A(nother !) formulation for finite strains is available in Code_Aster !
by J.-M. Proix and R. Bargellini, EDF R&D / AMA
Code_Aster offered yet two different formulations of thermo-elasto-plasticity at finite strains, for many applications.
An hyperelastic one, called SIMO_MIEHE (because of the authors : J.C.Simo and C.Miehe - 1992) and based on a multiplicative decomposition of the deformation gradient. This complete model has already shown its capabilities on different complex simulations with isotropic plastic hardening. It offers high performance in terms of robustness and efficiency… However, it is adapted only to isotropic plastic hardening in isotropic material context.
Then, GDEF_HYPO_ELAS was added in order to perform studies with kinematic hardening. This hypoelastic formulation, due to Simo and Hughes (1998), is based on an additive partition of the deformation gradient and a rotated configuration in order to offer an objective integration algorithm for rate formulations of elastoplasticity. It permits to deal with an important range of material behaviors (remaining in J2-flow theory), including elasto-visco-plasticity with coupled isotropic and kinematic hardening, but with an isotropic elasticity. Results are of good interest, with an objective response in all situations. However, it less efficient than SIMO_MIEHE in terms of performance, due to an inexact tangent stiffness.
That’s why GDEF_LOG is now available! This hypoelastic formulation, due to Miehe, Apel and Lambrecht (2002), consists in writing the constitutive model in the logarithmic strain space. The main feature is to define the stresses and consistent tangents work-conjugated to the logarithmic strain measure, permitting to define an analytical and symmetric consistent tangent operator in the Lagrangian space. Thus, convergence is far quicker than GDEF_HYPO_ELAS. In addition, it permits to include other admissible material behaviors, such as initially anisotropic. Numerical examples show that the results obtained are surprisingly closed to those obtained by a framework of multiplicative plasticity (namely SIMO_MIEHE). Finally, it permits now to use directly behaviors initially written in small strain the UMAT format !
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