the intermediate configuration, we end up with a model for evolving elastic and plastic anisotropy
Summary
Finite element analysis is increasingly being used in modern sheet forming processes, provided that it relies on modules that capture the realistic behaviour sufficiently well. Various approaches for introducing plastic anisotropy into the finite element analysis of sheet metal forming are popular nowadays. The kinematic hardening component represents a continuum extension of the classical Armstrong-Frederick concept based on a strain-like tensor-valued internal variable. The integration of the evolution equations can be efficiently performed by means of a newly-developed form of the exponential map algorithm [9] based on an implicit time integration scheme. It automatically satisfies plastic incompressibility in every time step, and in addition, has the advantage of retaining the symmetry of the internal variables
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