Anisotropic finite elastoplasticity with nonlinear kinematic and isotropic hardening and application to sheet metal forming

A large strain anisotropic elastoplastic continuum theory for nonlinear kinematic hardening and texture evolution

“…The split of the plastic strains is equivalent to the traditional split into plastic kinematic strains contribution and plastic isotropic strains contribution, which is the basis of the split of plastic strains (SPS) method (Bathe and Montans, 2004) ; the first contribution is due to the elastic strains which are recovered if the continuum stresses are locally released, whereas the second contribution accounts for elastic strains blocked in the system by successive plastic slips and which can be recovered only with local plastic flow along certain routes (as in a sliding puzzle). One can think of it as modelling two different scales, W(e e ) being the energy at a macroscopic scale (due to continuum stresses and strains) and W(e pe ) being the energy at a microscopic scale (not considered in the Cauchy stresses and strains, but later accounted for through a continuum stress measure: the backstress tensor), see Vladimirov et al (2010) • tfy ~ Ygy (6)…”

“…Many large strain simulations of metal sheet goods are performed using isotropic elastic relations with isotropic or anisotropic yield functions, using algorithms derived from the works of Weber and Anand (1990), Eterovic and Bathe (1990) and Simo (1992), among others, which use hyperelastic relations, objective stress integration algorithms and a simple modular structure in which large strain kinematics reduce to a geometric pre-and post-processor. Several formulations have been proposed for anisotropic elastoplasticity, but those do not inherit the modular structure and use plastic metrics, Green additive decompositions of total strains or elastic isotropy, see for example (Papadopoulos and Lu, 2001;Miehe et al, 2002;Menzel and Steinmann, 2003;Ulz, 2009;Vladimirov et al, 2010), among others. Additive splits of total (versus incremental) strains into elastic and plastic parts have been questioned in Ref.…”

“…The resulting (modified) plastic velocity gradient, plastic deformation rate and plastic spin tensors are then divided into energetic and dissipative contributions. The formulation is established from a decomposition similar to (but different from) that of Lion (2000) which was used recently by Hennan and Anand (2009) and Vladimirov et al (2010) to model the Armstrong and Frederick rule in isotropic elastoplasticity and anisotropic elastoplasticity respectively, see also therein references. However, our formulation, for which we justify our preference, allows for a simpler interpretation and procedure.…”

Earings prediction by a finite strain multiplicative formulation for anisotropic elastoplastic materials

“…The numerical integration of the evolution equations is performed by means of a type of the exponential map algorithm which automatically preserves the plastic volume and the symmetry of the internal variables (see [42]). This integration scheme relies on the use of the spectral decomposition to evaluate the exponential tensor functions in closed form and shows high accuracy and robustness.…”

Anisotropic multiplicative elastoplasticity for the prediction of earings in sheet forming

“…F p = F p e F p i is introduced. A thorough derivation of the constitutive equations of the model in a thermodynamic framework has been presented in a recent publication by the authors (see [1]). To enable a better understanding, the most important steps of the derivation are discussed below.…”