Insight into a model for large strain anisotropic elasto-plasticity

Abstract

Efficient and accurate simulation of the deformations in anisotropic metallic sheets requires a constitutive model and an accompanying algorithm at large strains which take into account the anisotropy of both the elastic and plastic material behaviors, as well as their evolution with plastic strains. Recently we proposed such a constitutive model based on continuum energy considerations, the Lee decomposition and an anisotropic stored energy function of the logarithmic strains in which the rotation of the orthotropic axes is also considered. We obtained a framework similar to the one used in isotropic elasto-plasticity. In the present work we give some physical insight into the parameters of the model and their effects on the predictions, both in proportional and in non-proportional loading problems. We also present a procedure to obtain the spin parameter of the model from Lankford R-values.

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

“…In References (Montans and Bathe, 2007) and (Kim et al, 2009) we presented a model for texture evolution which predicts the experimental results of Kim and Yin (1997). This model is more clearly explained and motivated by the present theory, being the practical (and computational) and a viscoplastic-like relationship between the effective plastic rotation rate and the effective plastic strain rate, which as with Eq.…”

“…The second Equation of (62) gives the associative flow rule for the dissipative spin. This spin is associated to texture evolution, see for example (Kim et al, 2009). The third Equation of (62) is the hardening rule and it is a direct consequence of the usual assumption f y (E s -B, K).…”

Anisotropic finite strain viscoelasticity based on the Sidoroff multiplicative decomposition and logarithmic strains

“…Another interesting view of this phenomenon may be obtained through the skew part of the Mandel stress tensor, used in Refs. [50,63,73] in the context of plasticity to account for the update of the principal material directions. This tensor, work-conjugate to spins and which may be interpreted as fictitious angular moments per unit volume (couple-stress), accounts for the lack of commutativity due to elastic anisotropy and is obtained from the elastic strains and stored energy function as…”

Non-associated Reuleaux plasticity: Analytical stress integration and consistent tangent for finite deformation mechanics

“…See [10], amongst others, for more details on the recovery of the infinitesimal format of the stress return algorithms. It is one of the most successful and straight-forward ways of implementing large strain elasto-plasticity [14]. The logarithmic strain is defined as…”